2sin (example 3.3)

Time bar (total: 7.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze663.0ms (9.4%)

Memory
-223.4MiB live, 42.4MiB allocated; 994ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample3.9s (55.6%)

Memory
53.2MiB live, 4 114.1MiB allocated; 756ms collecting garbage
Samples
1.8s26 352×0invalid
775.0ms5 546×1valid
170.0ms2 710×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-sin: 572.0ms (33.4% of total)
ival-fabs: 257.0ms (15% of total)
ival-sub!: 188.0ms (11% of total)
ival-<: 182.0ms (10.6% of total)
ival-add!: 163.0ms (9.5% of total)
adjust: 148.0ms (8.6% of total)
ival-mult!: 127.0ms (7.4% of total)
ival-and: 61.0ms (3.6% of total)
ival-assert: 13.0ms (0.8% of total)
Bogosity

explain92.0ms (1.3%)

Memory
6.2MiB live, 105.1MiB allocated; 13ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2323(-1.850409177714507e-304 3.8644703780191705e-307)6(5.9602954035502565e-36 9.21258888489744e-38)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
00-0-(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2297
Confusion
Predicted +Predicted -
+2266
-321
Precision
0.9868995633187773
Recall
0.9741379310344828
Confusion?
Predicted +Predicted MaybePredicted -
+22660
-3120
Precision?
0.9830508474576272
Recall?
1.0
Freqs
test
numberfreq
027
1229
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
37.0ms378×1valid
6.0ms132×0valid
3.0ms2×3valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-sin: 17.0ms (57.1% of total)
adjust: 8.0ms (26.9% of total)
ival-sub!: 2.0ms (6.7% of total)
ival-add!: 2.0ms (6.7% of total)

preprocess82.0ms (1.2%)

Memory
-22.6MiB live, 23.4MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
12550
23250
34050
45350
58150
614050
738550
8145150
9523050
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 14 to 12 computations (14.3% saved)

series5.0ms (0.1%)

Memory
5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Counts
6 → 36
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))

rewrite133.0ms (1.9%)

Memory
45.4MiB live, 134.0MiB allocated; 15ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150538
0155526
1931520
08567489
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
42 → 105
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))))))
(fma.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))))))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x))))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 (+.f64 eps x))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x)))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) (neg.f64 eps)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(+.f64 eps (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64)))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (sin (+ x eps)) (sin.f64 x))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)))
#s(approx eps eps)
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval20.0ms (0.3%)

Memory
-30.5MiB live, 22.7MiB allocated; 8ms collecting garbage
Compiler

Compiled 2 003 to 383 computations (80.9% saved)

prune8.0ms (0.1%)

Memory
12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New871198
Fresh000
Picked011
Done000
Total871299
Accuracy
100.0%
Counts
99 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶57.8%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
57.7%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶57.3%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
▶59.1%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
▶99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶96.4%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 433 to 296 computations (31.6% saved)

series61.0ms (0.9%)

Memory
1.4MiB live, 47.8MiB allocated; 3ms collecting garbage
Counts
46 → 212
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(literal 1/24 binary64)
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
#s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
(fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(*.f64 (*.f64 x x) x)
(-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64))
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x)
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal 1/6 binary64)
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) -1/6) #s(hole binary64 -1/6))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* 1/120 x)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* x (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* -1/6 (pow x 2))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1/5040 (pow x 3))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1/6 (cos x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
30.0ms
x
@inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (sin x) (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x))
8.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (sin x) (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x))
7.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (sin x) (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x))
4.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (sin x) (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x))
4.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (sin x) (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x))

rewrite264.0ms (3.8%)

