2cos (problem 3.3.5)

Time bar (total: 8.1s)

start0.0ms (0%)

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

analyze64.0ms (0.8%)

Memory
7.8MiB live, 83.3MiB allocated; 44ms 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)

sample5.9s (73.1%)

Memory
-2.3MiB live, 3 085.3MiB allocated; 1.8s collecting garbage
Samples
2.1s5 796×2valid
1.6s26 427×0invalid
303.0ms2 410×1valid
5.0ms50×0valid
Precisions
Click to see histograms. Total time spent on operations: 3.1s
ival-cos: 2.0s (63.3% of total)
adjust: 371.0ms (12% of total)
ival-fabs: 205.0ms (6.6% of total)
ival-<: 131.0ms (4.2% of total)
ival-mult!: 123.0ms (4% of total)
ival-sub!: 117.0ms (3.8% of total)
ival-add!: 109.0ms (3.5% of total)
ival-and: 63.0ms (2% of total)
ival-assert: 13.0ms (0.4% of total)
Bogosity

preprocess35.0ms (0.4%)

Memory
-22.7MiB live, 21.1MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02146
114342
2186342
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶51.0%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 12 to 12 computations (0% saved)

series4.0ms (0.1%)

Memory
5.6MiB live, 5.6MiB allocated; 0ms collecting garbage
Counts
6 → 33
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin 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 (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

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

rewrite140.0ms (1.7%)

Memory
31.1MiB live, 134.0MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0145529
0150505
11150505
08324483
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
39 → 176
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin 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 (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x)))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (fabs.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (fabs.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fabs.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fabs.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (fabs.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (fabs.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (fabs.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (+.f64 eps x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (+.f64 eps x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))))
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))))
(neg.f64 (-.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (cos.f64 x)))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (cos.f64 x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(+.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (cos.f64 eps)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 x) (sin.f64 eps))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)))))))
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#s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) (cos.f64 x)))
#s(approx (+ x eps) (+.f64 eps x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval76.0ms (0.9%)

Memory
-32.1MiB live, 13.9MiB allocated; 3ms collecting garbage
Compiler

Compiled 1 871 to 800 computations (57.2% saved)

prune8.0ms (0.1%)

Memory
5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1597166
Fresh000
Picked101
Done000
Total1607167
Accuracy
99.8%
Counts
167 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶50.5%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶50.2%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
81.6%
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
▶49.6%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
▶77.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
Compiler

Compiled 194 to 184 computations (5.2% saved)

series20.0ms (0.3%)

Memory
13.1MiB live, 13.1MiB allocated; 0ms collecting garbage
Counts
34 → 111
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#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 (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* 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 (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4))))
#s(approx (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#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 (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (+ (* 1/24 (* x x)) -1/2) 1/24 (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (+ (* -1/720 (* x x)) 1/24) -1/720)
3.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (+ (* 1/24 (* x x)) -1/2) 1/24 (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (+ (* -1/720 (* x x)) 1/24) -1/720)
3.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (+ (* 1/24 (* x x)) -1/2) 1/24 (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (+ (* -1/720 (* x x)) 1/24) -1/720)
3.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (+ (* 1/24 (* x x)) -1/2) 1/24 (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (+ (* -1/720 (* x x)) 1/24) -1/720)
3.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (+ (* 1/24 (* x x)) -1/2) 1/24 (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (+ (* -1/720 (* x x)) 1/24) -1/720)

rewrite167.0ms (2.1%)

Memory
2.2MiB live, 150.5MiB allocated; 24ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04902672
05382593
136672593
084052494
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
145 → 404
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#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 (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* 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 (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4))))
#s(approx (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#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 (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 eps (neg.f64 (sin.f64 x)) (*.f64 eps (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(+.f64 (*.f64 eps (neg.f64 (sin.f64 x))) (*.f64 eps (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x)))) (neg.f64 (sin.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (*.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(/.f64 (+.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (*.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))))
(neg.f64 (-.f64 (sin.f64 x) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(-.f64 (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(-.f64 (neg.f64 (sin.f64 x)) (neg.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(+.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(+.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x)))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) eps))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) eps))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (sin.f64 x) (*.f64 #s(literal 1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 x) eps)))
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (neg.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (neg.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
(+.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (fabs.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (fabs.f64 x)))
(cos.f64 (fabs.f64 (fabs.f64 x)))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 (fabs.f64 x))
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#s(approx (+ (* -1/720 (* x x)) 1/24) (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) (*.f64 x x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 eps (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (*.f64 eps eps) #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(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (fma.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 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (sin.f64 x)) #s(literal 1/6 binary64)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 eps eps)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (sin.f64 x)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 eps eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 eps eps)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
#s(approx (+ x eps) (+.f64 eps x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (neg.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (neg.f64 (*.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64)))))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval46.0ms (0.6%)

