Numeric.Integration.TanhSinh:simpson from integration-0.2.1

Time bar (total: 2.4s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 8 to 5 computations (37.5% saved)

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

sample1.0s (42.1%)

Results
875.0ms7237×0valid
90.0ms1018×0infinite
0.0ms1×0valid
Precisions
Click to see histograms. Total time spent on operations: 344.0ms
Operation ival-add, time spent: 259.0ms, 75.0% of total-time
Operation ival-mult, time spent: 72.0ms, 21.0% of total-time
Operation const, time spent: 13.0ms, 4.0% of total-time
Bogosity

preprocess108.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
290×fma-def
80×distribute-lft-neg-in
70×associate-*r*
54×cancel-sign-sub-inv
48×distribute-lft-in
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
10-0-(*.f64 x (+.f64 y y))
00-0-x
00-0-y
00-0-(+.f64 y y)
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
019141
158133
2153133
3382133
4540133
5628133
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
(*.f64 x (+.f64 y y))
(*.f64 (neg.f64 x) (+.f64 y y))
(*.f64 x (+.f64 (neg.f64 y) (neg.f64 y)))
(neg.f64 (*.f64 (neg.f64 x) (+.f64 y y)))
(neg.f64 (*.f64 x (+.f64 (neg.f64 y) (neg.f64 y))))
(*.f64 y (+.f64 x x))
Outputs
(*.f64 x (+.f64 y y))
(*.f64 x (*.f64 2 y))
(*.f64 x (*.f64 y 2))
(*.f64 x (+.f64 y y))
(*.f64 x (*.f64 2 y))
(*.f64 x (*.f64 y 2))
(*.f64 (neg.f64 x) (+.f64 y y))
(*.f64 (*.f64 2 y) (neg.f64 x))
(*.f64 x (*.f64 y -2))
(*.f64 x (+.f64 (neg.f64 y) (neg.f64 y)))
(*.f64 (*.f64 2 y) (neg.f64 x))
(*.f64 x (*.f64 y -2))
(neg.f64 (*.f64 (neg.f64 x) (+.f64 y y)))
(*.f64 x (*.f64 2 y))
(*.f64 x (*.f64 y 2))
(neg.f64 (*.f64 x (+.f64 (neg.f64 y) (neg.f64 y))))
(*.f64 x (*.f64 2 y))
(*.f64 x (*.f64 y 2))
(*.f64 y (+.f64 x x))
(*.f64 x (*.f64 2 y))
(*.f64 x (*.f64 y 2))
Symmetry

(negabs x)

(negabs y)

(sort x y)

Compiler

Compiled 33 to 14 computations (57.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
Operation ival-add, time spent: 11.0ms, 70.0% of total-time
Operation ival-mult, time spent: 4.0ms, 25.0% of total-time
Operation const, time spent: 1.0ms, 6.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(*.f64 x (+.f64 y y))
Compiler

Compiled 7 to 4 computations (42.9% saved)

localize28.0ms (1.2%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓99.6%
(*.f64 x (+.f64 y y))
Compiler

Compiled 13 to 5 computations (61.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
Operation ival-mult, time spent: 4.0ms, 48.0% of total-time
Operation ival-add, time spent: 4.0ms, 48.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time

series3.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 x (+.f64 y y))
1.0ms
y
@0
(*.f64 x (+.f64 y y))
1.0ms
x
@inf
(*.f64 x (+.f64 y y))
1.0ms
y
@inf
(*.f64 x (+.f64 y y))
0.0ms
y
@-inf
(*.f64 x (+.f64 y y))

rewrite177.0ms (7.4%)