Memory
-12.5MiB live, 173.6MiB allocated; 54ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08155431
08825135
145085115
080994915
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
258 → 433
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(literal 1/24 binary64)
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
#s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
(fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(*.f64 (*.f64 x x) x)
(-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64))
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x)
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal 1/6 binary64)
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) -1/6) #s(hole binary64 -1/6))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* 1/120 x)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* x (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* -1/6 (pow x 2))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1/5040 (pow x 3))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1/6 (cos x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(*.f64 eps (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(fma.f64 (cos.f64 x) eps (*.f64 eps (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(fma.f64 eps (cos.f64 x) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(fma.f64 eps (cos.f64 x) (*.f64 eps (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 eps (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 eps (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(-.f64 (cos.f64 x) (*.f64 (neg.f64 eps) (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(+.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
(fma.f64 eps (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(-.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))
(-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
(+.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
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(+.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x)
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(fma.f64 #s(literal 1/120 binary64) x (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) x))
(fma.f64 #s(literal 1/120 binary64) x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(fma.f64 x #s(literal 1/120 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) x))
(fma.f64 x #s(literal 1/120 binary64) (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(+.f64 (*.f64 #s(literal 1/120 binary64) x) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) x))
(+.f64 (*.f64 #s(literal 1/120 binary64) x) (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) #s(literal 1/14400 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(/.f64 (-.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) (-.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(/.f64 (fma.f64 #s(literal -1/128024064000 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal 1/1728000 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (-.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))
(/.f64 (+.f64 #s(literal 1/1728000 binary64) (*.f64 #s(literal -1/128024064000 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (+.f64 #s(literal 1/14400 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))
(fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
(-.f64 #s(literal 1/120 binary64) (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))
(+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal 1/6 binary64)
(*.f64 (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) (sin.f64 (+.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (sin.f64 (+.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (cos.f64 (+.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(+.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 #s(literal -8 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 eps eps (fma.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x) (*.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (*.f64 (*.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (*.f64 x x) (*.f64 (+.f64 eps x) x))))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 eps eps (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps (+.f64 x x)))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (+.f64 x x))
(+.f64 x (+.f64 eps x))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 eps eps) eps)) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(-.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (+.f64 eps x) x)) #s(literal -2 binary64))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x)) (*.f64 (*.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (fma.f64 x x (*.f64 (+.f64 eps x) x))))
(-.f64 (+.f64 eps x) x)
(+.f64 eps (-.f64 x x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (sin.f64 eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 eps x) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(literal -1/6 binary64))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) x) #s(literal 1/6 binary64)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)) x) #s(literal 1/6 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/5040 binary64) (*.f64 #s(literal 1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (* (cos x) -1/6) #s(literal -1/6 binary64))
#s(approx (* (cos x) -1/6) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/4320 binary64) (*.f64 x x)) #s(literal 1/144 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) x)
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* (* x x) -1/6) 1) #s(literal 1 binary64))
#s(approx (+ (* (* x x) -1/6) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) x)
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (* x x) x) (*.f64 (*.f64 x x) x))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(literal -1/6 binary64))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 #s(literal 1/120 binary64) x))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (sin.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (*.f64 #s(literal -2 binary64) x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (fma.f64 (neg.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))) x (sin.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) x (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))) x (sin.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (neg.f64 x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (neg.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (+ eps x) x) eps)
#s(approx (+ (+ eps x) x) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (sin (/ (- (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (/ (- (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (+ eps x) x) eps)
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) -1/6) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/6 binary64)))
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 (*.f64 x x) x)))
#s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))
#s(approx (+ (* (* x x) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x)))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (pow.f64 x #s(literal 7 binary64))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/5040 binary64))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/5040 binary64)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/5040 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/5040 binary64)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (*.f64 (*.f64 x x) x)))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (*.f64 x x)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) x)
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (+ eps x) x) (+.f64 x x))
#s(approx (+ (+ eps x) x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (neg.f64 (*.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (neg.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (neg.f64 (*.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 x) (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx eps eps)
#s(approx (sin eps) eps)
#s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin (+ x eps)) (sin.f64 x))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (*.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 x) eps))) eps (*.f64 #s(literal -1/4 binary64) (sin.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (*.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 (*.f64 eps eps) eps))))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) eps)) (sin.f64 x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 (*.f64 eps eps) eps))))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))) (*.f64 eps eps)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) eps))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (+ eps x) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (*.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (*.f64 eps eps)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (*.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64)))))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval66.0ms (0.9%)

