Hyperbolic secant

Time bar (total: 3.1s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%100%0%0%0%0%0%2
Compiler

Compiled 10 to 8 computations (20% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
Operation ival-div, time spent: 0.0ms, 0.0% of total-time
Operation ival-add, time spent: 0.0ms, 0.0% of total-time
Operation ival-exp, time spent: 0.0ms, 0.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.5s (50.1%)

Results
1.5s8255×0valid
0.0ms1×0valid
Precisions
Click to see histograms. Total time spent on operations: 660.0ms
Operation ival-add, time spent: 319.0ms, 48.0% of total-time
Operation ival-exp, time spent: 206.0ms, 31.0% of total-time
Operation ival-div, time spent: 77.0ms, 12.0% of total-time
Operation ival-neg, time spent: 39.0ms, 6.0% of total-time
Operation const, time spent: 20.0ms, 3.0% of total-time
Bogosity

preprocess237.0ms (7.8%)

Algorithm
1×egg-herbie
Rules
1900×fma-def
826×fabs-mul
624×swap-sqr
592×*-commutative
446×fabs-div
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-x
01(229.202595783928)0-(exp.f64 (neg.f64 x))
00-0-(neg.f64 x)
00-0-(exp.f64 x)
00-0-(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
00-0-(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
00-0-2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017124
133124
259124
392124
4166124
5331124
6850124
72446124
83669124
94774124
106716124
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Symmetry

(abs x)

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
Operation ival-exp, time spent: 32.0ms, 62.0% of total-time
Operation ival-add, time spent: 11.0ms, 21.0% of total-time
Operation ival-div, time spent: 4.0ms, 8.0% of total-time
Operation const, time spent: 2.0ms, 4.0% of total-time
Operation ival-neg, time spent: 2.0ms, 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
▶100.0%
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

localize52.0ms (1.7%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓100.0%
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓100.0%
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 25 to 9 computations (64% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
Operation ival-exp, time spent: 8.0ms, 37.0% of total-time
Operation ival-neg, time spent: 6.0ms, 28.0% of total-time
Operation ival-add, time spent: 5.0ms, 23.0% of total-time
Operation ival-div, time spent: 2.0ms, 9.0% of total-time
Operation const, time spent: 1.0ms, 5.0% of total-time

series3.0ms (0.1%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
x
@inf
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
x
@0
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms
x
@0
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms
x
@-inf
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite192.0ms (6.3%)

Algorithm
1×batch-egg-rewrite
Rules
94×associate-*r*
62×add-exp-log
62×add-log-exp
62×log1p-expm1-u
62×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01240
114440
2232940
Stop Event
1×unsound
Counts
2 → 20
Calls
Call 1
Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Outputs
-4
-2
-1
0
1/2
1
3/2
2
3
4
-4
-2
-1
0
1/2
1
3/2
2
3
4

simplify104.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
1614×distribute-lft-out
788×fma-def
710×fma-neg
618×*-commutative
580×associate-/l/
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
046462
196457
2201451
3541447
42008447
53744447
65209447
77885447
Stop Event
1×node limit
Counts
36 → 37
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
-4
-2
-1
0
1/2
1
3/2
2
3
4
-4
-2
-1
0
1/2
1
3/2
2
3
4
Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (*.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) 1)))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -61/720 (pow.f64 x 6) (fma.f64 5/24 (pow.f64 x 4) 1)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2
(+.f64 2 (pow.f64 x 2))
(fma.f64 x x 2)
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2)))
(+.f64 2 (fma.f64 1/12 (pow.f64 x 4) (pow.f64 x 2)))
(+.f64 2 (fma.f64 (pow.f64 x 4) 1/12 (pow.f64 x 2)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 2))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 x x 2))
(+.f64 2 (+.f64 (*.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))))
(+.f64 2 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (pow.f64 x 2))))
(+.f64 2 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (pow.f64 x 2))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 2)))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 x x 2)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
-4
-2
-1
0
1/2
1
3/2
2
3
4
-4
-2
-1
0
1/2
1
3/2
2
3
4

eval9.0ms (0.3%)

