2sin (example 3.3)

Time bar (total: 6.6s)

start0.0ms (0%)

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

analyze31.0ms (0.5%)

Memory
23.3MiB live, 23.3MiB allocated; 0ms 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)

sample4.0s (59.9%)

Memory
94.6MiB live, 4 236.9MiB allocated; 840ms collecting garbage
Samples
2.0s26 352×0invalid
628.0ms5 546×1valid
184.0ms2 710×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.8s
ival-sin: 681.0ms (38.1% of total)
ival-fabs: 300.0ms (16.8% of total)
ival-mult!: 191.0ms (10.7% of total)
ival-add!: 156.0ms (8.7% of total)
adjust: 140.0ms (7.8% of total)
ival-<: 140.0ms (7.8% of total)
ival-sub!: 98.0ms (5.5% of total)
ival-and: 66.0ms (3.7% of total)
ival-assert: 14.0ms (0.8% of total)
Bogosity

explain122.0ms (1.9%)

Memory
-37.4MiB live, 100.1MiB allocated; 17ms 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
35.0ms378×1valid
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: 28.0ms
ival-sin: 15.0ms (54.4% of total)
adjust: 8.0ms (29% of total)
ival-sub!: 2.0ms (7.3% of total)
ival-add!: 2.0ms (7.3% of total)

preprocess85.0ms (1.3%)

Memory
-8.7MiB live, 46.2MiB allocated; 6ms 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
7.4MiB live, 7.4MiB 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))

rewrite166.0ms (2.5%)

Memory
35.7MiB live, 170.2MiB allocated; 17ms 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 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (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))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.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))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(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 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.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))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(-.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 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (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 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (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) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.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) (fma.f64 #s(literal -1 binary64) (/.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) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))))

eval10.0ms (0.2%)

Memory
12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 915 to 372 computations (80.6% saved)

prune28.0ms (0.4%)

Memory
-35.5MiB live, 17.8MiB allocated; 7ms collecting garbage
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New87996
Fresh000
Picked011
Done000
Total871097
Accuracy
100.0%
Counts
97 → 10
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))
57.7%
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 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 343 to 238 computations (30.6% saved)

series45.0ms (0.7%)

Memory
16.2MiB live, 58.9MiB allocated; 7ms collecting garbage
Counts
35 → 207
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)
#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 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.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)))) #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)) (*.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))
(*.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)
(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))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
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) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 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) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin 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 (/ (+ (+ 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 x) eps) -1/6) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin 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 (/ (+ (+ 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) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -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))) 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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#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) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#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)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
Calls

6 calls:

TimeVariablePointExpression
10.0ms
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) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (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) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps))
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) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (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) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps))
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) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (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) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps))
6.0ms
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) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (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) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps))
6.0ms
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) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (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) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps))

rewrite190.0ms (2.9%)

Memory
18.2MiB live, 203.7MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08305591
08915345
148645325
080675099
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
242 → 378
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)
#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 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.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)))) #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)) (*.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))
(*.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)
(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))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
#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) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 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) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin 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 (/ (+ (+ 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 x) eps) -1/6) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin 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 (/ (+ (+ 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) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -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))) 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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#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) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#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)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
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)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.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 2 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 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 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.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))) (fma.f64 (cos.f64 x) (cos.f64 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)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/13824 binary64) (pow.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))
(/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
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(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
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#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) 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 x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.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 (* (* (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))) (pow.f64 eps #s(literal 4 binary64))))
#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))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (*.f64 #s(literal 1 binary64) 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 (*.f64 #s(literal 1 binary64) 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))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.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))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64)))))

eval75.0ms (1.1%)

Memory
-27.6MiB live, 63.5MiB allocated; 8ms collecting garbage
Compiler

Compiled 15 109 to 2 296 computations (84.8% saved)

prune22.0ms (0.3%)

Memory
28.9MiB live, 28.9MiB allocated; 0ms collecting garbage
Pruning

27 alts after pruning (25 fresh and 2 done)

