Numeric.Interval.Internal:bisect from intervals-0.7.1, A

Time bar (total: 2.6s)

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 10 to 7 computations (30% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-sub: 0.0ms (0% of total)
ival-div: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample785.0ms (30.7%)

Results
563.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 308.0ms
ival-sub: 123.0ms (39.9% of total)
ival-add: 104.0ms (33.8% of total)
ival-div: 67.0ms (21.7% of total)
const: 12.0ms (3.9% of total)
backward-pass: 3.0ms (1% of total)
Bogosity

preprocess316.0ms (12.3%)

Algorithm
1×egg-herbie
Rules
2980×fmm-def
653×fma-define
518×sub-neg
365×distribute-lft-out
349×+-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025220
156196
2161196
3463133
4845133
51493133
62939133
73539133
83564133
93582133
103582133
115283133
126297133
136523133
146588133
156652133
166652133
176675133
186683133
196683133
Stop Event
1×node limit
Calls
Call 1
Inputs
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(+.f64 (neg.f64 x) (/.f64 (-.f64 y (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 x (/.f64 (-.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(neg.f64 (+.f64 (neg.f64 x) (/.f64 (-.f64 y (neg.f64 x)) #s(literal 2 binary64))))
(neg.f64 (+.f64 x (/.f64 (-.f64 (neg.f64 y) x) #s(literal 2 binary64))))
(+.f64 y (/.f64 (-.f64 x y) #s(literal 2 binary64)))
Outputs
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+.f64 (neg.f64 x) (/.f64 (-.f64 y (neg.f64 x)) #s(literal 2 binary64)))
(-.f64 (/.f64 (+.f64 x y) #s(literal 2 binary64)) x)
(/.f64 (-.f64 y x) #s(literal 2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 x y))
(*.f64 (-.f64 x y) #s(literal -1/2 binary64))
(+.f64 x (/.f64 (-.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(+.f64 x (/.f64 (+.f64 x y) #s(literal -2 binary64)))
(/.f64 (-.f64 x y) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 x y))
(*.f64 (-.f64 x y) #s(literal 1/2 binary64))
(neg.f64 (+.f64 (neg.f64 x) (/.f64 (-.f64 y (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 x (/.f64 (-.f64 (neg.f64 y) x) #s(literal 2 binary64)))
(+.f64 x (/.f64 (+.f64 x y) #s(literal -2 binary64)))
(/.f64 (-.f64 x y) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 x y))
(*.f64 (-.f64 x y) #s(literal 1/2 binary64))
(neg.f64 (+.f64 x (/.f64 (-.f64 (neg.f64 y) x) #s(literal 2 binary64))))
(+.f64 (neg.f64 x) (/.f64 (-.f64 y (neg.f64 x)) #s(literal 2 binary64)))
(-.f64 (/.f64 (+.f64 x y) #s(literal 2 binary64)) x)
(/.f64 (-.f64 y x) #s(literal 2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 x y))
(*.f64 (-.f64 x y) #s(literal -1/2 binary64))
(+.f64 y (/.f64 (-.f64 x y) #s(literal 2 binary64)))
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
Symmetry

(sort x y)

explain144.0ms (5.6%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-x
00-0-(/.f64 (-.f64 y x) #s(literal 2 binary64))
00-0-y
00-0-#s(literal 2 binary64)
00-0-(-.f64 y x)
00-0-(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Results
120.0ms512×0valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-sub: 4.0ms (35.7% of total)
ival-div: 4.0ms (35.7% of total)
ival-add: 3.0ms (26.8% of total)
const: 1.0ms (8.9% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize27.0ms (1.1%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 x y)
✓cost-diff0
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
✓accuracy100.0%
(+.f64 x y)
✓accuracy100.0%
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
Rules
4×fma-define
3×*-commutative
2×distribute-rgt-in
2×distribute-lft-in
1×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01041
11241
22041
32741
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+.f64 x y)
x
y
#s(literal 1/2 binary64)
Outputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+.f64 x y)
x
y
#s(literal 1/2 binary64)
Results
15.0ms256×0valid
Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-add: 2.0ms (47% of total)
ival-mult: 2.0ms (47% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series4.0ms (0.1%)