Memory
-0.4MiB live, 46.0MiB allocated; 2ms collecting garbage
Compiler

Compiled 5 619 to 2 101 computations (62.6% saved)

prune34.0ms (0.4%)

Memory
-31.0MiB live, 16.8MiB allocated; 1ms collecting garbage
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New44716463
Fresh112
Picked415
Done000
Total45218470
Accuracy
100.0%
Counts
470 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
99.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
▶99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
99.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓77.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
77.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))))
77.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
▶76.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
▶97.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
▶98.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
94.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps))) eps))
50.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
Compiler

Compiled 798 to 744 computations (6.8% saved)

series33.0ms (0.4%)

Memory
17.8MiB live, 17.8MiB allocated; 0ms collecting garbage
Counts
44 → 165
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
eps
(*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) eps)
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
#s(literal -1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
(*.f64 #s(literal 1/4 binary64) eps)
#s(literal 1/4 binary64)
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps)
(-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x))
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (cos.f64 x) eps)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (pow eps 3)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* x (+ (* 1/4 (pow eps 2)) (* x (+ (* -1/36 (pow eps 3)) (* 1/6 eps)))))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#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) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* 1/6 (* (pow eps 3) x)))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* x (+ (* -1/36 (* (pow eps 3) x)) (* 1/4 (pow eps 2)))))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#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 (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (* 1/6 (pow eps 2)) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* 1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* 1/4 eps)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/6 (pow eps 2)) 1))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))) (/ 1 (pow x 2))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))))) (/ 1 (pow x 2))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))) (/ 1 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* x (+ 1/6 (* -1/36 (pow eps 2))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1/4 (/ eps x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)) x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/36 (pow eps 2)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1 (/ (+ (* -1/4 eps) (* -1/6 (/ (pow eps 2) x))) x)) (* -1/36 (pow eps 2)))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1/4 (/ eps x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))))
#s(approx (+ (* (* eps eps) 1/6) -1) #s(hole binary64 -1))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (* 1/6 (pow x 2)) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2)))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (+ (* 1/6 x) (* 1/4 eps))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 1/6))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 (+ 1/6 (* -1/36 (pow eps 2)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* 1/6 (* (pow eps 2) x))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (* eps eps) 1/6) -1) #s(hole binary64 (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (* x (+ 1/6 (* -1/36 (pow x 2)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* -1/36 (* (pow eps 2) x))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 (* -1/36 (pow eps 2))))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 (* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps))) eps)) (* -1/36 (pow x 2)))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (+ (* (* eps eps) 1/6) -1) (* eps eps) -1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* 1/4 eps) 1/4 (* (* eps eps) 1/6) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (- (* (* (cos x) eps) -1/2) (sin x)) (* (* (cos x) eps) -1/2) (* (cos x) eps))
5.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (+ (* (* eps eps) 1/6) -1) (* eps eps) -1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* 1/4 eps) 1/4 (* (* eps eps) 1/6) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (- (* (* (cos x) eps) -1/2) (sin x)) (* (* (cos x) eps) -1/2) (* (cos x) eps))
5.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (+ (* (* eps eps) 1/6) -1) (* eps eps) -1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* 1/4 eps) 1/4 (* (* eps eps) 1/6) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (- (* (* (cos x) eps) -1/2) (sin x)) (* (* (cos x) eps) -1/2) (* (cos x) eps))
5.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (+ (* (* eps eps) 1/6) -1) (* eps eps) -1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* 1/4 eps) 1/4 (* (* eps eps) 1/6) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (- (* (* (cos x) eps) -1/2) (sin x)) (* (* (cos x) eps) -1/2) (* (cos x) eps))
4.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (+ (* (* eps eps) 1/6) -1) (* eps eps) -1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* 1/4 eps) 1/4 (* (* eps eps) 1/6) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (- (* (* (cos x) eps) -1/2) (sin x)) (* (* (cos x) eps) -1/2) (* (cos x) eps))

rewrite191.0ms (2.4%)