Algorithm
1×batch-egg-rewrite
Rules
832×prod-diff
646×unpow-prod-down
418×log-prod
405×log1p-expm1-u
405×expm1-log1p-u
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0919
19816
213907
Stop Event
1×node limit
Counts
1 → 99
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
Outputs
(+.f64 y y)
(+.f64 0 (/.f64 0 0))
(+.f64 (*.f64 x y) (*.f64 x y))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x y)) (*.f64 (/.f64 0 0) (*.f64 x y)))
(+.f64 (*.f64 (/.f64 0 0) y) (*.f64 (/.f64 0 0) y))
(+.f64 (*.f64 (*.f64 x y) 1) (*.f64 (*.f64 x y) 1))
(+.f64 (*.f64 (*.f64 x y) (/.f64 0 0)) (*.f64 (*.f64 x y) (/.f64 0 0)))
(+.f64 (*.f64 y (/.f64 0 0)) (*.f64 y (/.f64 0 0)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 y 2) 0) (/.f64 (pow.f64 y 2) 0))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (fma.f64 y y 0) (*.f64 2 (pow.f64 y 3))))
(/.f64 (*.f64 2 (pow.f64 y 3)) (fma.f64 y y 0))
(/.f64 0 0)
(/.f64 (*.f64 (cbrt.f64 2) y) (cbrt.f64 (fma.f64 y y 0)))
(/.f64 (pow.f64 (*.f64 2 (pow.f64 y 3)) 2) (pow.f64 (fma.f64 y y 0) 2))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 y 3))) (sqrt.f64 (fma.f64 y y 0)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) 0) (*.f64 (fma.f64 y y 0) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 y 3))) (*.f64 0 (fma.f64 y y 0)))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 y 3))) (neg.f64 (fma.f64 y y 0)))
(/.f64 (+.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 (*.f64 x y) 2) (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 x y) 2))))
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 x y) 2)) (-.f64 (*.f64 x y) (*.f64 x y)))
(/.f64 (*.f64 x (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(/.f64 (*.f64 x 0) 0)
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) x) (fma.f64 y y 0))
(/.f64 (*.f64 0 x) 0)
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) (/.f64 0 0)) (fma.f64 y y 0))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) -1)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 7/2)
(pow.f64 (/.f64 0 0) 10/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 7/3)
(pow.f64 (/.f64 0 0) 5/6)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) -3)
(pow.f64 (/.f64 0 0) -2)
(pow.f64 (/.f64 0 0) -1/2)
(pow.f64 (/.f64 0 0) -1/3)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (/.f64 (fma.f64 y y 0) (*.f64 2 (pow.f64 y 3))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(hypot.f64 (sqrt.f64 y) (sqrt.f64 y))
(hypot.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (+.f64 (log.f64 (/.f64 0 0)) (log.f64 (pow.f64 x 3))))
(exp.f64 (+.f64 (log.f64 (pow.f64 x 3)) (log.f64 (/.f64 0 0))))
(exp.f64 (+.f64 (log.f64 (/.f64 0 0)) (*.f64 2 (log.f64 (cbrt.f64 x)))))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x y (*.f64 x y))
(fma.f64 y x (*.f64 x y))
(fma.f64 y (/.f64 0 0) (*.f64 y (/.f64 0 0)))
(fma.f64 y 1 y)
(fma.f64 (/.f64 0 0) y (*.f64 (/.f64 0 0) y))
(fma.f64 (/.f64 0 0) (*.f64 x y) (*.f64 (/.f64 0 0) (*.f64 x y)))
(fma.f64 1 y y)
(fma.f64 1 (*.f64 x y) (*.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) y) (*.f64 x y))
(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) x) (*.f64 x y))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) y) (*.f64 x y))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) y)
(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (*.f64 x y))
(fma.f64 (*.f64 x y) (/.f64 0 0) (*.f64 (*.f64 x y) (/.f64 0 0)))
(fma.f64 (*.f64 x y) 1 (*.f64 (*.f64 x y) 1))
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) (*.f64 x y))
(fma.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)) (*.f64 x y))
(fma.f64 (*.f64 y (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x y))
(fma.f64 (*.f64 y (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x y))
(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (*.f64 x y))
(fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (*.f64 x y))