Counts
2 → 42
Calls
Call 1
Inputs
#<alt (*.f64 (+.f64 x y) #s(literal 1/2 binary64))>
#<alt (+.f64 x y)>
Outputs
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))>
#<alt (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))>
#<alt (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))>
#<alt (*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))>
#<alt (*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))>
#<alt y>
#<alt x>
#<alt (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))>
#<alt (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))>
#<alt (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))>
#<alt x>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))>
#<alt x>
#<alt y>
#<alt (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))>
#<alt (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))>
#<alt (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))>
#<alt y>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))>
#<alt (*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))>
Calls

12 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(* (+ x y) 1/2)
0.0ms
x
@-inf
(* (+ x y) 1/2)
0.0ms
y
@inf
(* (+ x y) 1/2)
0.0ms
x
@-inf
(+ x y)
0.0ms
x
@0
(* (+ x y) 1/2)

rewrite232.0ms (9.1%)

Algorithm
1×batch-egg-rewrite
Rules
488×log1p-expm1-u
488×expm1-log1p-u
455×prod-diff
422×pow1
404×unpow-prod-down
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01032
19732
2130432
Stop Event
1×node limit
Counts
2 → 86
Calls
Call 1
Inputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+.f64 x y)
Outputs
(+.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 1/2 binary64)))
(+.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))))
(+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))) (-.f64 x y))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))) #s(literal 1/2 binary64)) (-.f64 x y))
(pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))) (sqrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y #s(literal 1/2 binary64)))
(fma.f64 y #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) y (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 x y)) (/.f64 (pow.f64 y #s(literal 2 binary64)) (-.f64 x y)))
(*.f64 (+.f64 x y) #s(literal 1 binary64))
(*.f64 (+.f64 x y) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (+.f64 x y))
(*.f64 (cbrt.f64 (+.f64 x y)) (pow.f64 (cbrt.f64 (+.f64 x y)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) #s(literal 2 binary64)) (cbrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 x y)))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x y))) #s(literal 2 binary64)) #s(literal 3 binary64)) (cbrt.f64 (+.f64 x y)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x y))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x y))) #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (+.f64 x y))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 x y) (cbrt.f64 (+.f64 x y))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (+.f64 x y))))
(*.f64 (pow.f64 (pow.f64 (+.f64 x y) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x y))))
(/.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))) (-.f64 x y))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))) (neg.f64 (-.f64 x y)))
(/.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (-.f64 y x))
(pow.f64 (+.f64 x y) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (+.f64 x y)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (+.f64 x y)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (+.f64 x y)))
(pow.f64 (/.f64 (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x y))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (+.f64 x y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x y)))) (sqrt.f64 (log.f64 (+.f64 x y))))
(sqrt.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)))
(log.f64 (exp.f64 (+.f64 x y)))
(cbrt.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (+.f64 x y)))
(log1p.f64 (expm1.f64 (+.f64 x y)))
(exp.f64 (log.f64 (+.f64 x y)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 x y))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (+.f64 x y))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x y))) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1 binary64) y)
(fma.f64 y #s(literal 1 binary64) x)
(fma.f64 #s(literal 1 binary64) x y)
(fma.f64 #s(literal 1 binary64) y x)
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) #s(literal 2 binary64)) y)
(fma.f64 (pow.f64 (cbrt.f64 x) #s(literal 2 binary64)) (cbrt.f64 x) y)
(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) #s(literal 2 binary64)) x)
(fma.f64 (pow.f64 (cbrt.f64 y) #s(literal 2 binary64)) (cbrt.f64 y) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) x)

simplify104.0ms (4.1%)