PrunedKeptTotal
New42024444
Fresh314
Picked415
Done011
Total42727454
Accuracy
100.0%
Counts
454 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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(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))
98.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) 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))
98.8%
#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 (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))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
▶98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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 (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))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
▶96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Compiler

Compiled 1 761 to 1 161 computations (34.1% saved)

series56.0ms (0.8%)

Memory
2.2MiB live, 58.3MiB allocated; 17ms collecting garbage
Counts
49 → 234
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 x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 #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 #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 #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 #s(literal -1/2 binary64) eps)
#s(literal -1/2 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 #s(literal -1/2 binary64) 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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* x (- (* -1/6 (/ eps x)) 1/2))))
#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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/6 (/ eps 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 x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -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) (* -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) (* -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) (* -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) (* -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) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps 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 (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin 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 x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))))
#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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/6))))
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* eps (+ 1/6 (* 1/2 (/ x 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)))))
#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
28.0ms
x
@-inf
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6.0ms
eps
@inf
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6.0ms
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 x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (+ (* -1/2 x) (* -1/6 eps)) (* -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
eps
@0
((* (* (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 x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (+ (* -1/2 x) (* -1/6 eps)) (* -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
((* (* (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 x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (+ (* -1/2 x) (* -1/6 eps)) (* -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)

rewrite221.0ms (3.3%)

Memory
-23.8MiB live, 246.2MiB allocated; 56ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08016414
08546096
143116076
082205807
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
283 → 458
Calls
Call 1
Inputs
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x
eps
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#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) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* x (- (* -1/6 (/ eps x)) 1/2))))
#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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/6 (/ eps 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 x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -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) (* -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) (* -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) (* -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) (* -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) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps 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 (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin 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 x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))))
#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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/6))))
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* eps (+ 1/6 (* 1/2 (/ x 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)))))
#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 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (*.f64 #s(literal 2 binary64) 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 #s(literal 2 binary64) x)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) 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 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) x)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) x)))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (*.f64 x x)) (-.f64 (+.f64 x eps) x))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (*.f64 eps eps)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps eps (+.f64 (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 2 binary64)) (*.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (-.f64 (*.f64 x x) (*.f64 (+.f64 x eps) x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(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 #s(literal 2 binary64) x) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 x (+.f64 x eps))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
#s(literal 2 binary64)
x
eps
#s(literal 1/2 binary64)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(exp.f64 (*.f64 (log.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
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#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.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))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (pow.f64 eps #s(literal -2 binary64))))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.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))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/12 binary64)))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/12 binary64)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64) (-.f64 (*.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))
#s(approx (- (* 1/12 (* eps eps)) 1/2) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
#s(approx (- (* 1/12 (* eps eps)) 1/2) (*.f64 (-.f64 #s(literal 1/12 binary64) (*.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.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 (+ (* -1/2 x) (* -1/6 eps)) (*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps))
#s(approx (/ (+ (+ eps x) x) 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 (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #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 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64))) (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) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/3840 binary64)) (*.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64))) (pow.f64 eps #s(literal 5 binary64))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/3840 binary64)))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/3840 binary64) (*.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64)))))
#s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/3840 binary64)) (*.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#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 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64))) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (*.f64 #s(literal 1 binary64) 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 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.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))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.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)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.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)) (*.f64 eps eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.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))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x)))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/6 binary64))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64)) #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 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64)) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 5 binary64)))))

eval64.0ms (1%)

Memory
12.1MiB live, 111.6MiB allocated; 16ms collecting garbage
Compiler

Compiled 20 467 to 2 770 computations (86.5% saved)

prune28.0ms (0.4%)

Memory
5.6MiB live, 52.3MiB allocated; 4ms collecting garbage
Pruning

30 alts after pruning (27 fresh and 3 done)

PrunedKeptTotal
New42716443
Fresh91120
Picked415
Done022
Total44030470
Accuracy
100.0%
Counts
470 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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))
▶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))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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(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))
98.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) 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))
98.8%
#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 (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))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
97.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) 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))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
▶97.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
▶97.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
✓96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Compiler

Compiled 2 212 to 1 443 computations (34.8% saved)

series38.0ms (0.6%)

