2sin (example 3.3)

Time bar (total: 14.4s)

analyze40.0ms (0.3%)

Memory
13.3MiB live, 56.6MiB allocated
Algorithm
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)

sample6.6s (45.6%)

Memory
94.7MiB live, 9 502.7MiB allocated
Samples
3.3s26 117×0invalid
861.0ms4 485×1valid
440.0ms3 771×0valid
Precisions
Click to see histograms. Total time spent on operations: 3.3s
ival-sin: 770.0ms (23.2% of total)
const: 689.0ms (20.8% of total)
ival-add: 332.0ms (10% of total)
ival-mult: 330.0ms (9.9% of total)
ival-<: 301.0ms (9.1% of total)
ival-<=: 246.0ms (7.4% of total)
ival-sub: 214.0ms (6.4% of total)
ival-fabs: 204.0ms (6.1% of total)
ival-and: 98.0ms (3% of total)
adjust: 78.0ms (2.4% of total)
exact: 44.0ms (1.3% of total)
ival-assert: 13.0ms (0.4% of total)
Bogosity

preprocess29.0ms (0.2%)

Memory
-23.1MiB live, 52.9MiB allocated
Algorithm
egg-herbie
Rules
114×sub-neg
80×accelerator-lowering-fma.f32
80×accelerator-lowering-fma.f64
76×cancel-sign-sub-inv
62×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02146
14342
29242
318142
432142
539842
648342
752542
853442
067
197
2147
3207
4287
5437
6767
71017
81447
91597
101677
01677
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (sin (+ x eps)) (sin x))
Outputs
(- (sin (+ x eps)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Call 2
Inputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(- (sin (+ x (neg eps))) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(neg (- (sin (+ x (neg eps))) (sin x)))
(- (sin (+ eps x)) (sin eps))
Outputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ x (neg eps))) (sin x))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ x (neg eps))) (sin x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ eps x)) (sin eps))
(- (sin (+ x eps)) (sin eps))

explain94.0ms (0.7%)

Memory
13.3MiB live, 171.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2261(3.192152945020566e-29 3.7730803252605763e-32)1(3.258346941814887e-131 3.5980737797046116e-133)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
00-0-(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2264
Confusion
Predicted +Predicted -
+2252
-128
Precision
0.995575221238938
Recall
0.9911894273127754
Confusion?
Predicted +Predicted MaybePredicted -
+22511
-1325
Precision?
0.9826086956521739
Recall?
0.9955947136563876
Freqs
test
numberfreq
030
1226
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
31.0ms292×1valid
10.0ms218×0valid
1.0ms3valid
Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-sin: 10.0ms (42.6% of total)
adjust: 5.0ms (21.3% of total)
ival-add: 4.0ms (17.1% of total)
ival-sub: 3.0ms (12.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory
11.3MiB live, 11.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Rules
80×accelerator-lowering-fma.f32
80×accelerator-lowering-fma.f64
48×*-lowering-*.f32
48×*-lowering-*.f64
36×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
1918
21418
32018
42818
54318
67618
710118
814418
915918
1016718
016718
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
x
eps
(sin x)
Outputs
(- (sin (+ x eps)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (+ x eps))
(sin.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(sin x)
(sin.f64 x)

localize60.0ms (0.4%)

Memory
-33.9MiB live, 51.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(sin.f64 x)
accuracy100.0%
(sin.f64 (+.f64 x eps))
accuracy61.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
20.0ms109×0valid
13.0ms146×1valid
1.0ms3valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-sin: 5.0ms (44.2% of total)
adjust: 2.0ms (17.7% of total)
ival-add: 2.0ms (17.7% of total)
ival-sub: 2.0ms (17.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
8.4MiB live, 8.4MiB allocated
Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- (sin (+ x eps)) (sin x))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (sin x)>
Outputs
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
Calls

21 calls:

TimeVariablePointExpression
1.0ms
eps
@inf
(- (sin (+ x eps)) (sin x))
0.0ms
x
@0
(- (sin (+ x eps)) (sin x))
0.0ms
eps
@0
(- (sin (+ x eps)) (sin x))
0.0ms
x
@inf
(+ x eps)
0.0ms
x
@-inf
(- (sin (+ x eps)) (sin x))

rewrite544.0ms (3.8%)

Memory
12.2MiB live, 475.3MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 986×accelerator-lowering-fma.f32
4 986×accelerator-lowering-fma.f64
4 676×*-lowering-*.f32
4 676×*-lowering-*.f64
2 176×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
14916
237616
3476316
0821216
Stop Event
iter limit
node limit
Counts
4 → 214
Calls
Call 1
Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
(sin x)
Outputs
(+.f64 (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))))
(fma.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps))))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps)))
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
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(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 x x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (+.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (-.f64 (*.f64 eps eps) (*.f64 x x))) #s(literal -1 binary64))
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (*.f64 x x) (*.f64 eps eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 eps eps))) #s(literal -1 binary64)))
(*.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)))))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps))))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps eps))))
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))))
(*.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))))
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))
(sin.f64 x)
(pow.f64 (sin.f64 x) #s(literal 1 binary64))

simplify628.0ms (4.4%)

