2sin (example 3.3)

Time bar (total: 24.2s)

start0.0ms (0%)

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

analyze81.0ms (0.3%)

Memory
-10.0MiB live, 39.0MiB allocated; 34ms 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)

sample4.3s (17.7%)

Memory
90.4MiB live, 4 315.1MiB allocated; 1.7s collecting garbage
Samples
1.7s26 303×0invalid
737.0ms5 554×1valid
179.0ms2 702×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-sin: 657.0ms (38.6% of total)
ival-fabs: 233.0ms (13.7% of total)
ival-add!: 204.0ms (12% of total)
adjust: 160.0ms (9.4% of total)
ival-mult!: 136.0ms (8% of total)
ival-<: 127.0ms (7.5% of total)
ival-sub!: 103.0ms (6% of total)
ival-and: 68.0ms (4% of total)
ival-assert: 15.0ms (0.9% of total)
Bogosity

explain88.0ms (0.4%)

Memory
14.7MiB live, 115.6MiB allocated; 3ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2241(3.2369755934634794 7.172416136631748e-5)4(4.4498555222472154e-85 5.965643538873561e-87)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
21(-3761.8017651054197 1942.1292520713973)1(-15.759348112389198 5.463676594966092e-11)(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))cancellation22110
sin.f64(sin.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+2214
-130
Precision
0.9954954954954955
Recall
0.9822222222222222
Confusion?
Predicted +Predicted MaybePredicted -
+22140
-1624
Precision?
0.9698275862068966
Recall?
1.0
Freqs
test
numberfreq
034
1221
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
33.0ms360×1valid
7.0ms150×0valid
1.0ms2×3valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-sin: 14.0ms (55.6% of total)
adjust: 7.0ms (27.8% of total)
ival-sub!: 2.0ms (7.9% of total)
ival-add!: 2.0ms (7.9% of total)

preprocess82.0ms (0.3%)

Memory
-26.5MiB live, 20.8MiB allocated; 1ms 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
▶61.1%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 14 to 12 computations (14.3% saved)

series5.0ms (0%)

Memory
6.3MiB live, 6.3MiB 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
eps
@-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
x
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms
x
@0
((- (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))

rewrite131.0ms (0.5%)

Memory
39.2MiB live, 131.3MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

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

eval21.0ms (0.1%)

Memory
-27.4MiB live, 24.1MiB allocated; 2ms collecting garbage
Compiler

Compiled 2 132 to 385 computations (81.9% saved)

prune11.0ms (0%)

Memory
15.5MiB live, 15.5MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1012103
Fresh000
Picked101
Done000
Total1022104
Accuracy
100.0%
Counts
104 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
▶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))
Compiler

Compiled 43 to 28 computations (34.9% saved)

series26.0ms (0.1%)

Memory
-13.9MiB live, 33.4MiB allocated; 2ms collecting garbage
Counts
20 → 124
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)
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(sin.f64 eps)
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(*.f64 (cos.f64 eps) (sin.f64 x))
(cos.f64 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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (sin eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (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 eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (cos eps) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (cos eps))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos 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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (- (* (cos eps) (sin x)) (sin x))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* (cos eps) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#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) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (sin x)))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (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 (* 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 (cos eps) #s(hole binary64 (cos eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
5.0ms
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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
5.0ms
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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
3.0ms
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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
3.0ms
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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin eps) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))

rewrite166.0ms (0.7%)