Memory
14.2MiB live, 202.5MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07715241
08345078
162235078
084514852
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
209 → 433
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
eps
(*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) eps)
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
#s(literal -1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
(*.f64 #s(literal 1/4 binary64) eps)
#s(literal 1/4 binary64)
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps)
(-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x))
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (cos.f64 x) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (pow eps 3)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* x (+ (* 1/4 (pow eps 2)) (* x (+ (* -1/36 (pow eps 3)) (* 1/6 eps)))))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#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) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* 1/6 (* (pow eps 3) x)))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* x (+ (* -1/36 (* (pow eps 3) x)) (* 1/4 (pow eps 2)))))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#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 (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (* 1/6 (pow eps 2)) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* 1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* 1/4 eps)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/6 (pow eps 2)) 1))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))) (/ 1 (pow x 2))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))))) (/ 1 (pow x 2))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))) (/ 1 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* x (+ 1/6 (* -1/36 (pow eps 2))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (* (cos x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1/4 (/ eps x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)) x)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/36 (pow eps 2)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow x 2) (+ 1/6 (+ (* -1 (/ (+ (* -1/4 eps) (* -1/6 (/ (pow eps 2) x))) x)) (* -1/36 (pow eps 2)))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1/4 (/ eps x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))))
#s(approx (+ (* (* eps eps) 1/6) -1) #s(hole binary64 -1))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (* 1/6 (pow x 2)) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2)))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (+ (* 1/6 x) (* 1/4 eps))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 1/6))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 (+ 1/6 (* -1/36 (pow eps 2)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* 1/6 (* (pow eps 2) x))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (* eps eps) 1/6) -1) #s(hole binary64 (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (* x (+ 1/6 (* -1/36 (pow x 2)))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* -1/36 (* (pow eps 2) x))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 (* -1/36 (pow eps 2))))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(hole binary64 (* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps))) eps)) (* -1/36 (pow x 2)))))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)) (*.f64 (neg.f64 eps) (sin.f64 x)))) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))) (-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps))))
(/.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps))) (*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps))))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(fma.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(fma.f64 (sin.f64 x) (neg.f64 eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(fma.f64 eps (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(fma.f64 eps (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) eps))
(-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (neg.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps))))
(+.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
(+.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1 binary64))
(neg.f64 (sin.f64 x))
(sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (neg.f64 x))
(sin.f64 (+.f64 x (PI.f64)))
(fma.f64 (sin.f64 x) (cos.f64 (PI.f64)) (*.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (fabs.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (PI.f64))) (*.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(sin.f64 x)
x
eps
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps))
(*.f64 eps (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 eps eps)))
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 eps eps)))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) eps))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))))
(+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) eps))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
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#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
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#s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))
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#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)))
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#s(approx (* (* (cos x) eps) -1/2) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (* (* (cos x) eps) -1/2) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/1440 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (neg (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (sin x) (sin.f64 x))
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#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
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#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))
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#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))))
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#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (+.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/6 binary64) (*.f64 (/.f64 eps x) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) x)))
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#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 (+.f64 (fma.f64 (/.f64 eps x) #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64))) #s(literal 1/6 binary64)) x))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
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#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
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#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (neg.f64 (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (neg.f64 (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (neg.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) x))) x)) (neg.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))) (*.f64 (*.f64 x x) x))))
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#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (*.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/2 binary64)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))
#s(approx (+ (* (* eps eps) 1/6) -1) #s(literal -1 binary64))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x) eps) #s(literal 1/2 binary64))) eps (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64))))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (-.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 #s(literal 1/6 binary64) x))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) #s(literal 1/6 binary64))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (sin.f64 x)) #s(literal 1/6 binary64)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 eps eps)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 eps eps)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (-.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (neg.f64 x) (*.f64 eps eps))) (/.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* (* eps eps) 1/6) -1) (*.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 eps eps)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x) (*.f64 eps eps)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)) (/.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/4 binary64) (-.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) (*.f64 eps eps))) (/.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (*.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (*.f64 (-.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (fma.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1/6 binary64) (*.f64 (/.f64 x eps) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (fma.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1/6 binary64) (*.f64 (/.f64 x eps) #s(literal 1/4 binary64)))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/36 binary64)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 (fma.f64 #s(literal -1/36 binary64) x (fma.f64 (/.f64 x (*.f64 eps eps)) #s(literal 1/6 binary64) (/.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps eps)))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)))
#s(approx (+ (* -1/36 (* eps eps)) 1/6) (*.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1/36 binary64)) (*.f64 eps eps)))
#s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (neg.f64 (/.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (neg.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))) #s(literal 1/2 binary64)) eps))) (*.f64 eps eps)))
#s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal -1/36 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/4 binary64) x)) eps))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/36 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) eps)))))
#s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))