Memory
37.3MiB live, 82.3MiB allocated; 4ms collecting garbage
Compiler

Compiled 16 755 to 2 521 computations (85% saved)

prune22.0ms (0.3%)

Memory
-5.0MiB live, 40.3MiB allocated; 4ms collecting garbage
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New47116487
Fresh336
Picked505
Done011
Total47920499
Accuracy
100.0%
Counts
499 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
57.7%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
99.7%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
▶99.7%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.6%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.1%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
▶99.9%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
▶98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
▶96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
Compiler

Compiled 1 453 to 930 computations (36% saved)

series42.0ms (0.6%)

Memory
-36.6MiB live, 60.2MiB allocated; 11ms collecting garbage
Counts
50 → 253
Calls
Call 1
Inputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (sin eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))
#s(literal 1/12 binary64)
(*.f64 eps eps)
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 #s(literal -1/6 binary64) eps)
(cos.f64 x)
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
#s(literal 1/3840 binary64)
#s(literal 1/48 binary64)
Outputs
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* x (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x))) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2)))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* -1/6 eps) #s(hole binary64 (* -1/6 eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 -1/48))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (- (* 1/3840 (pow eps 2)) 1/48)))
#s(approx (* 1/3840 (* eps eps)) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (* 1/12 (/ x eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/3840 (pow eps 5))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* 1/3840 (pow eps 4))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1/12 (/ x eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)) eps)) 1/24)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))))
Calls

6 calls:

TimeVariablePointExpression
10.0ms
eps
@inf
((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (- (* 1/3840 (* eps eps)) 1/48) (* 1/3840 (* eps eps)) 1/3840 1/48)
8.0ms
x
@inf
((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (- (* 1/3840 (* eps eps)) 1/48) (* 1/3840 (* eps eps)) 1/3840 1/48)
5.0ms
eps
@-inf
((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (- (* 1/3840 (* eps eps)) 1/48) (* 1/3840 (* eps eps)) 1/3840 1/48)
4.0ms
x
@-inf
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4.0ms
eps
@0
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rewrite197.0ms (2.8%)

Memory
35.7MiB live, 172.7MiB allocated; 19ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09308092
09897732
151527712
082037341
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
303 → 461
Calls
Call 1
Inputs
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#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* x (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x))) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2)))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* -1/6 eps) #s(hole binary64 (* -1/6 eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 -1/48))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (- (* 1/3840 (pow eps 2)) 1/48)))
#s(approx (* 1/3840 (* eps eps)) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (* 1/12 (/ x eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/3840 (pow eps 5))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* 1/3840 (pow eps 4))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1/12 (/ x eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)) eps)) 1/24)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))))
Outputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))))
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))))
(cos.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))))
(cos.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (*.f64 (+.f64 x eps) (+.f64 x eps)) (*.f64 x x)) (-.f64 (+.f64 x eps) x))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps)) (-.f64 (+.f64 x x) eps))
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#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (*.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))) eps))) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (*.f64 #s(literal -1/12 binary64) (/.f64 x eps)) #s(literal 1/24 binary64))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (neg.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) eps)) #s(literal 1/24 binary64))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/12 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) eps)) #s(literal 1/24 binary64))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (*.f64 (*.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps))) (*.f64 eps eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps)) #s(literal 1/3840 binary64)) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (neg.f64 (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps)) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))))

eval62.0ms (0.9%)

Memory
23.3MiB live, 111.3MiB allocated; 9ms collecting garbage
Compiler

Compiled 24 821 to 2 900 computations (88.3% saved)

prune33.0ms (0.5%)