Memory
17.1MiB live, 771.5MiB allocated
Algorithm
egg-herbie
Rules
16 678×accelerator-lowering-fma.f32
16 678×accelerator-lowering-fma.f64
4 132×*-lowering-*.f32
4 132×*-lowering-*.f64
2 614×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107496
1314496
2775489
32836489
46173489
08126458
Stop Event
iter limit
node limit
Counts
84 → 84
Calls
Call 1
Inputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (sin.f64 eps)) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (sin.f64 eps)) (*.f64 x (+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (cos.f64 eps))))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (*.f64 x (cos.f64 eps)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (sin.f64 eps)) (*.f64 (cos.f64 eps) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (*.f64 eps (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

eval35.0ms (0.2%)

Memory
3.4MiB live, 80.8MiB allocated
Compiler

Compiled 8 005 to 859 computations (89.3% saved)

prune36.0ms (0.2%)

Memory
11.6MiB live, 93.7MiB allocated
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New28810298
Fresh000
Picked011
Done000
Total28811299
Accuracy
100.0%
Counts
299 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.3%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
60.7%
(-.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (sin.f64 x))
60.6%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
60.8%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
60.9%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
61.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
100.0%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.9%
(*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))))
99.7%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
99.3%
(*.f64 eps (cos.f64 x))
98.1%
(sin.f64 eps)
Compiler

Compiled 331 to 224 computations (32.3% saved)

simplify410.0ms (2.9%)

Memory
-42.7MiB live, 581.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 x eps))
cost-diff0
(sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
cost-diff0
(-.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (sin.f64 x))
cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
cost-diff0
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
cost-diff0
(sin.f64 eps)
cost-diff0
(*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
cost-diff128
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff128
(+.f64 eps #s(literal 0 binary64))
Rules
12 230×accelerator-lowering-fma.f32
12 230×accelerator-lowering-fma.f64
2 654×*-lowering-*.f32
2 654×*-lowering-*.f64
2 478×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040286
1104286
2287278
3825278
42555278
54749278
66179278
77343270
87762270
08027246
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ eps 0)
eps
0
2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
(sin eps)
eps
(- (sin (+ x eps)) (* x (- 1 (* 1/6 (* x x)))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (- 1 (* 1/6 (* x x))))
(- 1 (* 1/6 (* x x)))
1
(* 1/6 (* x x))
1/6
(* x x)
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))
(+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))
1
(* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))
(* x x)
(+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))
-1/6
(* x (* x (+ 1/120 (* (* x x) -1/5040))))
(* x (+ 1/120 (* (* x x) -1/5040)))
(+ 1/120 (* (* x x) -1/5040))
1/120
(* (* x x) -1/5040)
-1/5040
(- (sin (/ 1 (/ 1 (+ x eps)))) (sin x))
(sin (/ 1 (/ 1 (+ x eps))))
(/ 1 (/ 1 (+ x eps)))
1
(/ 1 (+ x eps))
(+ x eps)
x
eps
(sin x)
Outputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(*.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))
(sin (/ (+ eps 0) 2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/ (+ eps 0) 2)
(/.f64 eps #s(literal 2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))
(/ (+ eps (* x 2)) 2)
(+.f64 (/.f64 eps #s(literal 2 binary64)) x)
(+ eps (* x 2))
(-.f64 eps (*.f64 x #s(literal -2 binary64)))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
x
(sin eps)
(sin.f64 eps)
eps
(- (sin (+ x eps)) (* x (- 1 (* 1/6 (* x x)))))
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (- 1 (* 1/6 (* x x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(- 1 (* 1/6 (* x x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))
1
#s(literal 1 binary64)
(* 1/6 (* x x))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
1/6
#s(literal 1/6 binary64)
(* x x)
(*.f64 x x)
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))
(+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))
1
#s(literal 1 binary64)
(* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))
(* x x)
(*.f64 x x)
(+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))
(+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))
-1/6
#s(literal -1/6 binary64)
(* x (* x (+ 1/120 (* (* x x) -1/5040))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))
(* x (+ 1/120 (* (* x x) -1/5040)))
(*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))
(+ 1/120 (* (* x x) -1/5040))
(+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))
1/120
#s(literal 1/120 binary64)
(* (* x x) -1/5040)
(*.f64 (*.f64 x x) #s(literal -1/5040 binary64))
-1/5040
#s(literal -1/5040 binary64)
(- (sin (/ 1 (/ 1 (+ x eps)))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (/ 1 (/ 1 (+ x eps))))
(sin.f64 (+.f64 eps x))
(/ 1 (/ 1 (+ x eps)))
(+.f64 eps x)
1
#s(literal 1 binary64)
(/ 1 (+ x eps))
(/.f64 #s(literal 1 binary64) (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin x)
(sin.f64 x)

localize194.0ms (1.4%)

Memory
31.6MiB live, 385.3MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (+.f64 x eps))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
accuracy61.4%
(-.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (sin.f64 x))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -1/5040 binary64))
accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))
accuracy99.6%
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))
accuracy61.8%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
accuracy100.0%
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
accuracy100.0%
(sin.f64 (+.f64 x eps))
accuracy99.6%
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
accuracy61.9%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
accuracy100.0%
(sin.f64 eps)
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
accuracy100.0%
(*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
accuracy100.0%
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
Samples
91.0ms151×1valid
33.0ms104×0valid
2.0ms5exit
Compiler

