ENA, Section 1.4, Mentioned, A

Time bar (total: 5.5s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.6%50.4%0%0%0%0
100%49.6%0%50.4%0%0%0%1
Compiler

Compiled 12 to 9 computations (25% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
Operation ival-sub, time spent: 0.0ms, 0.0% of total-time
Operation ival-and, time spent: 0.0ms, 0.0% of total-time
Operation ival-cos, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation ival-<=, time spent: 0.0ms, 0.0% of total-time

sample3.9s (71.1%)

Results
2.7s4242×2048valid
611.0ms2133×1024valid
173.0ms1057×512valid
143.0ms823×256valid
0.0ms1×1024valid
Precisions
Click to see histograms. Total time spent on operations: 2.3s
Operation ival-cos, time spent: 1.6s, 70.0% of total-time
Operation ival-sub, time spent: 318.0ms, 14.0% of total-time
Operation ival-<=, time spent: 283.0ms, 12.0% of total-time
Operation const, time spent: 55.0ms, 2.0% of total-time
Operation ival-and, time spent: 37.0ms, 2.0% of total-time
Bogosity

preprocess256.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
32×fma-neg
22×fma-define
18×sub-neg
14×associate--r+
12×associate-+l-
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1240-0-(-.f64 1 (cos.f64 x))
00-0-1
00-0-(cos.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 1 (cos.f64 x))cancellation1240
Confusion
Predicted +Predicted -
+1240
-0132
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+12400
-00132
Precision?
1.0
Recall?
1.0
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01360
12556
24456
36656
410656
513156
614156
714356
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 (neg.f64 x)))
(neg.f64 (-.f64 1 (cos.f64 (neg.f64 x))))
Outputs
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 (neg.f64 x)))
(-.f64 1 (cos.f64 x))
(neg.f64 (-.f64 1 (cos.f64 (neg.f64 x))))
(neg.f64 (-.f64 1 (cos.f64 x)))
(+.f64 -1 (cos.f64 x))
(+.f64 (cos.f64 x) -1)
Symmetry

(abs x)

Compiler

Compiled 30 to 20 computations (33.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 103.0ms
Operation ival-cos, time spent: 89.0ms, 86.0% of total-time
Operation ival-sub, time spent: 11.0ms, 11.0% of total-time
Operation const, time spent: 4.0ms, 4.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶56.8%
(-.f64 1 (cos.f64 x))
Compiler

Compiled 5 to 4 computations (20% saved)

localize131.0ms (2.4%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓56.8%
(-.f64 1 (cos.f64 x))
Compiler

Compiled 10 to 6 computations (40% saved)

Precisions
Click to see histograms. Total time spent on operations: 94.0ms
Operation ival-cos, time spent: 87.0ms, 92.0% of total-time
Operation ival-sub, time spent: 6.0ms, 6.0% of total-time
Operation const, time spent: 2.0ms, 2.0% of total-time

series1.0ms (0%)

Counts
1 → 4
Calls
Call 1
Inputs
#<alt (-.f64 1 (cos.f64 x))>
Outputs
#<alt (*.f64 1/2 (pow.f64 x 2))>
#<alt (*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2))))>
#<alt (*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/720 (pow.f64 x 2)) 1/24))))>
#<alt (*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (+.f64 1/720 (*.f64 -1/40320 (pow.f64 x 2)))) 1/24))))>
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(- 1 (cos x))
0.0ms
x
@inf
(- 1 (cos x))
0.0ms
x
@-inf
(- 1 (cos x))

rewrite221.0ms (4%)

Algorithm
1×batch-egg-rewrite
Rules
520×unpow-prod-down
361×log1p-expm1-u
361×expm1-log1p-u
344×add-exp-log
330×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
18214
295414
Stop Event
1×node limit
Counts
1 → 61
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 0 (-.f64 1 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(+.f64 (log.f64 (E.f64)) (neg.f64 (cos.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (-.f64 1 (pow.f64 (cos.f64 x) 3)))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)
(pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 3) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) 3)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))
(fma.f64 1 (neg.f64 (cos.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (cos.f64 x))) 2) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 -1 (cos.f64 x) 1)
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)
(fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)