Compiler

Compiled 355 to 283 computations (20.3% saved)

prune10.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New32537
Fresh000
Picked011
Done000
Total32638
Accuracy
100.0%
Counts
38 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶77.3%
(/.f64 2 (fma.f64 x x 2))
✓100.0%
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶52.9%
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
▶53.3%
1
▶11.4%
1/2
▶48.5%
0
Compiler

Compiled 51 to 43 computations (15.7% saved)

localize84.0ms (2.7%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓100.0%
(*.f64 -1/2 (pow.f64 x 2))
✓99.2%
(/.f64 2 (fma.f64 x x 2))
Compiler

Compiled 36 to 27 computations (25% saved)

Precisions
Click to see histograms. Total time spent on operations: 45.0ms
Operation ival-mult, time spent: 11.0ms, 25.0% of total-time
Operation ival-div, time spent: 11.0ms, 25.0% of total-time
Operation ival-pow, time spent: 8.0ms, 18.0% of total-time
Operation ival-fma, time spent: 7.0ms, 16.0% of total-time
Operation ival-add, time spent: 5.0ms, 11.0% of total-time
Operation const, time spent: 3.0ms, 7.0% of total-time

series2.0ms (0.1%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 -1/2 (pow.f64 x 2))
0.0ms
x
@inf
(/.f64 2 (fma.f64 x x 2))
0.0ms
x
@-inf
(/.f64 2 (fma.f64 x x 2))
0.0ms
x
@inf
(*.f64 -1/2 (pow.f64 x 2))
0.0ms
x
@0
(/.f64 2 (fma.f64 x x 2))

rewrite80.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
682×unpow-prod-down
512×log-prod
508×cbrt-prod
462×log1p-expm1-u
462×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01237
111837
2134137
Stop Event
1×node limit
Counts
2 → 69
Calls
Call 1
Inputs
(/.f64 2 (fma.f64 x x 2))
(*.f64 -1/2 (pow.f64 x 2))
Outputs
(+.f64 0 (/.f64 2 (fma.f64 x x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(-.f64 (+.f64 1 (/.f64 2 (fma.f64 x x 2))) 1)
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(*.f64 (/.f64 2 (fma.f64 x x 2)) (log.f64 (E.f64)))
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 -2 (/.f64 1 (neg.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(*.f64 (/.f64 1 (fma.f64 x x 2)) (log.f64 (exp.f64 2)))
(*.f64 (pow.f64 1 1/3) (/.f64 2 (fma.f64 x x 2)))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3)) 1/3))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 2) 1/3) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x 2) 1/2)) 2) -1) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (exp.f64 (log.f64 2)) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 2)) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(pow.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 1/2)
(pow.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(pow.f64 (E.f64) (log.f64 (/.f64 2 (fma.f64 x x 2))))
(pow.f64 (/.f64 (*.f64 (fma.f64 x x 2) 1/2) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))) (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))))
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(cbrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 2 (fma.f64 x x 2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x 2) 1/2)) -1))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (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) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(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))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))