Compiled 310 to 42 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 92.0ms
ival-mult: 24.0ms (26.1% of total)
const: 15.0ms (16.3% of total)
ival-sin: 14.0ms (15.2% of total)
ival-div: 11.0ms (12% of total)
ival-add: 11.0ms (12% of total)
adjust: 8.0ms (8.7% of total)
ival-sub: 7.0ms (7.6% of total)
ival-cos: 3.0ms (3.3% of total)
exact: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory
0.1MiB live, 37.8MiB allocated
Counts
22 → 408
Calls
Call 1
Inputs
#<alt (+ eps 0)>
#<alt (/ (+ eps (* x 2)) 2)>
#<alt (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (sin eps)>
#<alt (- (sin (+ x eps)) (* x (- 1 (* 1/6 (* x x)))))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (* x (- 1 (* 1/6 (* x x))))>
#<alt (- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))>
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))>
#<alt (/ 1 (/ 1 (+ x eps)))>
#<alt (- (sin (/ 1 (/ 1 (+ x eps)))) (sin x))>
#<alt (sin (/ 1 (/ 1 (+ x eps))))>
#<alt (/ 1 (+ x eps))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (sin (/ (+ eps 0) 2))>
#<alt (* x 2)>
#<alt (* 1/6 (* x x))>
#<alt (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))>
#<alt (* x (* x (+ 1/120 (* (* x x) -1/5040))))>
#<alt (* (* x x) -1/5040)>
Outputs
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (- (sin x) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (* -1/5040 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (/ 1 eps)>
#<alt (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))>
#<alt (+ (* x (- (/ x (pow eps 3)) (/ 1 (pow eps 2)))) (/ 1 eps))>
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1 (/ eps x))) x)>
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (/ eps x)) x)>
#<alt (/ (- (+ 1 (* -1 (/ (pow eps 3) (pow x 3)))) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ eps x) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) eps) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow eps 3) x) (pow eps 2)) x)) eps) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1 (/ eps (pow x 2))) (/ 1 x))>
#<alt (+ (* eps (- (/ eps (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* eps (- (* eps (+ (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ 1 eps)>
#<alt (/ (+ 1 (* -1 (/ x eps))) eps)>
#<alt (/ (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)) eps)>
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow eps 3)))) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))) eps)>
#<alt (/ 1 eps)>
#<alt (* -1 (/ (- (/ x eps) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) eps) x) eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (pow x 2)) eps)) x) eps)) 1) eps))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))>
#<alt (* -1/5040 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* -1/5040 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* -1/5040 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
#<alt (* -1/5040 (pow x 2))>
Calls

102 calls:

TimeVariablePointExpression
4.0ms
eps
@inf
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms
x
@0
(/ 1 (+ x eps))
1.0ms
x
@0
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms
x
@inf
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms
eps
@inf
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))

rewrite375.0ms (2.6%)

Memory
3.4MiB live, 514.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 590×*-lowering-*.f32
5 590×*-lowering-*.f64
4 164×/-lowering-/.f32
4 164×/-lowering-/.f64
3 506×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040187
1278183
22324183
09000168
Stop Event
iter limit
node limit
Counts
22 → 526
Calls
Call 1
Inputs
(+ eps 0)
(/ (+ eps (* x 2)) 2)
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin eps)
(- (sin (+ x eps)) (* x (- 1 (* 1/6 (* x x)))))
(sin (+ x eps))
(+ x eps)
(* x (- 1 (* 1/6 (* x x))))
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040)))))))))
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))))
(/ 1 (/ 1 (+ x eps)))
(- (sin (/ 1 (/ 1 (+ x eps)))) (sin x))
(sin (/ 1 (/ 1 (+ x eps))))
(/ 1 (+ x eps))
(cos (/ (+ eps (* x 2)) 2))
(sin (/ (+ eps 0) 2))
(* x 2)
(* 1/6 (* x x))
(* (* x x) (+ -1/6 (* x (* x (+ 1/120 (* (* x x) -1/5040))))))
(* x (* x (+ 1/120 (* (* x x) -1/5040))))
(* (* x x) -1/5040)
Outputs
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) eps) (*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) eps) eps))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) eps) (*.f64 (/.f64 eps (*.f64 eps eps)) #s(literal 0 binary64))) (*.f64 (/.f64 eps (*.f64 eps eps)) eps))
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) (*.f64 (*.f64 eps eps) #s(literal 0 binary64))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (*.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 0 binary64)) eps) (*.f64 (*.f64 eps eps) #s(literal 0 binary64))) (*.f64 eps (*.f64 eps eps)))
(/.f64 (-.f64 (*.f64 (neg.f64 (*.f64 eps eps)) eps) (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) eps) eps))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps) (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) eps) eps))
(/.f64 (-.f64 (*.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) eps) (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 0 binary64))) (*.f64 (neg.f64 (*.f64 eps eps)) eps))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64)))
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -2 binary64))
(/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 #s(literal -2 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (*.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 #s(literal -2 binary64) x))))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))))
(/.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))) #s(literal -1 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 1/2 binary64))
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(-.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 (/.f64 #s(literal 0 binary64) eps))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 #s(literal 0 binary64) eps))))
(sin.f64 eps)
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))) (sin.f64 (+.f64 eps x)))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))
(-.f64 (/.f64 (pow.f64 (sin.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 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))) (/.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 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 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))))
(-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))
(fma.f64 x (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (sin.f64 (+.f64 eps x)))
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (-.f64 #s(literal 0 binary64) x) (sin.f64 (+.f64 eps x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))
(fma.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (sin.f64 (+.f64 eps x)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (sin.f64 (+.f64 eps x)))
(fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) x (sin.f64 (+.f64 eps x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 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 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 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 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 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 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))) (*.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))))
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(/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/216 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))) (+.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (-.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) #s(literal -1/6 binary64)))))
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))) (-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))
(/.f64 (*.f64 (+.f64 #s(literal -1/216 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))) (*.f64 x x)) (+.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (-.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) #s(literal -1/6 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))) (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))
(*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))
(*.f64 (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))) (*.f64 x x))
(*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))) #s(literal 1 binary64))
(*.f64 (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))) x)
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))) (*.f64 x x))
(+.f64 (*.f64 x (*.f64 x #s(literal 1/120 binary64))) (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x)))))
(+.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal 1/120 binary64)) x) (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x))) x))
(+.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/120 binary64) (*.f64 x x)))
(fma.f64 x (*.f64 x #s(literal 1/120 binary64)) (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x)))))
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(fma.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) (*.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x x)))
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x x) (*.f64 #s(literal 1/120 binary64) (*.f64 x x)))
(fma.f64 (*.f64 x #s(literal 1/120 binary64)) x (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x))) x))
(/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/1728000 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))))) (+.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) #s(literal 1/120 binary64)))))
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64)))) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal 1/5040 binary64) (*.f64 x x))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))) (*.f64 x x))
(*.f64 (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) x)
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(*.f64 (*.f64 x x) #s(literal -1/5040 binary64))
(*.f64 #s(literal -1/5040 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal -1/5040 binary64)) x)