Memory
23.8MiB live, 165.4MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05313344
05613248
132703248
083523110
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
144 → 257
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)
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(sin.f64 eps)
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(*.f64 (cos.f64 eps) (sin.f64 x))
(cos.f64 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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (sin eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (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 eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (cos eps) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (cos eps))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos 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 eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (- (* (cos eps) (sin x)) (sin x))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* (cos eps) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#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) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (sin x)))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (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 (* 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 (cos eps) #s(hole binary64 (cos eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(*.f64 eps (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(fma.f64 eps (cos.f64 x) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
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(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)))
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(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(sin.f64 eps)
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(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(*.f64 (cos.f64 eps) (sin.f64 x))
(*.f64 (sin.f64 x) (cos.f64 eps))
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(sin.f64 (fma.f64 #s(literal -1 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (*.f64 #s(literal -1 binary64) eps)))
(cos.f64 (*.f64 #s(literal -1 binary64) eps))
(cos.f64 eps)
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#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
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#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(literal -1/6 binary64))
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#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (* (cos x) -1/6) #s(literal -1/6 binary64))
#s(approx (* (cos x) -1/6) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/4320 binary64) (*.f64 x x)) #s(literal 1/144 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
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#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))
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#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
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#s(approx (- (* (cos eps) (sin x)) (sin x)) (*.f64 (-.f64 (fma.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (cos.f64 eps) #s(literal 1/5040 binary64)) (*.f64 x x) (*.f64 #s(literal 1/120 binary64) (cos.f64 eps))) #s(literal 1/120 binary64)) (*.f64 x x) (*.f64 (cos.f64 eps) #s(literal -1/6 binary64))) #s(literal 1/6 binary64)) (*.f64 x x) (cos.f64 eps)) #s(literal 1 binary64)) x))
#s(approx (* (cos eps) (sin x)) (*.f64 (cos.f64 eps) x))
#s(approx (* (cos eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (cos.f64 eps)) #s(literal -1/6 binary64) (cos.f64 eps)) x))
#s(approx (* (cos eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) (cos.f64 eps)) #s(literal 1/120 binary64) (*.f64 (cos.f64 eps) #s(literal -1/6 binary64))) (*.f64 x x) (cos.f64 eps)) x))
#s(approx (* (cos eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) (cos.f64 eps)) #s(literal -1/5040 binary64) (*.f64 #s(literal 1/120 binary64) (cos.f64 eps))) (*.f64 x x) (*.f64 (cos.f64 eps) #s(literal -1/6 binary64))) (*.f64 x x) (cos.f64 eps)) x))
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#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) -1/6) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx (cos x) (cos.f64 x))
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#s(approx (- (* (cos eps) (sin x)) (sin x)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
#s(approx (* (cos eps) (sin x)) (*.f64 (cos.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (fma.f64 (sin.f64 eps) (cos.f64 (*.f64 #s(literal 1 binary64) x)) (*.f64 (cos.f64 eps) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 x)))
#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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
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#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx eps eps)
#s(approx (- (sin (+ 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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) (*.f64 eps eps)) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) (sin.f64 x) (*.f64 #s(literal -1/720 binary64) (sin.f64 x))) (*.f64 eps eps) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (* (cos eps) (sin x)) (sin.f64 x))
#s(approx (* (cos eps) (sin x)) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (sin.f64 x)))
#s(approx (* (cos eps) (sin x)) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps) (sin.f64 x)))
#s(approx (* (cos eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) (*.f64 eps eps)) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps) (sin.f64 x)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 (sin.f64 x) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 (sin.f64 x) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 (*.f64 eps eps) eps))))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) eps)) (sin.f64 x)))
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#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 (sin.f64 x) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 (sin.f64 x) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (*.f64 (*.f64 eps eps) eps))))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 (sin.f64 x) eps) (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)))
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#s(approx (sin eps) (sin.f64 eps))
#s(approx (cos eps) (cos.f64 eps))
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#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.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(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) #s(literal -1 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.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(literal -1 binary64) (*.f64 #s(literal -1/24 binary64) (sin.f64 x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) #s(literal -1 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/24 binary64) (sin.f64 x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 (fma.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(literal -1 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 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (*.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64))) eps) #s(literal -1 binary64)))

eval50.0ms (0.2%)

Memory
-16.7MiB live, 77.0MiB allocated; 4ms collecting garbage
Compiler

Compiled 12 231 to 1 467 computations (88% saved)

prune496.0ms (2.1%)

Memory
4.7MiB live, 532.1MiB allocated; 16ms collecting garbage
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3092311
Fresh000
Picked112
Done000
Total3103313
Accuracy
100.0%
Counts
313 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.3%
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
▶99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
▶99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
Compiler

Compiled 209 to 60 computations (71.3% saved)

series100.0ms (0.4%)