simplify102.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
756×times-frac
690×fma-def
656×associate-*r*
578×associate-*l*
536×log-prod
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02182689
14862562
211642497
342572435
Stop Event
1×node limit
Counts
81 → 113
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/4 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 4)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 4))) (*.f64 16 (/.f64 1 (pow.f64 x 8)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 4))) (*.f64 16 (/.f64 1 (pow.f64 x 8)))))
(+.f64 0 (/.f64 2 (fma.f64 x x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(-.f64 (+.f64 1 (/.f64 2 (fma.f64 x x 2))) 1)
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(*.f64 (/.f64 2 (fma.f64 x x 2)) (log.f64 (E.f64)))
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 -2 (/.f64 1 (neg.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(*.f64 (/.f64 1 (fma.f64 x x 2)) (log.f64 (exp.f64 2)))
(*.f64 (pow.f64 1 1/3) (/.f64 2 (fma.f64 x x 2)))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3)) 1/3))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 2) 1/3) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x 2) 1/2)) 2) -1) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (exp.f64 (log.f64 2)) (/.f64 1 (fma.f64 x x 2)))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 2)) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(pow.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 1/2)
(pow.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(pow.f64 (E.f64) (log.f64 (/.f64 2 (fma.f64 x x 2))))
(pow.f64 (/.f64 (*.f64 (fma.f64 x x 2) 1/2) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))) (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))))
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(cbrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 2 (fma.f64 x x 2)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x 2) 1/2)) -1))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (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) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(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))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))
Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 1/4 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (*.f64 1/4 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (*.f64 1/4 (pow.f64 x 4)))
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 1/4 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 -1/8 (pow.f64 x 6) (*.f64 1/4 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (pow.f64 x 2) 1) (fma.f64 1/4 (pow.f64 x 4) (*.f64 -1/8 (pow.f64 x 6))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 1/4 (pow.f64 x 4) (*.f64 -1/8 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/8 (pow.f64 x 6) (*.f64 -1/2 (pow.f64 x 2))) (fma.f64 1/4 (pow.f64 x 4) 1))
(/.f64 2 (pow.f64 x 2))
(-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4)))
(+.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 -4 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 4))) (*.f64 16 (/.f64 1 (pow.f64 x 8)))))
(-.f64 (+.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 8 (pow.f64 x 6))) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (-.f64 (/.f64 8 (pow.f64 x 6)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -16 (pow.f64 x 8))) (/.f64 -4 (pow.f64 x 4))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4)))
(+.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 -4 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 6))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 4))) (*.f64 16 (/.f64 1 (pow.f64 x 8)))))
(-.f64 (+.f64 (/.f64 2 (pow.f64 x 2)) (/.f64 8 (pow.f64 x 6))) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (-.f64 (/.f64 8 (pow.f64 x 6)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 2 (pow.f64 x 2)) (+.f64 (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -16 (pow.f64 x 8))) (/.f64 -4 (pow.f64 x 4))))
(+.f64 0 (/.f64 2 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))
(/.f64 2 (fma.f64 x x 2))
(-.f64 (+.f64 1 (/.f64 2 (fma.f64 x x 2))) 1)
(/.f64 2 (fma.f64 x x 2))
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 2 (fma.f64 x x 2)) (log.f64 (E.f64)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 -2 (/.f64 1 (neg.f64 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 1 (fma.f64 x x 2)) (log.f64 (exp.f64 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 1 1/3) (/.f64 2 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (/.f64 1 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3)) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3/2)) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3/2)))
(pow.f64 (pow.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3/2) 1/6) 4)
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 2) 1/3) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (*.f64 8 (pow.f64 (fma.f64 x x 2) -2))) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4) 2)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 8)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -1/2)))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (/.f64 1 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x 2) 1/2)) 2) -1) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x 2) 1/2)) 2)))
(/.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 2) 1/2 1)) 2))
(*.f64 (exp.f64 (log.f64 2)) (/.f64 1 (fma.f64 x x 2)))
(/.f64 2 (fma.f64 x x 2))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3/2)) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3/2)))
(pow.f64 (pow.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3/2) 1/6) 4)
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 2)) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (*.f64 8 (pow.f64 (fma.f64 x x 2) -2))) (cbrt.f64 (/.f64 1 (fma.f64 x x 2))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 x x 2)) (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 4) 2)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 8)) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 5/2)) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -1/2)))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)) 1/2)
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -2))
(fabs.f64 (/.f64 2 (fma.f64 x x 2)))
(pow.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3) 1/3)
(cbrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3))
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (E.f64) (log.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (/.f64 (*.f64 (fma.f64 x x 2) 1/2) 1) -1)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 1/2)))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))) (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 x x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 1/2))))) (sqrt.f64 (neg.f64 (log1p.f64 (*.f64 (pow.f64 x 2) 1/2)))))
(sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x 2) -2)))
(sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -2))
(fabs.f64 (/.f64 2 (fma.f64 x x 2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(cbrt.f64 (pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -3))
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 2) 1/2 1) -3))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2)))) 3))
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 2 (fma.f64 x x 2)))) 1/3))
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2)))) 2))
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x 2) 1/2)) -1))
(/.f64 2 (fma.f64 x x 2))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))
(/.f64 2 (fma.f64 x x 2))
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 x 2)))))
(*.f64 -1/2 (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 -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) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 -1/2) (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))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(*.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 -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))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))
(*.f64 -1/2 (pow.f64 x 2))