simplify20.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
80×sqr-pow
36×*-commutative
36×fma-udef
22×associate-/l*
20×unpow2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02184294968659
16264294968659
Stop Event
1×unsound
Counts
123 → 131
Calls
Call 1
Inputs
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(*.f64 2 (*.f64 x y))
(+.f64 y y)
(+.f64 0 (/.f64 0 0))
(+.f64 (*.f64 x y) (*.f64 x y))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x y)) (*.f64 (/.f64 0 0) (*.f64 x y)))
(+.f64 (*.f64 (/.f64 0 0) y) (*.f64 (/.f64 0 0) y))
(+.f64 (*.f64 (*.f64 x y) 1) (*.f64 (*.f64 x y) 1))
(+.f64 (*.f64 (*.f64 x y) (/.f64 0 0)) (*.f64 (*.f64 x y) (/.f64 0 0)))
(+.f64 (*.f64 y (/.f64 0 0)) (*.f64 y (/.f64 0 0)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 y 2) 0) (/.f64 (pow.f64 y 2) 0))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (fma.f64 y y 0) (*.f64 2 (pow.f64 y 3))))
(/.f64 (*.f64 2 (pow.f64 y 3)) (fma.f64 y y 0))
(/.f64 0 0)
(/.f64 (*.f64 (cbrt.f64 2) y) (cbrt.f64 (fma.f64 y y 0)))
(/.f64 (pow.f64 (*.f64 2 (pow.f64 y 3)) 2) (pow.f64 (fma.f64 y y 0) 2))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 y 3))) (sqrt.f64 (fma.f64 y y 0)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) 0) (*.f64 (fma.f64 y y 0) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 y 3))) (*.f64 0 (fma.f64 y y 0)))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 y 3))) (neg.f64 (fma.f64 y y 0)))
(/.f64 (+.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 (*.f64 x y) 2) (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 x y) 2))))
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 x y) 2)) (-.f64 (*.f64 x y) (*.f64 x y)))
(/.f64 (*.f64 x (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(/.f64 (*.f64 x 0) 0)
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) x) (fma.f64 y y 0))
(/.f64 (*.f64 0 x) 0)
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) (/.f64 0 0)) (fma.f64 y y 0))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) -1)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 7/2)
(pow.f64 (/.f64 0 0) 10/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 7/3)
(pow.f64 (/.f64 0 0) 5/6)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) -3)
(pow.f64 (/.f64 0 0) -2)
(pow.f64 (/.f64 0 0) -1/2)
(pow.f64 (/.f64 0 0) -1/3)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (/.f64 (fma.f64 y y 0) (*.f64 2 (pow.f64 y 3))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(hypot.f64 (sqrt.f64 y) (sqrt.f64 y))
(hypot.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (+.f64 (log.f64 (/.f64 0 0)) (log.f64 (pow.f64 x 3))))
(exp.f64 (+.f64 (log.f64 (pow.f64 x 3)) (log.f64 (/.f64 0 0))))
(exp.f64 (+.f64 (log.f64 (/.f64 0 0)) (*.f64 2 (log.f64 (cbrt.f64 x)))))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x y (*.f64 x y))
(fma.f64 y x (*.f64 x y))
(fma.f64 y (/.f64 0 0) (*.f64 y (/.f64 0 0)))
(fma.f64 y 1 y)
(fma.f64 (/.f64 0 0) y (*.f64 (/.f64 0 0) y))
(fma.f64 (/.f64 0 0) (*.f64 x y) (*.f64 (/.f64 0 0) (*.f64 x y)))
(fma.f64 1 y y)
(fma.f64 1 (*.f64 x y) (*.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) y) (*.f64 x y))
(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) x) (*.f64 x y))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) y) (*.f64 x y))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) y)
(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (*.f64 x y))
(fma.f64 (*.f64 x y) (/.f64 0 0) (*.f64 (*.f64 x y) (/.f64 0 0)))
(fma.f64 (*.f64 x y) 1 (*.f64 (*.f64 x y) 1))
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) (*.f64 x y))
(fma.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)) (*.f64 x y))
(fma.f64 (*.f64 y (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x y))
(fma.f64 (*.f64 y (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x y))
(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (*.f64 x y))
(fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (*.f64 x y))
Outputs
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(*.f64 2 (*.f64 x y))
(*.f64 y -2)
(+.f64 y y)
(*.f64 y -2)
(+.f64 0 (/.f64 0 0))
-2
(+.f64 (*.f64 x y) (*.f64 x y))
(*.f64 y -2)
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x y)) (*.f64 (/.f64 0 0) (*.f64 x y)))
(*.f64 y -2)
(+.f64 (*.f64 (/.f64 0 0) y) (*.f64 (/.f64 0 0) y))
(*.f64 y -2)
(+.f64 (*.f64 (*.f64 x y) 1) (*.f64 (*.f64 x y) 1))
(*.f64 y -2)
(+.f64 (*.f64 (*.f64 x y) (/.f64 0 0)) (*.f64 (*.f64 x y) (/.f64 0 0)))
(*.f64 y -2)
(+.f64 (*.f64 y (/.f64 0 0)) (*.f64 y (/.f64 0 0)))
(*.f64 y -2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
-2
(-.f64 (/.f64 (pow.f64 y 2) 0) (/.f64 (pow.f64 y 2) 0))
-2
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (fma.f64 y y 0) (*.f64 2 (pow.f64 y 3))))
-2
(/.f64 (*.f64 2 (pow.f64 y 3)) (fma.f64 y y 0))
-2
(/.f64 0 0)
-2
(/.f64 (*.f64 (cbrt.f64 2) y) (cbrt.f64 (fma.f64 y y 0)))
(/.f64 (*.f64 y -2) (cbrt.f64 (fma.f64 y y -2)))
(/.f64 (pow.f64 (*.f64 2 (pow.f64 y 3)) 2) (pow.f64 (fma.f64 y y 0) 2))
(/.f64 -2 (pow.f64 (fma.f64 y y -2) -2))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 y 3))) (sqrt.f64 (fma.f64 y y 0)))