eval74.0ms (0.9%)

Memory
7.2MiB live, 147.2MiB allocated; 28ms collecting garbage
Compiler

Compiled 6 226 to 2 574 computations (58.7% saved)

prune22.0ms (0.3%)

Memory
13.0MiB live, 58.3MiB allocated; 3ms collecting garbage
Pruning

23 alts after pruning (20 fresh and 3 done)

PrunedKeptTotal
New40512417
Fresh4812
Picked325
Done011
Total41223435
Accuracy
100.0%
Counts
435 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
99.3%
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
✓99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
▶99.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓77.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
77.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))))
▶77.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
✓76.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
98.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
98.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
▶50.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
97.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
49.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
98.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
97.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
▶77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
Compiler

Compiled 1 001 to 951 computations (5% saved)

series46.0ms (0.6%)

Memory
-28.2MiB live, 72.7MiB allocated; 23ms collecting garbage
Counts
40 → 110
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
eps
(*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 eps x))
(*.f64 eps x)
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps))
(*.f64 (*.f64 x x) eps)
(*.f64 x x)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x))
(*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (pow eps 3)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* x (+ (* 1/4 (pow eps 2)) (* x (+ (* -1/36 (pow eps 3)) (* 1/6 eps)))))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#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) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* 1/6 (* (pow eps 3) x)))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* x (+ (* -1/36 (* (pow eps 3) x)) (* 1/4 (pow eps 2)))))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#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 (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (- (* 1/6 (* eps (pow x 2))) eps)))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 -1/6))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* 1/6 (* eps (pow x 3)))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* 1/6 (* eps (pow x 2)))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* eps (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* eps (- (* 1/6 (pow x 2)) 1))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))))
Calls

6 calls:

TimeVariablePointExpression
23.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (* eps x) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (* (* x x) eps) (* x x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (+ (* 1/120 (* x x)) -1/6) 1/120 -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))))
6.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (* eps x) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (* (* x x) eps) (* x x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (+ (* 1/120 (* x x)) -1/6) 1/120 -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))))
4.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (* eps x) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (* (* x x) eps) (* x x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (+ (* 1/120 (* x x)) -1/6) 1/120 -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))))
4.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (* eps x) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (* (* x x) eps) (* x x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (+ (* 1/120 (* x x)) -1/6) 1/120 -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))))
4.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg (sin x)) (sin x) x eps (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (* eps x) 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (+ (* (* (* x x) eps) 1/6) (neg eps)) (* (* x x) eps) (* x x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (+ (* 1/120 (* x x)) -1/6) 1/120 -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))))

rewrite173.0ms (2.1%)