simplify401.0ms (2.8%)

Memory
11.9MiB live, 484.2MiB allocated
Algorithm
egg-herbie
Rules
10 668×accelerator-lowering-fma.f32
10 668×accelerator-lowering-fma.f64
6 278×*-lowering-*.f32
6 278×*-lowering-*.f64
3 342×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04483940
113413744
237203726
082893466
Stop Event
iter limit
node limit
Counts
408 → 408
Calls
Call 1
Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(- (sin x) (* x (- 1 (* 1/6 (pow x 2)))))
(- (+ (sin x) (* eps (cos x))) (* x (- 1 (* 1/6 (pow x 2)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (- 1 (* 1/6 (pow x 2)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (- 1 (* 1/6 (pow x 2)))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* 1/5040 (pow x 7))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 7))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(/ 1 eps)
(+ (* -1 (/ x (pow eps 2))) (/ 1 eps))
(+ (* x (- (/ x (pow eps 3)) (/ 1 (pow eps 2)))) (/ 1 eps))
(+ (* x (- (* x (+ (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(/ 1 x)
(/ (+ 1 (* -1 (/ eps x))) x)
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (/ eps x)) x)
(/ (- (+ 1 (* -1 (/ (pow eps 3) (pow x 3)))) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))) x)
(/ 1 x)
(* -1 (/ (- (/ eps x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) eps) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow eps 3) x) (pow eps 2)) x)) eps) x)) 1) x))
(/ 1 x)
(+ (* -1 (/ eps (pow x 2))) (/ 1 x))
(+ (* eps (- (/ eps (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* eps (- (* eps (+ (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ 1 eps)
(/ (+ 1 (* -1 (/ x eps))) eps)
(/ (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)) eps)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow eps 3)))) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))) eps)
(/ 1 eps)
(* -1 (/ (- (/ x eps) 1) eps))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) eps) x) eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (pow x 2)) eps)) x) eps)) 1) eps))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(* -1/5040 (pow x 6))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 6))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* 1/120 (pow x 2))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(* -1/5040 (pow x 4))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 4))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
(* -1/5040 (pow x 2))
Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
x
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (+.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 1/2 (* eps (cos x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
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(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
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(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
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(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
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(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
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(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)))))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
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(- (sin x) (* x (- 1 (* 1/6 (pow x 2)))))
(+.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(- (+ (sin x) (* eps (cos x))) (* x (- 1 (* 1/6 (pow x 2)))))
(+.f64 (*.f64 eps (cos.f64 x)) (+.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (- 1 (* 1/6 (pow x 2)))))
(+.f64 (*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))) (+.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (- 1 (* 1/6 (pow x 2)))))
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(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
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(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
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(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
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(- (sin (+ eps x)) (* x (- 1 (* 1/6 (pow x 2)))))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
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(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(* -1 (* x (- (* -1 (/ eps x)) 1)))
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(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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x
(* x (+ 1 (* -1/6 (pow x 2))))
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(* x (+ 1 (* -1/6 (pow x 2))))
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(* x (+ 1 (* -1/6 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* -1/6 (pow x 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* -1/6 (pow x 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
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(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
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(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
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(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal -1/120 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
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(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
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eps
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(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/8 binary64)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64))) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))
(* -1/5040 (pow x 6))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* -1/5040 (pow x 6))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* 1/120 (pow x 2))
(*.f64 #s(literal 1/120 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(* -1/5040 (pow x 4))
(*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* -1/5040 (pow x 4))
(*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))
(* -1/5040 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/5040 binary64)))

eval140.0ms (1%)

Memory
6.6MiB live, 237.2MiB allocated
Compiler

Compiled 31 970 to 2 659 computations (91.7% saved)

prune115.0ms (0.8%)