(/.f64 -2 (sqrt.f64 (fma.f64 y y -2)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) 0) (*.f64 (fma.f64 y y 0) 0))
-2
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 y 3))) (*.f64 0 (fma.f64 y y 0)))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 y 3))) (neg.f64 (fma.f64 y y 0)))
-2
(/.f64 (+.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 (*.f64 x y) 2) (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 x y) 2))))
(/.f64 (*.f64 -2 (pow.f64 (*.f64 y -2) 3)) (+.f64 -2 (pow.f64 (*.f64 y -2) -2)))
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 x y) 2)) (-.f64 (*.f64 x y) (*.f64 x y)))
-2
(/.f64 (*.f64 x (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
-2
(/.f64 (*.f64 x 0) 0)
-2
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) x) (fma.f64 y y 0))
-2
(/.f64 (*.f64 0 x) 0)
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 y 3)) (/.f64 0 0)) (fma.f64 y y 0))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 1/3)
-2
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 -2 3/2)
(pow.f64 (/.f64 0 0) -1)
-2
(pow.f64 (/.f64 0 0) 5)
-2
(pow.f64 (/.f64 0 0) 4/3)
-2
(pow.f64 (/.f64 0 0) 6)
-2
(pow.f64 (/.f64 0 0) 7/2)
(pow.f64 -2 7/2)
(pow.f64 (/.f64 0 0) 10/3)
(pow.f64 -2 10/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 -2 5/2)
(pow.f64 (/.f64 0 0) 7/3)
(*.f64 (pow.f64 -2 7/6) (pow.f64 -2 7/6))
(pow.f64 (/.f64 0 0) 5/6)
(pow.f64 -2 5/6)
(pow.f64 (/.f64 0 0) 2/3)
-2
(pow.f64 (/.f64 0 0) 9)
-2
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 -2 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(*.f64 (pow.f64 -2 1/18) (pow.f64 -2 1/18))
(pow.f64 (/.f64 0 0) -3)
-2
(pow.f64 (/.f64 0 0) -2)
-2
(pow.f64 (/.f64 0 0) -1/2)
-2
(pow.f64 (/.f64 0 0) -1/3)
(*.f64 (pow.f64 -2 -1/6) (pow.f64 -2 -1/6))
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
-2
(pow.f64 (/.f64 (fma.f64 y y 0) (*.f64 2 (pow.f64 y 3))) -1)
-2
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
-2
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
-2
(sqrt.f64 (/.f64 0 0))
-2
(fabs.f64 (/.f64 0 0))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(hypot.f64 (sqrt.f64 y) (sqrt.f64 y))
(hypot.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)))
(hypot.f64 (sqrt.f64 (*.f64 y -2)) (sqrt.f64 (*.f64 y -2)))
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 2))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
-2
(exp.f64 (+.f64 (log.f64 (/.f64 0 0)) (log.f64 (pow.f64 x 3))))
(*.f64 -2 (exp.f64 (*.f64 3 (log.f64 x))))
(exp.f64 (+.f64 (log.f64 (pow.f64 x 3)) (log.f64 (/.f64 0 0))))
(*.f64 -2 (exp.f64 (*.f64 3 (log.f64 x))))
(exp.f64 (+.f64 (log.f64 (/.f64 0 0)) (*.f64 2 (log.f64 (cbrt.f64 x)))))
(exp.f64 (+.f64 -2 (*.f64 -2 (log.f64 (cbrt.f64 x)))))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(fma.f64 x y (*.f64 x y))
(*.f64 y -2)
(fma.f64 y x (*.f64 x y))
(*.f64 y -2)
(fma.f64 y (/.f64 0 0) (*.f64 y (/.f64 0 0)))
(*.f64 y -2)
(fma.f64 y 1 y)
(fma.f64 y -2 y)
(fma.f64 (/.f64 0 0) y (*.f64 (/.f64 0 0) y))
(*.f64 y -2)
(fma.f64 (/.f64 0 0) (*.f64 x y) (*.f64 (/.f64 0 0) (*.f64 x y)))
(*.f64 y -2)
(fma.f64 1 y y)
(fma.f64 y -2 y)
(fma.f64 1 (*.f64 x y) (*.f64 x y))
(*.f64 y -2)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) y) (*.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 y (cbrt.f64 x)) (*.f64 y -2))
(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2) y)
(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) -2) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) y)
(fma.f64 (pow.f64 (cbrt.f64 y) -2) (cbrt.f64 y) y)
(fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) x) (*.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 y) -2) (*.f64 x (cbrt.f64 y)) (*.f64 y -2))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) y) (*.f64 x y))
(fma.f64 (sqrt.f64 x) (*.f64 y (sqrt.f64 x)) (*.f64 y -2))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) y)
(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (*.f64 x y))
(fma.f64 (sqrt.f64 y) (*.f64 x (sqrt.f64 y)) (*.f64 y -2))
(fma.f64 (*.f64 x y) (/.f64 0 0) (*.f64 (*.f64 x y) (/.f64 0 0)))
(*.f64 y -2)
(fma.f64 (*.f64 x y) 1 (*.f64 (*.f64 x y) 1))
(*.f64 y -2)
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) (*.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 (*.f64 y -2)) -2) (cbrt.f64 (*.f64 y -2)) (*.f64 y -2))
(fma.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 (*.f64 x y)) (*.f64 x y))
(fma.f64 (sqrt.f64 (*.f64 y -2)) (sqrt.f64 (*.f64 y -2)) (*.f64 y -2))
(fma.f64 (*.f64 y (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x y))
(fma.f64 (*.f64 y (pow.f64 (cbrt.f64 x) -2)) (cbrt.f64 x) (*.f64 y -2))
(fma.f64 (*.f64 y (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x y))
(fma.f64 (*.f64 y (sqrt.f64 x)) (sqrt.f64 x) (*.f64 y -2))
(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (*.f64 x y))
(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 y) -2)) (cbrt.f64 y) (*.f64 y -2))
(fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (*.f64 x y))
(fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (*.f64 y -2))