Memory
20.5MiB live, 252.8MiB allocated; 42ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05093143
05503040
138103040
082042876
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
150 → 311
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(neg.f64 (sin.f64 x))
(sin.f64 x)
x
eps
(*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 eps x))
(*.f64 eps x)
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps))
(*.f64 (*.f64 x x) eps)
(*.f64 x x)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x))
(*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (pow eps 3)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x))))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (+ (* 1/6 (pow eps 3)) (* x (+ (* 1/4 (pow eps 2)) (* x (+ (* -1/36 (pow eps 3)) (* 1/6 eps)))))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#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) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* 1/6 (* (pow eps 3) x)))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/6 (pow eps 3)) (* x (+ (* -1/36 (* (pow eps 3) x)) (* 1/4 (pow eps 2)))))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#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 (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (- (* 1/6 (* eps (pow x 2))) eps)))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 -1/6))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* 1/6 (* eps (pow x 3)))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* 1/6 (* eps (pow x 2)))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (+ (* 1/120 (* x x)) -1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* eps (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* eps (- (* 1/6 (pow x 2)) 1))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) #s(hole binary64 (* -1 (* eps (* x (+ 1 (* -1/6 (pow x 2))))))))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1/6 (pow x 2)))))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (+.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 eps (+.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) #s(literal 2 binary64))) (-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 #s(literal -1 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 (sin.f64 x) (neg.f64 eps) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 eps (neg.f64 (sin.f64 x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(fma.f64 eps (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) eps))
(-.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (neg.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(+.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps))
(+.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1 binary64))
(neg.f64 (sin.f64 x))
(sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (neg.f64 x))
(sin.f64 (+.f64 x (PI.f64)))
(fma.f64 (sin.f64 x) (cos.f64 (PI.f64)) (*.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (fabs.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (PI.f64))) (*.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(sin.f64 x)
x
eps
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)
(*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps))
(*.f64 eps (*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(*.f64 (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))))) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 3 binary64)) #s(literal 1/216 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (fma.f64 (pow.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 3 binary64)) #s(literal 1/216 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x))))
(fma.f64 #s(literal 1/6 binary64) #s(approx (* (sin x) eps) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
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#s(approx (neg (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64)))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (neg.f64 eps) (*.f64 x x))) (*.f64 (*.f64 x x) x)))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (neg.f64 eps) (*.f64 x x))) (*.f64 x x)))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64)))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (*.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/120 binary64)))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
#s(approx (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) (*.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
#s(approx (+ (* 1/120 (* x x)) -1/6) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
#s(approx (+ (* 1/120 (* x x)) -1/6) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 x x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 #s(literal -1/6 binary64) eps (/.f64 eps (*.f64 x x)))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (+ (* (+ (* 1/120 (* x x)) -1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 eps (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx eps eps)
#s(approx (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps) (*.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) (sin.f64 x)) #s(literal 1/6 binary64)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (*.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 eps eps)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (*.f64 eps eps)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 eps eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (neg (sin x)) eps) (* (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) eps)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) (*.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps)))
#s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (neg.f64 eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
#s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))))

eval38.0ms (0.5%)

Memory
-21.4MiB live, 84.1MiB allocated; 5ms collecting garbage
Compiler

Compiled 4 245 to 1 692 computations (60.1% saved)

prune26.0ms (0.3%)

Memory
16.4MiB live, 61.3MiB allocated; 3ms collecting garbage
Pruning

27 alts after pruning (21 fresh and 6 done)

PrunedKeptTotal
New28910299
Fresh41115
Picked235
Done033
Total29527322
Accuracy
100.0%
Counts
322 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
99.3%
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
✓99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
99.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
✓99.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
98.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
98.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
97.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
99.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
✓77.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
77.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))))
✓77.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
✓76.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
98.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
98.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
✓50.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
97.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
98.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
49.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
Compiler

Compiled 1 231 to 909 computations (26.2% saved)

regimes35.0ms (0.4%)

Memory
-10.9MiB live, 79.9MiB allocated; 4ms collecting garbage
Counts
46 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
Calls

3 calls:

12.0ms
eps
11.0ms
x
10.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
100.0%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
100.0%1x
100.0%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes31.0ms (0.4%)

Memory
22.2MiB live, 79.3MiB allocated; 1ms collecting garbage
Counts
44 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps)))
Calls

3 calls:

12.0ms
x
10.0ms
eps
7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
100.0%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
100.0%1x
100.0%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes31.0ms (0.4%)

Memory
-18.2MiB live, 73.3MiB allocated; 4ms collecting garbage
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
Calls

3 calls:

11.0ms
x
9.0ms
eps
7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes29.0ms (0.4%)

Memory
23.2MiB live, 68.8MiB allocated; 1ms collecting garbage
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
Calls

3 calls:

9.0ms
eps
9.0ms
x
7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes27.0ms (0.3%)