Memory
-13.3MiB live, 128.3MiB allocated; 7ms collecting garbage
Counts
30 → 234
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
(*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps)
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))))
(/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))
(pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64))
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)
(fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(cos.f64 x)
x
#s(literal -1/6 binary64)
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
#s(literal 3 binary64)
(fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))
(-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))
(/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) 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 (* (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) eps) #s(hole binary64 (* eps (+ (* -1/216 (/ (pow eps 6) (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))))) (/ 1 (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))))))))
#s(approx (* (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) eps) #s(hole binary64 (+ (* eps (* x (- (+ (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))) 2)) (/ (* (pow eps 3) (+ (* 1/36 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* 1/18 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))))) (+ (* -1/3 (/ (* (pow eps 3) (- (* 1/24 (pow eps 2)) 1/2)) (pow (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))) 2))) (* -1/216 (/ (* (pow eps 6) (- (* -1/3 (* (pow eps 3) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (- (* 1/24 (pow eps 2)) 1/2)))) (pow (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))) 2))))))) (* eps (+ (* -1/216 (/ (pow eps 6) (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2))))) (/ 1 (- (+ 1 (* 1/36 (pow eps 4))) (* -1/6 (pow eps 2)))))))))
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#s(approx (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) #s(hole binary64 -1/6))
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#s(approx (cos x) #s(hole binary64 1))
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#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
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#s(approx x #s(hole binary64 x))
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#s(approx (pow (cos x) 3) #s(hole binary64 1))
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#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))))
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#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))))))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
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#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
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#s(approx (pow (cos x) 3) #s(hole binary64 (pow (cos x) 3)))
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#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
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#s(approx (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) #s(hole binary64 (/ (+ (* -1 (/ (- (+ (* -36864 (/ (pow (cos x) 5) (* eps (pow (sin x) 4)))) (* 331776 (/ (* (pow (cos x) 3) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (* eps (pow (sin x) 4))))) (* 4608 (/ (pow (cos x) 4) (pow (sin x) 3)))) eps)) (* 576 (/ (pow (cos x) 3) (pow (sin x) 2)))) (pow eps 6))))
#s(approx (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) #s(hole binary64 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2654208 (/ (* (pow (cos x) 4) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (* eps (pow (sin x) 5)))) (+ (* -8 (/ (* (cos x) (+ (* -36864 (/ (pow (cos x) 5) (pow (sin x) 4))) (* 331776 (/ (* (pow (cos x) 3) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (pow (sin x) 4))))) (* eps (sin x)))) (* 331776 (/ (* (pow (cos x) 3) (- (* -1/6 (* (cos x) (sin x))) (* -1/24 (* (cos x) (sin x))))) (* eps (pow (sin x) 4)))))) (+ (* -36864 (/ (pow (cos x) 5) (pow (sin x) 4))) (* 331776 (/ (* (pow (cos x) 3) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (pow (sin x) 4))))) eps)) (* 4608 (/ (pow (cos x) 4) (pow (sin x) 3)))) eps)) (* 576 (/ (pow (cos x) 3) (pow (sin x) 2)))) (pow eps 6))))
#s(approx (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 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 (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
Calls

6 calls:

TimeVariablePointExpression
18.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (* (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) eps) (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) (cos x) x -1/6 (* (* (sin x) eps) 1/24) (* (sin x) eps) (sin x) eps 1/24 (* -1/2 (sin x)) -1/2 3 (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))) (pow (cos x) 2) 2 (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (pow (cos x) 3) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps))
16.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (* (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) eps) (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) (cos x) x -1/6 (* (* (sin x) eps) 1/24) (* (sin x) eps) (sin x) eps 1/24 (* -1/2 (sin x)) -1/2 3 (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))) (pow (cos x) 2) 2 (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (pow (cos x) 3) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps))
14.0ms
x
@inf
((- (sin (+ x eps)) (sin x)) (* (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) eps) (+ (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))))) (/ (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (pow (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 3) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) (cos x) x -1/6 (* (* (sin x) eps) 1/24) (* (sin x) eps) (sin x) eps 1/24 (* -1/2 (sin x)) -1/2 3 (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)))) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))) (pow (cos x) 2) 2 (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)) (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (pow (cos x) 3) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps))
12.0ms
eps
@-inf
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9.0ms
eps
@inf
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rewrite275.0ms (1.1%)