Memory
-18.7MiB live, 189.4MiB allocated
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1 17581 183
Fresh415
Picked505
Done101
Total1 18591 194
Accuracy
100.0%
Counts
1 194 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.9%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
3.4%
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
99.7%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
98.1%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
99.3%
(*.f64 eps (cos.f64 x))
98.1%
eps
Compiler

Compiled 258 to 174 computations (32.6% saved)

simplify225.0ms (1.6%)

Memory
25.1MiB live, 292.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
cost-diff0
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
cost-diff0
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
cost-diff128
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff0
(*.f64 eps #s(literal 1/2 binary64))
cost-diff0
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
cost-diff128
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff256
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
cost-diff0
(+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 x (*.f64 x x))
cost-diff256
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
cost-diff0
(*.f64 eps #s(literal 1/2 binary64))
cost-diff0
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
Rules
6 922×accelerator-lowering-fma.f32
6 922×accelerator-lowering-fma.f64
3 110×*-lowering-*.f32
3 110×*-lowering-*.f64
2 420×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034269
188269
2221267
3498263
41291260
52418259
64063259
76713251
08160226
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
eps
1/2
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
2
eps
(* (* x (* x x)) (+ 1/6 (/ -1 (* x x))))
(* x (* x x))
x
(* x x)
(+ 1/6 (/ -1 (* x x)))
1/6
(/ -1 (* x x))
-1
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(* eps 1/2)
eps
1/2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))))
eps
(+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))
1/2
(* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))
(* eps (+ -1/48 (* (* eps eps) 1/3840)))
(+ -1/48 (* (* eps eps) 1/3840))
-1/48
(* (* eps eps) 1/3840)
(* eps eps)
1/3840
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
Outputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(sin (* eps 1/2))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(cos (+ x (* eps 1/2)))
(cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(+ x (* eps 1/2))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
x
2
#s(literal 2 binary64)
eps
(* (* x (* x x)) (+ 1/6 (/ -1 (* x x))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(+ 1/6 (/ -1 (* x x)))
(+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
1/6
#s(literal 1/6 binary64)
(/ -1 (* x x))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
-1
#s(literal -1 binary64)
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(*.f64 eps (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(/ (+ eps (* x 2)) 2)
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (*.f64 eps #s(literal 2 binary64))))
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
eps
(+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
1/2
#s(literal 1/2 binary64)
(* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))
(* eps (+ -1/48 (* (* eps eps) 1/3840)))
(*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(+ -1/48 (* (* eps eps) 1/3840))
(+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) 1/3840)
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* eps eps)
(*.f64 eps eps)
1/3840
#s(literal 1/3840 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(/ (+ eps (* x 2)) 2)
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)

localize126.0ms (0.9%)

Memory
-6.0MiB live, 191.9MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
accuracy99.8%
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
accuracy99.8%
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))
accuracy99.5%
(*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(*.f64 eps #s(literal 1/2 binary64))
accuracy100.0%
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
accuracy100.0%
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
accuracy100.0%
(+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
accuracy99.8%
(*.f64 x (*.f64 x x))
accuracy99.8%
(/.f64 #s(literal -1 binary64) (*.f64 x x))
accuracy40.5%
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
accuracy100.0%
(*.f64 eps #s(literal 1/2 binary64))
accuracy100.0%
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
accuracy100.0%
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
Samples
75.0ms256×0valid
Compiler

Compiled 283 to 36 computations (87.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-mult: 25.0ms (44.7% of total)
ival-add: 9.0ms (16.1% of total)
const: 9.0ms (16.1% of total)
ival-div: 7.0ms (12.5% of total)
ival-cos: 3.0ms (5.4% of total)
ival-sin: 2.0ms (3.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series32.0ms (0.2%)

Memory
-7.0MiB live, 69.6MiB allocated
Counts
21 → 360
Calls
Call 1
Inputs
#<alt (* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)>
#<alt (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))>
#<alt (sin (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (* (* x (* x x)) (+ 1/6 (/ -1 (* x x))))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (+ 1/6 (/ -1 (* x x)))>
#<alt (* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (/ (+ eps (* x 2)) 2)>
#<alt (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))))>
#<alt (cos (+ x (* eps 1/2)))>
#<alt (/ -1 (* x x))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* x 2)>
#<alt (* eps (+ -1/48 (* (* eps eps) 1/3840)))>
#<alt (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))>
#<alt (* (* eps eps) 1/3840)>
Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1 x)>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ -1 (pow x 2))>
#<alt (/ (- (* 1/6 (pow x 2)) 1) (pow x 2))>
#<alt (/ (- (* 1/6 (pow x 2)) 1) (pow x 2))>
#<alt (/ (- (* 1/6 (pow x 2)) 1) (pow x 2))>
#<alt 1/6>
#<alt (- 1/6 (/ 1 (pow x 2)))>
#<alt (- 1/6 (/ 1 (pow x 2)))>
#<alt (- 1/6 (/ 1 (pow x 2)))>
#<alt 1/6>
#<alt (- 1/6 (/ 1 (pow x 2)))>
#<alt (- 1/6 (/ 1 (pow x 2)))>
#<alt (- 1/6 (/ 1 (pow x 2)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))>
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* -1/48 eps)>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* 1/3840 (pow eps 3))>
#<alt (* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
Calls