Memory
-31.6MiB live, 70.8MiB allocated; 2ms collecting garbage
Counts
37 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal 1/6 binary64) #s(approx (* -1/2 (cos x)) (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))) eps) eps)))
Calls

3 calls:

10.0ms
eps
9.0ms
x
7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes25.0ms (0.3%)

Memory
17.8MiB live, 65.4MiB allocated; 1ms collecting garbage
Counts
35 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
Calls

3 calls:

9.0ms
x
8.0ms
eps
6.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.5%1x
99.5%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes27.0ms (0.3%)

Memory
-27.5MiB live, 67.6MiB allocated; 4ms collecting garbage
Counts
33 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
Calls

3 calls:

8.0ms
eps
8.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
8.0ms
x
Results
AccuracySegmentsBranch
99.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.5%1x
99.5%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes23.0ms (0.3%)

Memory
15.0MiB live, 62.3MiB allocated; 1ms collecting garbage
Counts
32 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
Calls

3 calls:

8.0ms
x
8.0ms
eps
6.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes22.0ms (0.3%)

Memory
15.6MiB live, 63.0MiB allocated; 1ms collecting garbage
Counts
30 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps))) (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (*.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) eps)))
Calls

3 calls:

8.0ms
x
7.0ms
eps
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.3%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.3%1x
99.3%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes21.0ms (0.3%)

Memory
5.1MiB live, 50.6MiB allocated; 2ms collecting garbage
Counts
27 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
Calls

3 calls:

9.0ms
eps
7.0ms
x
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.1%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes22.0ms (0.3%)

Memory
0.3MiB live, 52.0MiB allocated; 3ms collecting garbage
Counts
26 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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))) eps))
Calls

3 calls:

9.0ms
eps
7.0ms
x
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.7%1x
98.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes19.0ms (0.2%)

Memory
3.8MiB live, 49.0MiB allocated; 2ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.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 (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x #s(literal -1 binary64)))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Calls

3 calls:

8.0ms
eps
6.0ms
x
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.4%1x
98.4%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes17.0ms (0.2%)

Memory
-7.1MiB live, 38.3MiB allocated; 2ms collecting garbage
Counts
20 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Calls

3 calls:

7.0ms
eps
5.0ms
x
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.4%1x
98.4%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes16.0ms (0.2%)

Memory
-9.2MiB live, 35.9MiB allocated; 2ms collecting garbage
Counts
19 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
Calls

3 calls:

7.0ms
eps
5.0ms
x
3.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.2%1x
98.2%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes13.0ms (0.2%)

Memory
-26.6MiB live, 33.8MiB allocated; 1ms collecting garbage
Counts
16 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 #s(approx (- (+ (* (+ (* (+ (* -1/36 (* eps eps)) 1/6) x) (* 1/4 eps)) x) (* (* eps eps) 1/6)) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Calls

3 calls:

4.0ms
x
4.0ms
eps
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.2%1x
98.2%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes11.0ms (0.1%)

Memory
27.4MiB live, 27.4MiB allocated; 0ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) #s(approx (* (+ (* (* (* x x) eps) 1/6) (neg eps)) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (+.f64 (*.f64 (neg.f64 eps) x) (*.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) x))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) eps) -1/2) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

4.0ms
eps
4.0ms
x
3.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.8%1x
97.8%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes7.0ms (0.1%)

Memory
-28.1MiB live, 18.9MiB allocated; 1ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) eps) -1/2) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 #s(approx (+ (* (* (* x x) eps) 1/6) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (+ (* (* eps eps) 1/6) -1) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64)))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(literal -1/2 binary64)) eps) #s(approx (sin x) x)) eps))
Calls

3 calls:

3.0ms
x
2.0ms
eps
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.6%1x
97.6%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0%)

Memory
11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Accuracy

Total -16.4b remaining (-109.7%)

Threshold costs -16.4b (-109.7%)

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

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
76.6%1x
76.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
76.6%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

derivations446.0ms (5.5%)

Memory
-21.1MiB live, 560.3MiB allocated; 61ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 240 to 155 computations (35.4% saved)

preprocess142.0ms (1.8%)

Memory
37.1MiB live, 421.8MiB allocated; 20ms collecting garbage
Compiler

Compiled 274 to 186 computations (32.1% saved)

end0.0ms (0%)

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

Profiling

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