Memory
-51.3MiB live, 51.8MiB allocated; 13ms collecting garbage
Pruning

27 alts after pruning (24 fresh and 3 done)

PrunedKeptTotal
New44118459
Fresh8614
Picked325
Done011
Total45227479
Accuracy
100.0%
Counts
479 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶57.7%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
▶99.7%
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) eps) eps) eps)))) #s(literal 2 binary64))
24.3%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) eps))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.7%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
99.6%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
99.1%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
▶99.9%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
✓98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
▶97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
97.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶97.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
Compiler

Compiled 2 343 to 1 471 computations (37.2% saved)

series38.0ms (0.5%)

Memory
22.9MiB live, 69.3MiB allocated; 2ms collecting garbage
Counts
61 → 303
Calls
Call 1
Inputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
(*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)
(fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
(fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(*.f64 (*.f64 x x) x)
(-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64))
(*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x)
(*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x)
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64))
#s(literal 1/120 binary64)
#s(literal 1/6 binary64)
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
#s(literal 1/3840 binary64)
(*.f64 eps eps)
#s(literal 1/48 binary64)
Outputs
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx x #s(hole binary64 x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* 1/120 x)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* x (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/6 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))) (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 x))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))) 1/2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1/5040 (pow x 3))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ eps x)) (* 1/2 (/ (PI) x)))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 x))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x))) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* 1/2 eps) (* 1/2 (PI))) x)) 1)))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* -1/6 eps) #s(hole binary64 (* -1/6 eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI))))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* 2 (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI))))))))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/24 (* eps (cos (+ x (* 1/2 (PI)))))) (* 2 (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (sin (+ x (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos (+ x (* 1/2 (PI)))))) (* 1/2 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin (+ x (* 1/2 (PI))))) (* eps (+ (* 1/4 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin (+ x (* 1/2 (PI))))) (* eps (+ (* 1/4 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (+ (* -1/48 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI)))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/8 (* eps (sin (+ x (* 1/2 (PI)))))) (* 1/2 (cos (+ x (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/8 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 -1/48))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (- (* 1/3840 (pow eps 2)) 1/48)))
#s(approx (* 1/3840 (* eps eps)) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/3840 (pow eps 5))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* 1/3840 (pow eps 4))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))))
Calls

6 calls:

TimeVariablePointExpression
6.0ms
x
@inf
((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) 2 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) -1/6 (cos x) (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* (+ (* -1/720 (* x x)) 1/24) (* x x)) (+ (* -1/720 (* x x)) 1/24) -1/720 1/24 (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) 1/120 1/6 (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (/ (+ (* 2 x) eps) 2) (+ (* 2 x) eps) (/ (PI) 2) (PI) (sin (/ (- (+ eps x) x) 2)) (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (- (* 1/3840 (* eps eps)) 1/48) (* 1/3840 (* eps eps)) 1/3840 (* eps eps) 1/48)
6.0ms
x
@-inf
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5.0ms
eps
@0
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5.0ms
x
@0
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4.0ms
eps
@-inf
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rewrite218.0ms (3.1%)