simplify71.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
908×unswap-sqr
854×associate-*r*
804×fma-neg
764×associate-*l*
700×fma-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01852109
13731995
210181941
346161913
Stop Event
1×node limit
Counts
65 → 83
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/720 (pow.f64 x 2)) 1/24))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (+.f64 1/720 (*.f64 -1/40320 (pow.f64 x 2)))) 1/24))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 0 (-.f64 1 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(+.f64 (log.f64 (E.f64)) (neg.f64 (cos.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (-.f64 1 (pow.f64 (cos.f64 x) 3)))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)
(pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 3) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) 3)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))
(fma.f64 1 (neg.f64 (cos.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (cos.f64 x))) 2) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 -1 (cos.f64 x) 1)
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)
(fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 -1/24 (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) -1/24)))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) -1/24 1/2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/720 (pow.f64 x 2)) 1/24))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (fma.f64 1/720 (pow.f64 x 2) -1/24))))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 1/720 -1/24) 1/2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (+.f64 1/720 (*.f64 -1/40320 (pow.f64 x 2)))) 1/24))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (+.f64 1/720 (*.f64 (pow.f64 x 2) -1/40320)) -1/24))))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) -1/40320 1/720) -1/24) 1/2))
(fma.f64 1/2 (pow.f64 x 2) (*.f64 (fma.f64 (pow.f64 x 2) 1/720 (fma.f64 -1/40320 (pow.f64 x 4) -1/24)) (pow.f64 x 4)))
(+.f64 1 (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 0 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(+.f64 (log.f64 (E.f64)) (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) (log.f64 (E.f64)))
(-.f64 1 (cos.f64 x))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (-.f64 1 (pow.f64 (cos.f64 x) 3)))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (pow.f64 (-.f64 1 (cos.f64 x)) 2))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (-.f64 1 (cos.f64 x)) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(-.f64 1 (cos.f64 x))
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(-.f64 1 (cos.f64 x))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(-.f64 1 (cos.f64 x))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(-.f64 1 (cos.f64 x))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 3) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) 3)))
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))
(-.f64 1 (cos.f64 x))
(exp.f64 (*.f64 (*.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))
(-.f64 1 (cos.f64 x))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))
(-.f64 1 (cos.f64 x))
(fma.f64 1 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (cos.f64 x))) 2) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 -1 (cos.f64 x) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))

eval25.0ms (0.5%)

Compiler

Compiled 1010 to 673 computations (33.4% saved)

prune11.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New81283
Fresh000
Picked011
Done000
Total81384
Accuracy
100.0%
Counts
84 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓56.8%
(-.f64 1 (cos.f64 x))
▶100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶99.5%
(*.f64 1/2 (pow.f64 x 2))
Compiler

Compiled 19 to 15 computations (21.1% saved)

localize108.0ms (2%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓100.0%
(tan.f64 (/.f64 x 2))
✓100.0%
(*.f64 1/2 (pow.f64 x 2))
Compiler

Compiled 31 to 21 computations (32.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 67.0ms
Operation ival-pow, time spent: 49.0ms, 73.0% of total-time
Operation ival-tan, time spent: 5.0ms, 7.0% of total-time
Operation ival-div, time spent: 5.0ms, 7.0% of total-time
Operation ival-mult, time spent: 4.0ms, 6.0% of total-time
Operation ival-sin, time spent: 3.0ms, 4.0% of total-time
Operation const, time spent: 2.0ms, 3.0% of total-time

series4.0ms (0.1%)

Counts
2 → 12
Calls
Call 1
Inputs
#<alt (*.f64 1/2 (pow.f64 x 2))>
#<alt (tan.f64 (/.f64 x 2))>
Outputs
#<alt (*.f64 1/2 x)>
#<alt (*.f64 x (+.f64 1/2 (*.f64 1/24 (pow.f64 x 2))))>
#<alt (*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 1/240 (pow.f64 x 2))))))>
#<alt (*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 17/40320 (pow.f64 x 2))))))))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
#<alt (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))>
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(tan (/ x 2))
1.0ms
x
@inf
(tan (/ x 2))
1.0ms
x
@-inf
(tan (/ x 2))
1.0ms
x
@0
(* 1/2 (pow x 2))
0.0ms
x
@inf
(* 1/2 (pow x 2))