90 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms
eps
@inf
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms
eps
@0
(* eps (+ -1/48 (* (* eps eps) 1/3840)))
1.0ms
eps
@inf
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms
x
@-inf
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite397.0ms (2.8%)

Memory
1.9MiB live, 650.7MiB allocated
Algorithm
batch-egg-rewrite
Rules
6 432×accelerator-lowering-fma.f32
6 432×accelerator-lowering-fma.f64
4 154×*-lowering-*.f32
4 154×*-lowering-*.f64
3 510×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034200
1181197
21307194
08736176
Stop Event
iter limit
node limit
Counts
21 → 504
Calls
Call 1
Inputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
(* (* x (* x x)) (+ 1/6 (/ -1 (* x x))))
(* x (* x x))
(* x x)
(+ 1/6 (/ -1 (* x x)))
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(/ (+ eps (* x 2)) 2)
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840)))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))))
(cos (+ x (* eps 1/2)))
(/ -1 (* x x))
(cos (/ (+ eps (* x 2)) 2))
(* x 2)
(* eps (+ -1/48 (* (* eps eps) 1/3840)))
(* eps (* eps (+ -1/48 (* (* eps eps) 1/3840))))
(* (* eps eps) 1/3840)
Outputs
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(fma.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))) #s(literal -2 binary64))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)))
(*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(*.f64 (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal 1/2 binary64))
(*.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) #s(literal 1/56623104000 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/3840 binary64))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal -1/14745600 binary64))))))
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) #s(literal 1/56623104000 binary64)))) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)))))
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal -1/14745600 binary64)))) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/3840 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) #s(literal 1/56623104000 binary64))))) (+.f64 #s(literal -1/2304 binary64) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))))))
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal -1/14745600 binary64))))) (+.f64 #s(literal 1/48 binary64) (neg.f64 (*.f64 (*.f64 eps eps) #s(literal -1/3840 binary64)))))
(/.f64 (+.f64 (pow.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (-.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps)) (-.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps)) (*.f64 (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps)) (*.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps))) (-.f64 (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)))) (-.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))
(*.f64 (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 eps eps))
(*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) eps)
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) #s(literal 1/56623104000 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))))))
(*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal -1/14745600 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/3840 binary64)))))
(*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps #s(literal 1/3840 binary64)) eps)

simplify481.0ms (3.3%)

Memory
-6.7MiB live, 683.1MiB allocated
Algorithm
egg-herbie
Rules
10 468×accelerator-lowering-fma.f32
10 468×accelerator-lowering-fma.f64
7 748×*-lowering-*.f32
7 748×*-lowering-*.f64
3 916×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03744386
112024186
238554147
084853801
Stop Event
iter limit
node limit
Counts
360 → 360
Calls
Call 1
Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ -1 (pow x 2))
(/ (- (* 1/6 (pow x 2)) 1) (pow x 2))
(/ (- (* 1/6 (pow x 2)) 1) (pow x 2))
(/ (- (* 1/6 (pow x 2)) 1) (pow x 2))
1/6
(- 1/6 (/ 1 (pow x 2)))
(- 1/6 (/ 1 (pow x 2)))
(- 1/6 (/ 1 (pow x 2)))
1/6
(- 1/6 (/ 1 (pow x 2)))
(- 1/6 (/ 1 (pow x 2)))
(- 1/6 (/ 1 (pow x 2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 eps))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* 1/3840 (pow eps 5))
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -1/48 eps)
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(* 1/3840 (pow eps 3))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (+.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
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(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* eps (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* 1/3840 (pow eps 3))
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* 1/3840 (pow eps 3))
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* -1 (* (pow eps 3) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))
(* -1/48 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* 1/3840 (pow eps 4))
(*.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* 1/3840 (pow eps 4))
(*.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))

eval120.0ms (0.8%)

Memory
24.4MiB live, 250.4MiB allocated
Compiler

Compiled 27 146 to 2 445 computations (91% saved)

prune107.0ms (0.7%)

Memory
-4.1MiB live, 157.5MiB allocated
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1 03381 041
Fresh134
Picked415
Done000
Total1 038121 050
Accuracy
100.0%
Counts
1 050 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.6%
(-.f64 #s(literal 0 binary64) x)
7.6%
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
100.0%
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
99.9%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
99.7%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64))
2.3%
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
7.6%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
99.7%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
98.1%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
99.7%
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
99.3%
(*.f64 eps (cos.f64 x))
98.1%
eps
Compiler

Compiled 339 to 216 computations (36.3% saved)

simplify180.0ms (1.2%)