Memory
27.0MiB live, 273.7MiB allocated; 36ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150828532
0156324774
0822023998
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
264 → 307
Calls
Call 1
Inputs
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(fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(cos.f64 x)
x
#s(literal -1/6 binary64)
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
#s(literal 3 binary64)
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(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
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(pow.f64 (cos.f64 x) #s(literal 3 binary64))
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#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)))))
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#s(approx (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) #s(hole binary64 -1/6))
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#s(approx (cos x) #s(hole binary64 1))
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#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
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#s(approx x #s(hole binary64 x))
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#s(approx (pow (cos x) 3) #s(hole binary64 1))
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#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))))
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#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))))))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
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#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
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#s(approx (pow (cos x) 3) #s(hole binary64 (pow (cos x) 3)))
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#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
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#s(approx (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) #s(hole binary64 (/ (+ (* -1 (/ (- (+ (* -36864 (/ (pow (cos x) 5) (* eps (pow (sin x) 4)))) (* 331776 (/ (* (pow (cos x) 3) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (* eps (pow (sin x) 4))))) (* 4608 (/ (pow (cos x) 4) (pow (sin x) 3)))) eps)) (* 576 (/ (pow (cos x) 3) (pow (sin x) 2)))) (pow eps 6))))
#s(approx (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) #s(hole binary64 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2654208 (/ (* (pow (cos x) 4) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (* eps (pow (sin x) 5)))) (+ (* -8 (/ (* (cos x) (+ (* -36864 (/ (pow (cos x) 5) (pow (sin x) 4))) (* 331776 (/ (* (pow (cos x) 3) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (pow (sin x) 4))))) (* eps (sin x)))) (* 331776 (/ (* (pow (cos x) 3) (- (* -1/6 (* (cos x) (sin x))) (* -1/24 (* (cos x) (sin x))))) (* eps (pow (sin x) 4)))))) (+ (* -36864 (/ (pow (cos x) 5) (pow (sin x) 4))) (* 331776 (/ (* (pow (cos x) 3) (+ (* -1/24 (pow (sin x) 2)) (* 1/36 (pow (cos x) 2)))) (pow (sin x) 4))))) eps)) (* 4608 (/ (pow (cos x) 4) (pow (sin x) 3)))) eps)) (* 576 (/ (pow (cos x) 3) (pow (sin x) 2)))) (pow eps 6))))
#s(approx (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) 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 (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3/2 binary64)) (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) eps))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3/2 binary64)) (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) eps)
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) (*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))))) (-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) 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(/.f64 (+.f64 (pow.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))) #s(literal 3 binary64))) (+.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64))) (-.f64 (*.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))) (*.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (*.f64 eps eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))
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(fma.f64 (fabs.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) (fabs.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))
(+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))
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(/.f64 (-.f64 (pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))))
(fma.f64 (pow.f64 (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 x) (*.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) (cos.f64 x)))
(-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))
(+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) (cos.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (cos.f64 x) (cos.f64 x))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))
#s(literal 2 binary64)
(*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))
(/.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))))
(/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (cos.f64 x))
(*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 3 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) eps)) (*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
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(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) eps))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (sin.f64 eps) (*.f64 x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 eps) (*.f64 (neg.f64 x) (-.f64 (-.f64 (cos.f64 eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64)))))
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#s(approx (cos x) #s(literal 1 binary64))
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#s(approx x x)
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#s(approx (sin x) x)
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#s(approx (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (cos.f64 x) (sin.f64 x)) eps) (*.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (*.f64 #s(literal -1/24 binary64) (*.f64 (cos.f64 x) (sin.f64 x)))))))
#s(approx (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -36864 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 5 binary64)) (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) (*.f64 #s(literal 331776 binary64) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 4 binary64)))))) (*.f64 #s(literal 4608 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) eps) (*.f64 #s(literal 576 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 6 binary64))))
#s(approx (/ (pow (cos x) 3) (+ (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps)) (- (pow (cos x) 2) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) (cos x))))) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -2654208 binary64) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (fma.f64 #s(literal -1/24 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 5 binary64)))) (fma.f64 #s(literal -8 binary64) (*.f64 (/.f64 (cos.f64 x) eps) (/.f64 (fma.f64 #s(literal -36864 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 5 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 331776 binary64) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (sin.f64 x) #s(literal 4 binary64))))) (sin.f64 x))) (*.f64 #s(literal 331776 binary64) (*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) (sin.f64 x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) (sin.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 4 binary64))))))) (fma.f64 #s(literal -36864 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 5 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 331776 binary64) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))))) eps) (*.f64 #s(literal -4608 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) eps) (*.f64 #s(literal 576 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 6 binary64))))
#s(approx (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))))
#s(approx (+ (* (cos x) eps) (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))))
#s(approx (* (* (+ (* (+ (* (cos x) -1/6) (* (* (sin x) eps) 1/24)) eps) (* -1/2 (sin x))) eps) eps) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))))

eval228.0ms (0.9%)

Memory
0.6MiB live, 331.6MiB allocated; 25ms collecting garbage
Compiler

Compiled 193 734 to 5 724 computations (97% saved)

prune18.0s (74.5%)

Memory
76.8MiB live, 27 865.5MiB allocated; 928ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1 12801 128
Fresh000
Picked022
Done011
Total1 12831 131
Accuracy
100.0%
Counts
1 131 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.3%
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
✓99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
✓99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
Compiler

Compiled 455 to 108 computations (76.3% saved)

regimes6.0ms (0%)

Memory
12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))
Calls

3 calls:

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

regimes4.0ms (0%)

Memory
9.7MiB live, 9.7MiB allocated; 0ms collecting garbage
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
#s(approx (- (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))
Outputs
#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))
Calls

3 calls:

1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory
8.4MiB live, 8.4MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) eps))
Calls

3 calls:

1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations72.0ms (0.3%)

Memory
-31.9MiB live, 63.6MiB allocated; 2ms collecting garbage
Stop Event
1×done
Compiler

Compiled 226 to 40 computations (82.3% saved)

preprocess31.0ms (0.1%)

Memory
13.0MiB live, 60.7MiB allocated; 4ms collecting garbage
Compiler

Compiled 466 to 92 computations (80.3% saved)

end0.0ms (0%)

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

Profiling

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