eval30.0ms (1.3%)

Compiler

Compiled 1090 to 747 computations (31.5% saved)

prune18.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1283131
Fresh000
Picked101
Done000
Total1293132
Accuracy
100.0%
Counts
132 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶6.1%
(+.f64 y y)
▶100.0%
(*.f64 2 (*.f64 x y))
▶1.7%
-2
Compiler

Compiled 15 to 11 computations (26.7% saved)

localize34.0ms (1.4%)

Compiler

Compiled 19 to 9 computations (52.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
Operation ival-mult, time spent: 5.0ms, 50.0% of total-time
Operation ival-add, time spent: 4.0ms, 40.0% of total-time
Operation const, time spent: 1.0ms, 10.0% of total-time

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked033
Done000
Total033
Accuracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓6.1%
(+.f64 y y)
✓100.0%
(*.f64 2 (*.f64 x y))
✓1.7%
-2
Compiler

Compiled 31 to 19 computations (38.7% saved)

regimes15.0ms (0.6%)

Counts
4 → 1
Calls
Call 1
Inputs
-2
(+.f64 y y)
(*.f64 2 (*.f64 x y))
(*.f64 x (+.f64 y y))
Outputs
(*.f64 2 (*.f64 x y))
Calls

4 calls:

4.0ms
y
4.0ms
x
4.0ms
(+.f64 y y)
3.0ms
(*.f64 x (+.f64 y y))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(*.f64 x (+.f64 y y))
100.0%1(+.f64 y y)
Compiler

Compiled 18 to 11 computations (38.9% saved)

regimes10.0ms (0.4%)

Counts
2 → 1
Calls
Call 1
Inputs
-2
(+.f64 y y)
Outputs
(+.f64 y y)
Calls

3 calls:

4.0ms
y
3.0ms
x
3.0ms
(+.f64 y y)
Results
AccuracySegmentsBranch
6.1%1x
6.1%1y
6.1%1(+.f64 y y)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
-2
Outputs
-2
Calls

2 calls:

3.0ms
y
3.0ms
x
Results
AccuracySegmentsBranch
1.7%1y
1.7%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
11433
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 2 (*.f64 x y))
(+.f64 y y)
-2
Outputs
(*.f64 2 (*.f64 x y))
(+.f64 y y)
-2
Compiler

Compiled 15 to 11 computations (26.7% saved)

soundness876.0ms (36.8%)

Rules
832×prod-diff
832×prod-diff
646×unpow-prod-down
646×unpow-prod-down
418×log-prod
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0919
19816
213907
02184294968659
16264294968659
0919
19816
213907
Stop Event
1×node limit
1×unsound
1×node limit
Compiler

Compiled 463 to 193 computations (58.3% saved)

end0.0ms (0%)

preprocess47.0ms (2%)

Remove

(sort x y)

(negabs y)

(negabs x)

Compiler

Compiled 204 to 142 computations (30.4% saved)

Profiling

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