Memory
-27.0MiB live, 218.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 eps #s(literal 1/2 binary64))
cost-diff0
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
cost-diff0
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
cost-diff0
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
cost-diff128
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x))
cost-diff256
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)
cost-diff256
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
cost-diff640
(*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x)))
cost-diff0
(*.f64 x #s(literal 1/6 binary64))
cost-diff0
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
cost-diff0
(+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
cost-diff0
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
cost-diff0
(-.f64 #s(literal 0 binary64) x)
cost-diff0
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))
cost-diff0
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
cost-diff0
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
Rules
3 328×*-lowering-*.f32
3 328×*-lowering-*.f64
2 844×/-lowering-/.f32
2 844×/-lowering-/.f64
2 838×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035288
1105269
2357214
31815214
43503214
55461214
67461214
08070197
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
(* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2)))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))
1/2
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))
(* eps eps)
eps
(+ -1/48 (* (* eps eps) 1/3840))
-1/48
(* (* eps eps) 1/3840)
1/3840
(* eps (cos (+ x (* eps 1/2))))
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
(* eps 1/2)
2
(- 0 x)
0
x
(* x (+ -1 (* x (* x 1/6))))
x
(+ -1 (* x (* x 1/6)))
-1
(* x (* x 1/6))
(* x 1/6)
1/6
(* (* x (* x x)) (+ 1/6 (/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x))))))
(* x (* x x))
x
(* x x)
(+ 1/6 (/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x)))))
1/6
(/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x))))
-1
(* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x)))
(* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x))
(* (/ -1 (* x x)) x)
(/ -1 (* x x))
(* (* x x) (* x x))
(* eps (cos (+ x (* eps 1/2))))
eps
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
(* eps 1/2)
1/2
Outputs
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))))
(* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2)))))
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))
1/2
#s(literal 1/2 binary64)
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))
(* eps eps)
(*.f64 eps eps)
eps
(+ -1/48 (* (* eps eps) 1/3840))
(+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) 1/3840)
(*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))
1/3840
#s(literal 1/3840 binary64)
(* eps (cos (+ x (* eps 1/2))))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(cos (+ x (* eps 1/2)))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(+ x (* eps 1/2))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
(* eps 1/2)
(*.f64 #s(literal 1/2 binary64) eps)
2
#s(literal 2 binary64)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
x
(* x (+ -1 (* x (* x 1/6))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
x
(+ -1 (* x (* x 1/6)))
(+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
-1
#s(literal -1 binary64)
(* x (* x 1/6))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* (* x (* x x)) (+ 1/6 (/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x))))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(+ 1/6 (/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x)))))
(+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
1/6
#s(literal 1/6 binary64)
(/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x))))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
-1
#s(literal -1 binary64)
(* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x)))
(*.f64 x x)
(* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(* (/ -1 (* x x)) x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 (* x x))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(* (* x x) (* x x))
(*.f64 x (*.f64 x (*.f64 x x)))
(* eps (cos (+ x (* eps 1/2))))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
eps
(cos (+ x (* eps 1/2)))
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(+ x (* eps 1/2))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
(* eps 1/2)
(*.f64 #s(literal 1/2 binary64) eps)
1/2
#s(literal 1/2 binary64)

localize125.0ms (0.9%)

Memory
9.8MiB live, 165.0MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 eps #s(literal 1/2 binary64))
accuracy100.0%
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
accuracy100.0%
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
accuracy99.6%
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x))
accuracy57.4%
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)
accuracy40.5%
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
accuracy33.4%
(*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x)))
accuracy100.0%
(+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
accuracy99.8%
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
accuracy99.4%
(*.f64 x #s(literal 1/6 binary64))
accuracy100.0%
(-.f64 #s(literal 0 binary64) x)
accuracy100.0%
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
accuracy100.0%
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
accuracy99.8%
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
accuracy99.7%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
Samples
71.0ms256×0valid
Compiler

Compiled 325 to 37 computations (88.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-mult: 23.0ms (48.3% of total)
const: 9.0ms (18.9% of total)
ival-add: 5.0ms (10.5% of total)
ival-cos: 5.0ms (10.5% of total)
ival-div: 4.0ms (8.4% of total)
ival-sub: 1.0ms (2.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory
11.9MiB live, 11.9MiB allocated
Counts
18 → 276
Calls
Call 1
Inputs
#<alt (* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)>
#<alt (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2)))))>
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))>
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))>
#<alt (- 0 x)>
#<alt (* x (+ -1 (* x (* x 1/6))))>
#<alt (+ -1 (* x (* x 1/6)))>
#<alt (* x (* x 1/6))>
#<alt (* x 1/6)>
#<alt (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x)))>
#<alt (* (* x (* x x)) (+ 1/6 (/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x))))))>
#<alt (* (/ -1 (* x x)) x)>
#<alt (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x))>
#<alt (* eps (cos (+ x (* eps 1/2))))>
#<alt (cos (+ x (* eps 1/2)))>
#<alt (+ x (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (* (* eps eps) 1/3840)>
Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 4))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt -1>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 x)>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
Calls

69 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
1.0ms
x
@-inf
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
1.0ms
eps
@inf
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
1.0ms
eps
@-inf
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
1.0ms
eps
@-inf
(* eps (cos (+ x (* eps 1/2))))

rewrite438.0ms (3%)