Algorithm
1×egg-herbie
Rules
396×fmm-def
328×fma-define
316×distribute-lft-neg-in
307×distribute-lft-in
301×distribute-rgt-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02353538
15013490
213203430
347332674
Stop Event
1×node limit
Counts
128 → 116
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) y)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))
y
x
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))
x
y
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 1/2 binary64)))
(+.f64 (*.f64 y #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))))
(+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))) (-.f64 x y))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))) #s(literal 1/2 binary64)) (-.f64 x y))
(pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))) (sqrt.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 (+.f64 x y))))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y #s(literal 1/2 binary64)))
(fma.f64 y #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) y (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 x y)) (/.f64 (pow.f64 y #s(literal 2 binary64)) (-.f64 x y)))
(*.f64 (+.f64 x y) #s(literal 1 binary64))
(*.f64 (+.f64 x y) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (+.f64 x y))
(*.f64 (cbrt.f64 (+.f64 x y)) (pow.f64 (cbrt.f64 (+.f64 x y)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) #s(literal 2 binary64)) (cbrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (+.f64 x y)))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x y))) #s(literal 2 binary64)) #s(literal 3 binary64)) (cbrt.f64 (+.f64 x y)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x y))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 x y))) #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (+.f64 x y))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 x y) (cbrt.f64 (+.f64 x y))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (+.f64 x y))))
(*.f64 (pow.f64 (pow.f64 (+.f64 x y) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x y))))
(/.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64))) (-.f64 x y))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))) (neg.f64 (-.f64 x y)))
(/.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (-.f64 y x))
(pow.f64 (+.f64 x y) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (+.f64 x y)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (+.f64 x y)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (+.f64 x y)))
(pow.f64 (/.f64 (fma.f64 y (-.f64 y x) (pow.f64 x #s(literal 2 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x y))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (+.f64 x y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x y)))) (sqrt.f64 (log.f64 (+.f64 x y))))
(sqrt.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)))
(log.f64 (exp.f64 (+.f64 x y)))
(cbrt.f64 (pow.f64 (+.f64 x y) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (+.f64 x y)))
(log1p.f64 (expm1.f64 (+.f64 x y)))
(exp.f64 (log.f64 (+.f64 x y)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 x y))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (+.f64 x y))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x y))) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1 binary64) y)
(fma.f64 y #s(literal 1 binary64) x)
(fma.f64 #s(literal 1 binary64) x y)
(fma.f64 #s(literal 1 binary64) y x)
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) #s(literal 2 binary64)) y)
(fma.f64 (pow.f64 (cbrt.f64 x) #s(literal 2 binary64)) (cbrt.f64 x) y)
(fma.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 y) #s(literal 2 binary64)) x)
(fma.f64 (pow.f64 (cbrt.f64 y) #s(literal 2 binary64)) (cbrt.f64 y) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) x)
Outputs
(*.f64 #s(literal 1/2 binary64) y)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 y (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 x y))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 x y)) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
y
x
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
x
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 y x)) #s(literal 1 binary64))))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
x
y
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
y
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(*.f64 #s(literal -1 binary64) (*.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x y)) #s(literal 1 binary64))))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(+.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))
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(+.f64 y x)
(fma.f64 (pow.f64 (cbrt.f64 y) #s(literal 2 binary64)) (cbrt.f64 y) x)
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) y)
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) x)
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(fma.f64 x (/.f64 y x) x)
(+.f64 y x)

eval15.0ms (0.6%)

Compiler

Compiled 1278 to 356 computations (72.1% saved)

prune60.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1142116
Fresh000
Picked011
Done000
Total1143117
Accuracy
100.0%
Counts
117 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
▶52.0%
(*.f64 y #s(literal 1/2 binary64))
▶50.2%
(*.f64 x #s(literal 1/2 binary64))
Compiler

Compiled 17 to 13 computations (23.5% saved)

localize31.0ms (1.2%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 y #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 y #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
Rules
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01030
11230
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(*.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
Outputs
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
y
#s(literal 1/2 binary64)
Results
19.0ms256×0valid
Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 7.0ms (95.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series2.0ms (0.1%)