Memory
-9.6MiB live, 172.5MiB allocated; 40ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011359706
011978904
164858884
084078374
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
364 → 525
Calls
Call 1
Inputs
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#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx x #s(hole binary64 x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* 1/120 x)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* x (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/6 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))) (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 x))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))) 1/2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
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#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1/5040 (pow x 3))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 x))
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#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 x))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x))) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* 1/2 eps) (* 1/2 (PI))) x)) 1)))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* -1/6 eps) #s(hole binary64 (* -1/6 eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI))))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* 2 (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI))))))))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/24 (* eps (cos (+ x (* 1/2 (PI)))))) (* 2 (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (sin (+ x (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos (+ x (* 1/2 (PI)))))) (* 1/2 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin (+ x (* 1/2 (PI))))) (* eps (+ (* 1/4 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (* -1/48 (sin (+ x (* 1/2 (PI)))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin (+ x (* 1/2 (PI))))) (* eps (+ (* 1/4 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/16 (sin (+ x (* 1/2 (PI))))) (+ (* -1/48 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* 1/2 (* eps (cos (+ x (* 1/2 (PI)))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/8 (* eps (sin (+ x (* 1/2 (PI)))))) (* 1/2 (cos (+ x (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* 1/2 (cos (+ x (* 1/2 (PI))))) (* eps (+ (* -1/8 (sin (+ x (* 1/2 (PI))))) (* -1/48 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 -1/48))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (- (* 1/3840 (pow eps 2)) 1/48)))
#s(approx (* 1/3840 (* eps eps)) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/3840 (pow eps 5))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* 1/3840 (pow eps 4))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* 1/3840 (pow eps 2))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(hole binary64 (* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))))
Outputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (neg.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (+.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 (+.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(fma.f64 (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 0 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 1 binary64)))
(sin.f64 (+.f64 (neg.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(cos.f64 (neg.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
(+.f64 (*.f64 (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 0 binary64)) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 1 binary64)))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64)) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (fma.f64 (*.f64 x x) x (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
(-.f64 x (*.f64 #s(literal -1/2 binary64) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
#s(literal 1/2 binary64)
eps
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 2 binary64)
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
(*.f64 eps #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
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#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (fma.f64 (neg.f64 x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (fma.f64 (neg.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* 1/2 eps) x) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* 1/2 eps) x) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx x x)
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (sin.f64 eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64))
#s(approx (+ (* (* x x) -1/2) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) (* x x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64))
#s(approx (+ (* -1/720 (* x x)) 1/24) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 x eps))
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) x)
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ (* (* (* x x) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (* x x) x) (*.f64 (*.f64 x x) x))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(literal -1/6 binary64))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (-.f64 (*.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (*.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 #s(literal 1/120 binary64) x))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 (fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64)) x))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 #s(literal 2 binary64) (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (neg.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) x (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) x (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
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#s(approx (+ (* 1/2 eps) x) x)
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#s(approx (sin (+ x eps)) (sin.f64 (+.f64 x eps)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (sin x) (sin.f64 x))
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#s(approx (+ (* -1/5040 (* x x)) 1/120) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))
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#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) x)
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#s(approx (/ (+ (* 2 x) eps) 2) x)
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#s(approx (+ (* 2 x) eps) (+.f64 x x))
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#s(approx (sin (+ x eps)) (sin.f64 (-.f64 eps (neg.f64 x))))
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#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x eps)))))
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#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (cos.f64 x) eps))
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#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) x) #s(literal 1/24 binary64)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 #s(literal 1/24 binary64) x (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps)) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) x (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (fma.f64 (/.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) eps)) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) x (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) eps)))))) (/.f64 #s(literal 1/6 binary64) eps)) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))) (*.f64 eps eps)))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (*.f64 (+.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps) #s(literal 1/2 binary64)) eps))
#s(approx (/ (+ (* 2 x) eps) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* 2 x) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/3840 binary64)))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (*.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/3840 binary64)))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))
#s(approx (- (* 1/3840 (* eps eps)) 1/48) (*.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 eps eps)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (*.f64 (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 1/2 eps) x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (neg.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/24 binary64) (sin.f64 x))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps))) (*.f64 eps eps)))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps)))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (* 2 x) eps) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps)) #s(literal 1/3840 binary64)) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (neg.f64 (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps)) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))))

eval68.0ms (1%)

Memory
38.9MiB live, 129.3MiB allocated; 9ms collecting garbage
Compiler

Compiled 26 698 to 3 108 computations (88.4% saved)

prune46.0ms (0.7%)

Memory
-20.8MiB live, 81.0MiB allocated; 13ms collecting garbage
Pruning

34 alts after pruning (30 fresh and 4 done)