Memory
-19.1MiB live, 619.6MiB allocated
Algorithm
batch-egg-rewrite
Rules
6 306×accelerator-lowering-fma.f32
6 306×accelerator-lowering-fma.f64
3 882×*-lowering-*.f32
3 882×*-lowering-*.f64
3 768×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035163
1205154
21682139
09420124
Stop Event
iter limit
node limit
Counts
18 → 1 236
Calls
Call 1
Inputs
(* (* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2))))) 2)
(* (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) (* eps (cos (+ x (* eps 1/2)))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))
(- 0 x)
(* x (+ -1 (* x (* x 1/6))))
(+ -1 (* x (* x 1/6)))
(* x (* x 1/6))
(* x 1/6)
(* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x)))
(* (* x (* x x)) (+ 1/6 (/ -1 (* (* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x)) (* (* x x) (* x x))))))
(* (/ -1 (* x x)) x)
(* (* (/ -1 (* x x)) x) (* (/ -1 (* x x)) x))
(* eps (cos (+ x (* eps 1/2))))
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
(* eps 1/2)
(* (* eps eps) 1/3840)
Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) #s(literal 1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))))))
(/.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) #s(literal 2 binary64)))
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(*.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(+.f64 (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 1/2 binary64)) (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(+.f64 (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(+.f64 (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(fma.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(fma.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 1/2 binary64) (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(fma.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 1/2 binary64)))
(/.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) #s(literal 1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))))
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(fma.f64 (+.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (cos.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (-.f64 (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))) (neg.f64 (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))
(*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))))
(-.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 x (/.f64 x x) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (/.f64 #s(literal -1 binary64) x)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (*.f64 x (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 x x) x (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (+.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64)))) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 x (*.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) x) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) x) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) (*.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) (*.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) (*.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (neg.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (*.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) (neg.f64 (neg.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))))) (neg.f64 (neg.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (+.f64 (*.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) (*.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps))))
(*.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))))
(*.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps #s(literal 1/3840 binary64)) eps)

simplify530.0ms (3.7%)

Memory
29.5MiB live, 771.1MiB allocated
Algorithm
egg-herbie
Rules
13 500×accelerator-lowering-fma.f32
13 500×accelerator-lowering-fma.f64
6 306×*-lowering-*.f32
6 306×*-lowering-*.f64
4 810×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02672931
18632912
228472780
373312780
080192560
Stop Event
iter limit
node limit
Counts
276 → 276
Calls
Call 1
Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))
(* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps)))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 4))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
-1
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
(* 1/3840 (pow eps 2))
Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))))))
(* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/1920 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (*.f64 #s(literal 1/1920 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (*.f64 #s(literal 1/1920 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64))))))
(* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/1920 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (*.f64 #s(literal 1/1920 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(*.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 (*.f64 #s(literal 1/1920 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(*.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (+.f64 (*.f64 (*.f64 eps #s(literal 2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps #s(literal -2 binary64)) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
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(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
x
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))

eval452.0ms (3.1%)

Memory
-198.4MiB live, 465.9MiB allocated
Compiler

Compiled 46 022 to 4 018 computations (91.3% saved)

prune181.0ms (1.3%)

Memory
30.7MiB live, 420.4MiB allocated
Pruning

12 alts after pruning (8 fresh and 4 done)

PrunedKeptTotal
New1 73331 736
Fresh156
Picked235
Done011
Total1 736121 748
Accuracy
100.0%
Counts
1 748 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.6%
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
100.0%
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
99.9%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
2.3%
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
7.6%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
99.7%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
98.1%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
99.7%
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
99.7%
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
99.3%
(*.f64 eps (cos.f64 x))
7.6%
(neg.f64 x)
98.1%
eps
Compiler

Compiled 576 to 250 computations (56.6% saved)

regimes28.0ms (0.2%)

Memory
12.2MiB live, 49.8MiB allocated
Counts
30 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
(-.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (sin.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))))
Outputs
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
Calls

3 calls:

10.0ms
eps
8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory
-18.0MiB live, 19.4MiB allocated
Counts
19 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))
Outputs
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
Calls

2 calls:

8.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
99.9%1x
99.9%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes26.0ms (0.2%)

Memory
-26.3MiB live, 29.9MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))) #s(literal 2 binary64))
Outputs
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
Calls

2 calls:

5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory
35.3MiB live, 35.3MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
Outputs
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
Calls

2 calls:

4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory
-13.8MiB live, 18.8MiB allocated
Counts
11 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
Outputs
(*.f64 eps (cos.f64 x))
Calls

2 calls:

9.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
99.3%1x
99.3%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory
18.9MiB live, 18.9MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(sin.f64 eps)
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
Calls

2 calls:

3.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
98.1%1x
98.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Memory
-30.0MiB live, 8.0MiB allocated
Accuracy

Total -57.9b remaining (-4842.7%)

Threshold costs -57.9b (-4842.7%)

Counts
3 → 1
Calls
Call 1
Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
Outputs
eps
Calls

2 calls:

3.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
98.1%1x
98.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory
15.2MiB live, 15.2MiB allocated
Algorithm
egg-herbie
Rules
30×*-commutative_binary64
12×+-commutative_binary64
1-exp_binary64
1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03676
16076
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
eps
Outputs
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))))
(*.f64 eps (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 eps (cos.f64 x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
eps

soundness1.1s (7.3%)

Memory
-26.2MiB live, 724.9MiB allocated
Rules
16 678×accelerator-lowering-fma.f32
16 678×accelerator-lowering-fma.f64
10 668×accelerator-lowering-fma.f32
10 668×accelerator-lowering-fma.f64
10 468×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035163
1205154
21682139
09420124
0107496
1314496
2775489
32836489
46173489
08126458
04483940
113413744
237203726
082893466
03744386
112024186
238554147
084853801
0616
14916
237616
3476316
0821216
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 245 to 153 computations (37.6% saved)

preprocess109.0ms (0.8%)

Memory
-11.7MiB live, 104.4MiB allocated
Compiler

Compiled 268 to 146 computations (45.5% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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