eval60.0ms (2%)

Compiler

Compiled 1502 to 1232 computations (18% saved)

prune17.0ms (0.6%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New1121113
Fresh000
Picked055
Done011
Total1127119
Accuracy
100.0%
Counts
119 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓77.3%
(/.f64 2 (fma.f64 x x 2))
▶27.5%
(/.f64 2 (pow.f64 x 2))
✓100.0%
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓52.9%
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓53.3%
1
✓11.4%
1/2
✓48.5%
0
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize49.0ms (1.6%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓99.1%
(/.f64 2 (pow.f64 x 2))
Compiler

Compiled 12 to 9 computations (25% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
Operation ival-pow, time spent: 6.0ms, 63.0% of total-time
Operation ival-div, time spent: 2.0ms, 21.0% of total-time
Operation const, time spent: 1.0ms, 11.0% of total-time

series1.0ms (0%)

Counts
1 → 0
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 2 (pow.f64 x 2))
0.0ms
x
@inf
(/.f64 2 (pow.f64 x 2))
0.0ms
x
@-inf
(/.f64 2 (pow.f64 x 2))

rewrite67.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
1322×frac-times
398×unpow-prod-down
300×log-prod
298×cbrt-prod
277×log1p-expm1-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
17516
284116
Stop Event
1×node limit
Counts
1 → 51
Calls
Call 1
Inputs
(/.f64 2 (pow.f64 x 2))
Outputs
(+.f64 0 (*.f64 2 (pow.f64 x -2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x -2))) 1)
(*.f64 2 (pow.f64 x -2))
(*.f64 (*.f64 2 (pow.f64 x -2)) 1)
(*.f64 (*.f64 2 (pow.f64 x -2)) (log.f64 (E.f64)))
(*.f64 1 (*.f64 2 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))
(*.f64 (cbrt.f64 (*.f64 4 (pow.f64 x -4))) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(*.f64 -2 (pow.f64 x -2))
(*.f64 (pow.f64 x -2) 2)
(*.f64 (pow.f64 x -2) (log.f64 (exp.f64 2)))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 2 (pow.f64 x 4))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) x)) (sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 3)))
(*.f64 (pow.f64 1 1/3) (*.f64 2 (pow.f64 x -2)))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (pow.f64 x -2))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) 2) 1/3) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4)))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2) 1/3) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x -2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 4) 4)) -1) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 (exp.f64 (log.f64 2)) (pow.f64 x -2))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) 2)) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 3)) (sqrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 2 (pow.f64 x -2)) 2)) (/.f64 1 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 5)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(pow.f64 (*.f64 2 (pow.f64 x -2)) 1)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 3)
(pow.f64 (*.f64 4 (pow.f64 x -4)) 1/2)
(pow.f64 (/.f64 8 (pow.f64 x 6)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(pow.f64 (*.f64 (pow.f64 x 2) 1/2) -1)
(pow.f64 (E.f64) (log.f64 (*.f64 2 (pow.f64 x -2))))
(pow.f64 (/.f64 (*.f64 (pow.f64 x 2) 1/2) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))))
(sqrt.f64 (*.f64 4 (pow.f64 x -4)))
(fabs.f64 (*.f64 2 (pow.f64 x -2)))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))
(cbrt.f64 (/.f64 8 (pow.f64 x 6)))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x -2))))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 8 (pow.f64 x 6))) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) x)) 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 2) 1/2)) -1))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x -2))))