PrunedKeptTotal
New50816524
Fresh51419
Picked325
Done123
Total51734551
Accuracy
100.0%
Counts
551 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.1%
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) eps) eps) eps)))) #s(literal 2 binary64))
24.3%
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) eps))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
✓99.9%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
99.7%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
99.6%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
99.1%
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
97.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
97.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
97.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
5.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
✓97.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
97.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
52.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
5.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
98.5%
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
Compiler

Compiled 4 570 to 1 550 computations (66.1% saved)

regimes49.0ms (0.7%)

Memory
-16.5MiB live, 76.6MiB allocated; 3ms collecting garbage
Counts
62 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 (*.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) eps) eps) eps)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
Outputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
Calls

3 calls:

16.0ms
eps
14.0ms
x
14.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
99.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.6%)

Memory
43.6MiB live, 43.6MiB allocated; 0ms collecting garbage
Counts
54 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 (*.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) eps) eps) eps)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Outputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
Calls

3 calls:

13.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms
x
12.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes59.0ms (0.8%)

Memory
-17.8MiB live, 32.1MiB allocated; 4ms collecting garbage
Counts
44 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 (*.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
Calls

3 calls:

10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms
x
10.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.5%)

Memory
-17.3MiB live, 28.8MiB allocated; 2ms collecting garbage
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
Outputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
Calls

3 calls:

12.0ms
x
9.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.4%)

Memory
25.7MiB live, 25.7MiB allocated; 0ms collecting garbage
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
Outputs
(*.f64 #s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
Calls

3 calls:

8.0ms
x
8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms
eps
Results
AccuracySegmentsBranch
99.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.4%)

Memory
-22.8MiB live, 23.4MiB allocated; 2ms collecting garbage
Counts
31 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
Outputs
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
Calls

3 calls:

11.0ms
x
8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.3%)

Memory
22.7MiB live, 22.7MiB allocated; 0ms collecting garbage
Counts
29 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

7.0ms
eps
7.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes24.0ms (0.3%)

Memory
-15.8MiB live, 30.5MiB allocated; 2ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/12 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
Calls

3 calls:

9.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
98.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.0%1x
98.0%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.4%)

Memory
-8.7MiB live, 39.1MiB allocated; 7ms collecting garbage
Counts
26 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
Calls

3 calls:

10.0ms
eps
6.0ms
x
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
97.8%1eps
97.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.8%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.3%)

Memory
13.8MiB live, 60.9MiB allocated; 1ms collecting garbage
Counts
22 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) x) x #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 eps x) (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))) eps))
Calls

3 calls:

7.0ms
x
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
97.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.5%1x
97.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.2%)

Memory
23.7MiB live, 23.7MiB allocated; 0ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
Calls

3 calls:

4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
97.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.4%1x
97.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.2%)

Memory
-24.1MiB live, 22.5MiB allocated; 2ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/720 binary64))))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
Calls

3 calls:

5.0ms
eps
4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
Results
AccuracySegmentsBranch
97.3%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.3%1x
97.3%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory
13.9MiB live, 13.9MiB allocated; 0ms collecting garbage
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
97.3%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.3%1x
97.3%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory
12.8MiB live, 12.8MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps #s(approx (cos x) #s(approx (+ (* (- (* (+ (* -1/720 (* x x)) 1/24) (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
97.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.1%1x
97.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0.1%)

Memory
-37.6MiB live, 9.4MiB allocated; 2ms collecting garbage
Accuracy

Total -58.5b remaining (-2525.8%)

Threshold costs -58.5b (-2525.8%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
Calls

3 calls:

2.0ms
x
1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
eps
Results
AccuracySegmentsBranch
96.4%1eps
96.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
96.4%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations514.0ms (7.3%)

Memory
-23.7MiB live, 429.2MiB allocated; 106ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 742 to 175 computations (76.4% saved)

preprocess114.0ms (1.6%)

Memory
16.7MiB live, 251.8MiB allocated; 14ms collecting garbage
Compiler

Compiled 1 498 to 362 computations (75.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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