Memory
20.8MiB live, 66.9MiB allocated; 5ms collecting garbage
Counts
49 → 265
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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 eps x) #s(literal 1/12 binary64))
(*.f64 eps x)
#s(literal 1/12 binary64)
(*.f64 #s(literal -1/2 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 (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)
#s(literal -1/6 binary64)
(cos.f64 x)
(*.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 (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)))
(cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)))
#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))
(*.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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* 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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (- (* 1/12 (* eps x)) 1/2)))
#s(approx (* (* eps x) 1/12) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps 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 (+ 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 (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 (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* 1/12 (* eps (pow x 3)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* eps (pow x 2)))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 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 (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 (* (* (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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 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 (* (* (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -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) (* -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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -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 (* 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 (* -1/6 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 (* 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 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 (+ (* (+ (* 1/24 (* (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 (* (+ (* (- (* 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
#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 (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 (* (+ (* (- (* 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
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)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 (* -1/2 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)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) -1/6 (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) (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
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) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) 2 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 (* -1/2 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)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) -1/6 (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) (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)
5.0ms
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)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 (* -1/2 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)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) -1/6 (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) (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)
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) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) 2 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 (* -1/2 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)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (* -1/6 eps) -1/6 (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) (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)
4.0ms
eps
@0
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rewrite212.0ms (3.2%)

Memory
-42.0MiB live, 259.7MiB allocated; 48ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09488194
09887894
152717874
080277309
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
314 → 439
Calls
Call 1
Inputs
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x
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#s(approx (* eps x) #s(hole binary64 (* eps x)))
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#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 (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 (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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) (* -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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* 1/12 (* eps (pow x 3)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* eps (pow x 2)))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 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 (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 (* (* (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) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 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 (* (* (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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) (* -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) (* -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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -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 (* 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 (* -1/6 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 (* 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 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 (+ (* (+ (* 1/24 (* (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 (* (+ (* (- (* 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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
#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 (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 (* (+ (* (- (* 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))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 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))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64))) (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 x x (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 2 binary64)) (*.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
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(exp.f64 (*.f64 (log.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
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#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (*.f64 #s(literal 1 binary64) 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 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.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))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.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)) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (neg.f64 eps) (*.f64 (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (neg.f64 eps) (fma.f64 (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/12 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
#s(approx (- (* (* eps x) 1/12) 1/2) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) x (/.f64 #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 (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))) (pow.f64 eps #s(literal 4 binary64))))
#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))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (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 (+ (* (+ (* 1/24 (* (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 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) 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 (* (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) eps) (neg.f64 (*.f64 (-.f64 (*.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64)) #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 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/48 binary64)) #s(literal 1/3840 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 5 binary64)))))

eval53.0ms (0.8%)

Memory
5.6MiB live, 99.1MiB allocated; 6ms collecting garbage
Compiler

Compiled 19 150 to 2 421 computations (87.4% saved)

prune34.0ms (0.5%)

Memory
19.7MiB live, 67.1MiB allocated; 1ms collecting garbage
Pruning

33 alts after pruning (25 fresh and 8 done)

PrunedKeptTotal
New40313416
Fresh101222
Picked055
Done033
Total41333446
Accuracy
100.0%
Counts
446 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓59.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.7%
(*.f64 (*.f64 (sin.f64 (+.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.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 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #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))
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 (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 #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))
99.6%
(*.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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
99.1%
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #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))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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(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))
98.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) 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))
97.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
98.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
97.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
✓97.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
5.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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))
✓97.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
97.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
96.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
5.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
97.3%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
✓96.4%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Compiler

Compiled 3 646 to 1 283 computations (64.8% saved)

regimes111.0ms (1.7%)

Memory
-26.0MiB live, 70.7MiB allocated; 8ms collecting garbage
Counts
63 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) 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 (*.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 (*.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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 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))) (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 (cos.f64 x)) eps))
(*.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #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 #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 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #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))
(*.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 (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 (*.f64 (sin.f64 (+.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.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 #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 (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))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) 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))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(*.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 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) 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)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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(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)) (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))
(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:

61.0ms
eps
31.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms
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)

regimes46.0ms (0.7%)

Memory
7.3MiB live, 54.4MiB allocated; 2ms collecting garbage
Counts
53 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) 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 (*.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 (*.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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 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))) (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 (cos.f64 x)) eps))
(*.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #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 #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 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #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))
(*.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 (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 (*.f64 (sin.f64 (+.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.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 #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 (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))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
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 (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:

18.0ms
(-.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)

regimes36.0ms (0.5%)

Memory
14.2MiB live, 58.7MiB allocated; 4ms collecting garbage
Counts
42 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) 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 (*.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 (*.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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 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))) (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 (cos.f64 x)) eps))
(*.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #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 #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 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #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))
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)) (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))
Calls

3 calls:

14.0ms
x
10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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)

regimes36.0ms (0.5%)

Memory
11.1MiB live, 61.7MiB allocated; 5ms collecting garbage
Counts
41 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) 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 (*.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 (*.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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 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))) (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 (cos.f64 x)) eps))
(*.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #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 #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))
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:

14.0ms
x
10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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)

regimes33.0ms (0.5%)

Memory
-32.1MiB live, 62.0MiB allocated; 3ms collecting garbage
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) 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 (*.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 (*.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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 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))) (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 (cos.f64 x)) eps))
(*.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #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 #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 #s(approx (- (* 1/3840 (* eps eps)) 1/48) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
Calls

3 calls:

11.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms
eps
10.0ms
x
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)

regimes27.0ms (0.4%)

Memory
11.0MiB live, 54.6MiB allocated; 3ms collecting garbage
Counts
32 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) 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 (*.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 (*.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 #s(approx (+ (* (- (* 1/3840 (* eps eps)) 1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
Calls

3 calls:

10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms
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)

regimes33.0ms (0.5%)

Memory
25.5MiB live, 72.6MiB allocated; 14ms collecting garbage
Counts
29 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Calls

3 calls:

17.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
98.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.6%1x
98.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes38.0ms (0.6%)

Memory
-2.8MiB live, 36.4MiB allocated; 16ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 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 (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

23.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
98.5%1eps
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.5%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.3%)

Memory
-16.5MiB live, 30.2MiB allocated; 3ms collecting garbage
Counts
26 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #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
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
6.0ms
x
Results
AccuracySegmentsBranch
97.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.8%1x
97.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.3%)

Memory
27.9MiB live, 27.9MiB allocated; 0ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) 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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -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(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 (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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #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 (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
Calls

3 calls:

6.0ms
eps
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
x
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)

regimes84.0ms (1.3%)

Memory
-30.0MiB live, 16.1MiB allocated; 2ms collecting garbage
Counts
18 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) x (fma.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 (+ (* (+ (* (* (cos x) eps) -1/6) (* -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 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
Calls

3 calls:

73.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
x
5.0ms
eps
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)

regimes14.0ms (0.2%)

Memory
14.1MiB live, 14.1MiB allocated; 0ms collecting garbage
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x 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 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
4.0ms
eps
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)

regimes12.0ms (0.2%)

Memory
14.5MiB live, 14.5MiB allocated; 0ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
Calls

3 calls:

4.0ms
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)

regimes8.0ms (0.1%)

Memory
8.3MiB live, 8.3MiB allocated; 0ms collecting garbage
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
Calls

3 calls:

3.0ms
(-.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)

regimes48.0ms (0.7%)

Memory
-92.9MiB live, 7.8MiB allocated; 58ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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:

43.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
x
2.0ms
eps
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
8.1MiB live, 8.1MiB allocated; 0ms collecting garbage
Accuracy

Total -58.5b remaining (-2525.8%)

Threshold costs -58.5b (-2525.8%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -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)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
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)

derivations480.0ms (7.3%)

Memory
27.4MiB live, 353.1MiB allocated; 33ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 611 to 171 computations (72% saved)

preprocess113.0ms (1.7%)

Memory
3.2MiB live, 242.5MiB allocated; 18ms collecting garbage
Compiler

Compiled 1 236 to 354 computations (71.4% saved)

end0.0ms (0%)

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

Profiling

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