simplify53.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1468×times-frac
1188×fma-def
732×associate-*r/
694×distribute-lft-in
674×unswap-sqr
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01431337
13051292
26901282
322321282
Stop Event
1×node limit
Counts
51 → 63
Calls
Call 1
Inputs
(+.f64 0 (*.f64 2 (pow.f64 x -2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x -2))) 1)
(*.f64 2 (pow.f64 x -2))
(*.f64 (*.f64 2 (pow.f64 x -2)) 1)
(*.f64 (*.f64 2 (pow.f64 x -2)) (log.f64 (E.f64)))
(*.f64 1 (*.f64 2 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))
(*.f64 (cbrt.f64 (*.f64 4 (pow.f64 x -4))) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(*.f64 -2 (pow.f64 x -2))
(*.f64 (pow.f64 x -2) 2)
(*.f64 (pow.f64 x -2) (log.f64 (exp.f64 2)))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 2 (pow.f64 x 4))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) x)) (sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 3)))
(*.f64 (pow.f64 1 1/3) (*.f64 2 (pow.f64 x -2)))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (pow.f64 x -2))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) 2) 1/3) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4)))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2) 1/3) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x -2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 4) 4)) -1) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 (exp.f64 (log.f64 2)) (pow.f64 x -2))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) 2)) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 3)) (sqrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 2 (pow.f64 x -2)) 2)) (/.f64 1 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 5)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(pow.f64 (*.f64 2 (pow.f64 x -2)) 1)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 3)
(pow.f64 (*.f64 4 (pow.f64 x -4)) 1/2)
(pow.f64 (/.f64 8 (pow.f64 x 6)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(pow.f64 (*.f64 (pow.f64 x 2) 1/2) -1)
(pow.f64 (E.f64) (log.f64 (*.f64 2 (pow.f64 x -2))))
(pow.f64 (/.f64 (*.f64 (pow.f64 x 2) 1/2) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))))
(sqrt.f64 (*.f64 4 (pow.f64 x -4)))
(fabs.f64 (*.f64 2 (pow.f64 x -2)))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))
(cbrt.f64 (/.f64 8 (pow.f64 x 6)))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x -2))))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 8 (pow.f64 x 6))) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) x)) 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 2) 1/2)) -1))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x -2))))
Outputs
(+.f64 0 (*.f64 2 (pow.f64 x -2)))
(*.f64 2 (pow.f64 x -2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))) 3)
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))
(*.f64 2 (pow.f64 x -2))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x -2))) 1)
(*.f64 2 (pow.f64 x -2))
(*.f64 2 (pow.f64 x -2))
(*.f64 (*.f64 2 (pow.f64 x -2)) 1)
(*.f64 2 (pow.f64 x -2))
(*.f64 (*.f64 2 (pow.f64 x -2)) (log.f64 (E.f64)))
(*.f64 2 (pow.f64 x -2))
(*.f64 1 (*.f64 2 (pow.f64 x -2)))
(*.f64 2 (pow.f64 x -2))
(*.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))
(*.f64 (cbrt.f64 (*.f64 4 (pow.f64 x -4))) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(*.f64 2 (pow.f64 x -2))
(*.f64 -2 (pow.f64 x -2))
(*.f64 (pow.f64 x -2) 2)
(*.f64 2 (pow.f64 x -2))
(*.f64 (pow.f64 x -2) (log.f64 (exp.f64 2)))
(*.f64 2 (pow.f64 x -2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 2 (pow.f64 x 4))))
(*.f64 2 (pow.f64 x -2))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) x)) (sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 3)))