rewrite73.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
852×unpow-prod-down
526×log-prod
520×cbrt-prod
456×log1p-expm1-u
456×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01230
111830
2134130
Stop Event
1×node limit
Counts
2 → 63
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(tan.f64 (/.f64 x 2))
Outputs
(+.f64 (*.f64 (pow.f64 x 2) 1/4) (*.f64 (pow.f64 x 2) 1/4))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) 1)
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))) (sqrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2)))) 3))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 1/8)) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))
(+.f64 0 (tan.f64 (*.f64 1/2 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(*.f64 (tan.f64 (*.f64 1/2 x)) 1)
(*.f64 (tan.f64 (*.f64 1/2 x)) (log.f64 (E.f64)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(*.f64 1 (tan.f64 (*.f64 1/2 x)))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 1/2 x)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3)) 1/3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) 1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 1/2 x))))
(pow.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(neg.f64 (tan.f64 (/.f64 x -2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 1/2 x)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))) 2))

simplify106.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1784×prod-exp
628×fma-define
566×associate-+l+
548×fma-neg
528×associate-+r+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01921967
13531911
28471893
324551893
443801893
572151893
Stop Event
1×node limit
Counts
75 → 86
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 x (+.f64 1/2 (*.f64 1/24 (pow.f64 x 2))))
(*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 1/240 (pow.f64 x 2))))))
(*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 17/40320 (pow.f64 x 2))))))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(+.f64 (*.f64 (pow.f64 x 2) 1/4) (*.f64 (pow.f64 x 2) 1/4))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) 1)
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))) (sqrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2)))) 3))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 1/8)) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))
(+.f64 0 (tan.f64 (*.f64 1/2 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(*.f64 (tan.f64 (*.f64 1/2 x)) 1)
(*.f64 (tan.f64 (*.f64 1/2 x)) (log.f64 (E.f64)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(*.f64 1 (tan.f64 (*.f64 1/2 x)))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 1/2 x)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3)) 1/3))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) 1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 1/2 x))))
(pow.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(neg.f64 (tan.f64 (/.f64 x -2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 1/2 x)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))) 2))
Outputs
(*.f64 1/2 x)
(*.f64 x (+.f64 1/2 (*.f64 1/24 (pow.f64 x 2))))
(*.f64 x (fma.f64 1/24 (pow.f64 x 2) 1/2))
(*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 1/240 (pow.f64 x 2))))))
(*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 (pow.f64 x 2) 1/240)))))
(*.f64 x (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 1/240 1/24) 1/2))
(*.f64 x (fma.f64 1/24 (pow.f64 x 2) (fma.f64 1/240 (pow.f64 x 4) 1/2)))
(*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 17/40320 (pow.f64 x 2))))))))
(*.f64 x (+.f64 1/2 (*.f64 (pow.f64 x 2) (+.f64 1/24 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 (pow.f64 x 2) 17/40320)))))))
(*.f64 x (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 17/40320 1/240) 1/24) 1/2))
(*.f64 x (fma.f64 1/24 (pow.f64 x 2) (fma.f64 (fma.f64 (pow.f64 x 2) 17/40320 1/240) (pow.f64 x 4) 1/2)))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 (fma.f64 (pow.f64 x 2) 17/40320 1/240) (pow.f64 x 5))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(+.f64 (*.f64 (pow.f64 x 2) 1/4) (*.f64 (pow.f64 x 2) 1/4))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 2)))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) 1)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))) 3)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(cbrt.f64 (*.f64 1/8 (pow.f64 x 6)))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (E.f64) (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))) (sqrt.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2)))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(cbrt.f64 (*.f64 1/8 (pow.f64 x 6)))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2)))) 3))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 1/8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(cbrt.f64 (*.f64 1/8 (pow.f64 x 6)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 0 (tan.f64 (*.f64 1/2 x)))
(tan.f64 (*.f64 1/2 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 1/2 x)) 1)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 1/2 x)) (log.f64 (E.f64)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(*.f64 1 (tan.f64 (*.f64 1/2 x)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 1 1/3) (tan.f64 (*.f64 1/2 x)))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3)) 1/3))
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 8)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))))
(tan.f64 (*.f64 1/2 x))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 8)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) (cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 5/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(tan.f64 (/.f64 (-.f64 (+.f64 x 1) 1) 2))
(tan.f64 (/.f64 (+.f64 x 0) 2))
(tan.f64 (/.f64 x 2))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) 1/2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))) -1)
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))) (sqrt.f64 (log.f64 (tan.f64 (*.f64 1/2 x)))))
(neg.f64 (tan.f64 (/.f64 x -2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 3))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (tan.f64 (*.f64 1/2 x)))) 1/3))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))) 2))
(tan.f64 (*.f64 1/2 x))

eval41.0ms (0.7%)