(*.f64 2 (pow.f64 x -2))
(*.f64 (pow.f64 1 1/3) (*.f64 2 (pow.f64 x -2)))
(*.f64 2 (pow.f64 x -2))
(*.f64 (pow.f64 (cbrt.f64 2) 3) (pow.f64 x -2))
(*.f64 2 (pow.f64 x -2))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) 2) 1/3) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 4 (pow.f64 x -4)))) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 x -4) 8)) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4)))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (cbrt.f64 (*.f64 4 (*.f64 (pow.f64 x -4) (cbrt.f64 (*.f64 4 (pow.f64 x -4)))))) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2) 1/3) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x -2))
(*.f64 2 (pow.f64 x -2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 4) 4)) -1) (cbrt.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 (/.f64 (pow.f64 x 4) 4))))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) (cbrt.f64 (/.f64 (pow.f64 x 4) 4)))
(*.f64 (exp.f64 (log.f64 2)) (pow.f64 x -2))
(*.f64 2 (pow.f64 x -2))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) 2)) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 4 (pow.f64 x -4)))) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 x -4) 8)) (cbrt.f64 (pow.f64 x -2)))
(*.f64 (cbrt.f64 (*.f64 (*.f64 4 (pow.f64 x -4)) (cbrt.f64 (*.f64 4 (pow.f64 x -4))))) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (cbrt.f64 (*.f64 4 (*.f64 (pow.f64 x -4) (cbrt.f64 (*.f64 4 (pow.f64 x -4)))))) (cbrt.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 5/2)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 3)) (sqrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 2 (pow.f64 x -2))
(*.f64 (sqrt.f64 (*.f64 (*.f64 2 (pow.f64 x -2)) 2)) (/.f64 1 x))
(*.f64 2 (pow.f64 x -2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 5)) (cbrt.f64 (/.f64 (sqrt.f64 2) x)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) x)) (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 5)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) x)) (pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 5/2))
(pow.f64 (*.f64 2 (pow.f64 x -2)) 1)
(*.f64 2 (pow.f64 x -2))
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 3)
(*.f64 2 (pow.f64 x -2))
(pow.f64 (*.f64 4 (pow.f64 x -4)) 1/2)
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 8 (pow.f64 x 6)) 1/3)
(cbrt.f64 (/.f64 8 (pow.f64 x 6)))
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(*.f64 2 (pow.f64 x -2))
(pow.f64 (*.f64 (pow.f64 x 2) 1/2) -1)
(*.f64 2 (pow.f64 x -2))
(pow.f64 (E.f64) (log.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 (*.f64 (pow.f64 x 2) 1/2) 1) -1)
(*.f64 2 (pow.f64 x -2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))) 2)) (cbrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 -2 (log.f64 x) (log.f64 2))) 2)) (cbrt.f64 (fma.f64 -2 (log.f64 x) (log.f64 2))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))) (sqrt.f64 (log.f64 (*.f64 2 (pow.f64 x -2)))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 -2 (log.f64 x) (log.f64 2)))) (sqrt.f64 (fma.f64 -2 (log.f64 x) (log.f64 2))))
(sqrt.f64 (*.f64 4 (pow.f64 x -4)))
(*.f64 2 (pow.f64 x -2))
(fabs.f64 (*.f64 2 (pow.f64 x -2)))
(*.f64 2 (pow.f64 x -2))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (/.f64 8 (pow.f64 x 6)))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2)))) 3))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (*.f64 (log.f64 (/.f64 8 (pow.f64 x 6))) 1/3))
(cbrt.f64 (/.f64 8 (pow.f64 x 6)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) x)) 2))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 2) 1/2)) -1))
(*.f64 2 (pow.f64 x -2))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x -2))))
(*.f64 2 (pow.f64 x -2))