Compiler

Compiled 1082 to 817 computations (24.5% saved)

prune14.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New85186
Fresh000
Picked022
Done011
Total85489
Accuracy
100.0%
Counts
89 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓56.8%
(-.f64 1 (cos.f64 x))
▶99.5%
(*.f64 (sin.f64 x) (*.f64 1/2 x))
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓99.5%
(*.f64 1/2 (pow.f64 x 2))
Compiler

Compiled 26 to 20 computations (23.1% saved)

localize34.0ms (0.6%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓100.0%
(*.f64 (sin.f64 x) (*.f64 1/2 x))
Compiler

Compiled 15 to 9 computations (40% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
Operation ival-mult, time spent: 5.0ms, 48.0% of total-time
Operation ival-sin, time spent: 4.0ms, 38.0% of total-time
Operation const, time spent: 1.0ms, 10.0% of total-time

series3.0ms (0.1%)

Counts
1 → 12
Calls
Call 1
Inputs
#<alt (*.f64 (sin.f64 x) (*.f64 1/2 x))>
Outputs
#<alt (*.f64 1/2 (pow.f64 x 2))>
#<alt (*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 -1/12 (pow.f64 x 2))))>
#<alt (*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/240 (pow.f64 x 2)) 1/12))))>
#<alt (*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 -1/10080 (pow.f64 x 2)))) 1/12))))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
#<alt (*.f64 1/2 (*.f64 x (sin.f64 x)))>
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(* (sin x) (* 1/2 x))
1.0ms
x
@-inf
(* (sin x) (* 1/2 x))
1.0ms
x
@0
(* (sin x) (* 1/2 x))

rewrite67.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
810×unpow-prod-down
472×log-prod
468×cbrt-prod
370×log1p-expm1-u
370×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
18723
2101623
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (*.f64 1/2 x))
Outputs
(+.f64 0 (*.f64 x (*.f64 (sin.f64 x) 1/2)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) x))) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(-.f64 (+.f64 1 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 1)
(pow.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 3)
(pow.f64 (*.f64 1/4 (pow.f64 (*.f64 x (sin.f64 x)) 2)) 1/2)
(pow.f64 (*.f64 1/8 (pow.f64 (*.f64 x (sin.f64 x)) 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))) (sqrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))))
(sqrt.f64 (*.f64 1/4 (pow.f64 (*.f64 x (sin.f64 x)) 2)))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))
(cbrt.f64 (*.f64 1/8 (pow.f64 (*.f64 x (sin.f64 x)) 3)))
(expm1.f64 (log1p.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(exp.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 2))