eval21.0ms (0.7%)

Compiler

Compiled 690 to 592 computations (14.2% saved)

prune28.0ms (0.9%)

Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New63063
Fresh000
Picked011
Done066
Total63770
Accuracy
100.0%
Counts
70 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓77.3%
(/.f64 2 (fma.f64 x x 2))
✓27.5%
(/.f64 2 (pow.f64 x 2))
✓100.0%
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓52.9%
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓53.3%
1
✓11.4%
1/2
✓48.5%
0
Compiler

Compiled 66 to 54 computations (18.2% saved)

regimes10.0ms (0.3%)

Counts
7 → 1
Calls
Call 1
Inputs
0
1/2
1
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (fma.f64 x x 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Calls

3 calls:

5.0ms
x
2.0ms
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
100.0%1(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes11.0ms (0.4%)

Counts
6 → 2
Calls
Call 1
Inputs
0
1/2
1
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (fma.f64 x x 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
Outputs
(/.f64 2 (fma.f64 x x 2))
0
Calls

1 calls:

11.0ms
x
Results
AccuracySegmentsBranch
99.0%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.3%)

Counts
4 → 2
Calls
Call 1
Inputs
0
1/2
1
(/.f64 2 (pow.f64 x 2))
Outputs
1
0
Calls

1 calls:

7.0ms
x
Results
AccuracySegmentsBranch
98.8%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes9.0ms (0.3%)

Counts
2 → 2
Calls
Call 1
Inputs
0
1/2
Outputs
1/2
0
Calls

1 calls:

9.0ms
x
Results
AccuracySegmentsBranch
56.8%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
0
Outputs
0
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
48.5%1x
Compiler

Compiled 2 to 1 computations (50% saved)

bsearch19.0ms (0.6%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
229.202595783928
3452.0751126965097
Results
17.0ms95×0valid
0.0ms1×0valid
Compiler

Compiled 79 to 64 computations (19% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
Operation ival-exp, time spent: 7.0ms, 68.0% of total-time
Operation ival-add, time spent: 2.0ms, 19.0% of total-time
Operation ival-div, time spent: 1.0ms, 10.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch14.0ms (0.5%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
229.202595783928
3452.0751126965097
Results
12.0ms95×0valid
0.0ms1×0valid
Compiler

Compiled 49 to 46 computations (6.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
Operation ival-exp, time spent: 2.0ms, 40.0% of total-time
Operation ival-add, time spent: 2.0ms, 40.0% of total-time
Operation ival-div, time spent: 1.0ms, 20.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch16.0ms (0.5%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
16.0ms
229.202595783928
3452.0751126965097
Results
14.0ms95×0valid
0.0ms1×0valid
Compiler

Compiled 49 to 46 computations (6.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
Operation ival-exp, time spent: 4.0ms, 56.0% of total-time
Operation ival-add, time spent: 2.0ms, 28.0% of total-time
Operation ival-div, time spent: 1.0ms, 14.0% of total-time
Operation ival-neg, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02894
13694
23894
33994
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 360) (/.f64 2 (fma.f64 x x 2)) 0)
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0
Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 360) (/.f64 2 (fma.f64 x x 2)) 0)
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0
Compiler

Compiled 37 to 30 computations (18.9% saved)

soundness208.0ms (6.8%)

Rules
1614×distribute-lft-out
788×fma-def
710×fma-neg
618×*-commutative
580×associate-/l/
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01240
114440
2232940
01240
114440
2232940
046462
196457
2201451
3541447
42008447
53744447
65209447
77885447
Stop Event
1×node limit
1×unsound
1×unsound
Compiler

Compiled 28 to 22 computations (21.4% saved)

end0.0ms (0%)

preprocess49.0ms (1.6%)

Remove

(abs x)

Compiler

Compiled 138 to 108 computations (21.7% saved)

Profiling

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