simplify105.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1268×distribute-lft-in
1218×distribute-rgt-in
896×associate-*r*
634×distribute-lft-out
594×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0941011
1188995
2429995
31064995
42478995
55143995
67405995
Stop Event
1×node limit
Counts
33 → 42
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 -1/12 (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/240 (pow.f64 x 2)) 1/12))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 -1/10080 (pow.f64 x 2)))) 1/12))))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(+.f64 0 (*.f64 x (*.f64 (sin.f64 x) 1/2)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) x))) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(-.f64 (+.f64 1 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 1)
(pow.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 3)
(pow.f64 (*.f64 1/4 (pow.f64 (*.f64 x (sin.f64 x)) 2)) 1/2)
(pow.f64 (*.f64 1/8 (pow.f64 (*.f64 x (sin.f64 x)) 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))) (sqrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))))
(sqrt.f64 (*.f64 1/4 (pow.f64 (*.f64 x (sin.f64 x)) 2)))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))
(cbrt.f64 (*.f64 1/8 (pow.f64 (*.f64 x (sin.f64 x)) 3)))
(expm1.f64 (log1p.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(exp.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 2))
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 -1/12 (pow.f64 x 2))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) -1/12)))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) -1/12 1/2))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 1/240 (pow.f64 x 2)) 1/12))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (fma.f64 1/240 (pow.f64 x 2) -1/12))))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 1/240 -1/12) 1/2))
(*.f64 (pow.f64 x 2) (fma.f64 1/240 (pow.f64 x 4) (fma.f64 (pow.f64 x 2) -1/12 1/2)))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (-.f64 (*.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 -1/10080 (pow.f64 x 2)))) 1/12))))
(*.f64 (pow.f64 x 2) (+.f64 1/2 (*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (+.f64 1/240 (*.f64 (pow.f64 x 2) -1/10080)) -1/12))))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) -1/10080 1/240) -1/12) 1/2))
(*.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 1/240 (fma.f64 -1/10080 (pow.f64 x 4) -1/12)) 1/2))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(+.f64 0 (*.f64 x (*.f64 (sin.f64 x) 1/2)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) x))) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) x))) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (sin.f64 x))) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (sin.f64 x))) x))))
(-.f64 (+.f64 1 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 1)
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)) 1)
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 3)
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (*.f64 1/4 (pow.f64 (*.f64 x (sin.f64 x)) 2)) 1/2)
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (*.f64 1/8 (pow.f64 (*.f64 x (sin.f64 x)) 3)) 1/3)
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))) 2)
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (E.f64) (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 1/2 (*.f64 x (sin.f64 x))))) 2)) (cbrt.f64 (log.f64 (*.f64 1/2 (*.f64 x (sin.f64 x))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sin.f64 x) (*.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (*.f64 (sin.f64 x) (*.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))) (sqrt.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 1/2 (*.f64 x (sin.f64 x)))))) (sqrt.f64 (log.f64 (*.f64 1/2 (*.f64 x (sin.f64 x))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sin.f64 x) (*.f64 1/2 x))))) (sqrt.f64 (log.f64 (*.f64 (sin.f64 x) (*.f64 1/2 x)))))
(sqrt.f64 (*.f64 1/4 (pow.f64 (*.f64 x (sin.f64 x)) 2)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (sin.f64 x)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(cbrt.f64 (*.f64 1/8 (pow.f64 (*.f64 x (sin.f64 x)) 3)))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(exp.f64 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2))))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 3))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 1/3))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (*.f64 (sin.f64 x) 1/2)))) 2))
(*.f64 1/2 (*.f64 x (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))

eval13.0ms (0.2%)

Compiler

Compiled 537 to 354 computations (34.1% saved)

prune7.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New42042
Fresh000
Picked011
Done033
Total42446
Accuracy
100.0%
Counts
46 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓56.8%
(-.f64 1 (cos.f64 x))
✓99.5%
(*.f64 (sin.f64 x) (*.f64 1/2 x))
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓99.5%
(*.f64 1/2 (pow.f64 x 2))
Compiler

Compiled 49 to 36 computations (26.5% saved)

regimes7.0ms (0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Calls

3 calls:

3.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 1 (cos.f64 x))
100.0%1(cos.f64 x)
Compiler

Compiled 10 to 7 computations (30% saved)

regimes12.0ms (0.2%)

Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
Outputs
(*.f64 (sin.f64 x) (*.f64 1/2 x))
Calls

3 calls:

6.0ms
(cos.f64 x)
3.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(-.f64 1 (cos.f64 x))
99.5%1(cos.f64 x)
Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
(*.f64 1/2 (pow.f64 x 2))
Outputs
(*.f64 1/2 (pow.f64 x 2))
Calls

3 calls:

3.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(-.f64 1 (cos.f64 x))
99.5%1(cos.f64 x)
Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(-.f64 1 (cos.f64 x))
Calls

3 calls:

3.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
56.8%1x
56.8%1(-.f64 1 (cos.f64 x))
56.8%1(cos.f64 x)
Compiler

Compiled 10 to 7 computations (30% saved)

simplify13.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
10×*-commutative
4×sub-neg
4×+-commutative
3×1-exp
2×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01980
13080
23480
33680
43780
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (pow.f64 x 2))
(-.f64 1 (cos.f64 x))
Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 (sin.f64 x) (*.f64 x 1/2))
(*.f64 1/2 (pow.f64 x 2))
(-.f64 1 (cos.f64 x))
Compiler

Compiled 26 to 20 computations (23.1% saved)

soundness201.0ms (3.7%)

Rules
908×unswap-sqr
854×associate-*r*
804×fma-neg
764×associate-*l*
700×fma-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
18214
295414
01852109
13731995
210181941
346161913
Stop Event
1×node limit
1×node limit
Compiler

Compiled 131 to 76 computations (42% saved)

end0.0ms (0%)

preprocess52.0ms (0.9%)

Remove

(abs x)

Compiler

Compiled 158 to 114 computations (27.8% saved)

Profiling

Loading profile data...