Counts
2 → 24
Calls
Call 1
Inputs
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt (*.f64 y #s(literal 1/2 binary64))>
Outputs
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
#<alt (*.f64 #s(literal 1/2 binary64) y)>
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(* x 1/2)
0.0ms
x
@0
(* x 1/2)
0.0ms
x
@-inf
(* x 1/2)
0.0ms
y
@inf
(* y 1/2)
0.0ms
y
@-inf
(* y 1/2)

rewrite68.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
351×unpow-prod-down
337×log1p-expm1-u
337×expm1-log1p-u
323×add-exp-log
309×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01020
18620
294420
Stop Event
1×node limit
Counts
2 → 42
Calls
Call 1
Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 y #s(literal 1/2 binary64))
Outputs
(+.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 x))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 x)))
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 x #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 y))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 y)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) y)) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) y)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 1/2 binary64) y)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y)))) (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 (*.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 y)))
(cbrt.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) y)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 1/2 binary64) y)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 2 binary64)))

simplify103.0ms (4%)

Algorithm
1×egg-herbie
Rules
1090×fmm-def
686×div-sub
522×distribute-lft-in
478×distribute-rgt-in
400×fma-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01201026
11961026
23221026
34811026
48531026
519931026
655131026
779741026
Stop Event
1×node limit
Counts
66 → 53
Calls
Call 1
Inputs
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(+.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 x))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 x)))
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 x #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) y))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 y))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 y)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) y)) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) y)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 1/2 binary64) y)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y)))) (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 (*.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(log.f64 (sqrt.f64 (exp.f64 y)))
(cbrt.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) y)))
(log1p.f64 (expm1.f64 (*.f64 #s(literal 1/2 binary64) y)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 2 binary64)))
Outputs
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 #s(literal 1/2 binary64) y)
(+.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 (log.f64 (cbrt.f64 (exp.f64 x))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))))
(*.f64 #s(literal 2 binary64) (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))))
(*.f64 (log.f64 (pow.f64 (exp.f64 x) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(pow.f64 (cbrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(pow.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))))
(pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(pow.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(pow.f64 (E.f64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 1/2 binary64) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x))))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))))
(log.f64 (sqrt.f64 (exp.f64 x)))
(*.f64 #s(literal 1/2 binary64) x)
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(log1p.f64 (expm1.f64 (*.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 1/3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) y)
(+.f64 (log.f64 (cbrt.f64 (exp.f64 y))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 y)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))))
(*.f64 #s(literal 2 binary64) (log.f64 (pow.f64 (exp.f64 y) #s(literal 1/4 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) y)) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(pow.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(pow.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(pow.f64 (*.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 2 binary64))))
(pow.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1/3 binary64))
(cbrt.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) y)) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(pow.f64 (E.f64) (log.f64 (*.f64 #s(literal 1/2 binary64) y)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y)))) (sqrt.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 (*.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 2 binary64))))
(log.f64 (sqrt.f64 (exp.f64 y)))
(*.f64 #s(literal 1/2 binary64) y)
(cbrt.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(cbrt.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 1/2 binary64) y)))
(*.f64 #s(literal 1/2 binary64) y)
(log1p.f64 (expm1.f64 (*.f64 #s(literal 1/2 binary64) y)))
(*.f64 #s(literal 1/2 binary64) y)
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y)))
(*.f64 #s(literal 1/2 binary64) y)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 3 binary64)))
(*.f64 #s(literal 1/2 binary64) y)
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 1/3 binary64)))
(cbrt.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) y))) #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) y)

eval21.0ms (0.8%)

Compiler

Compiled 383 to 132 computations (65.5% saved)

prune8.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New53053
Fresh000
Picked022
Done011
Total53356
Accuracy
100.0%
Counts
56 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
✓52.0%
(*.f64 y #s(literal 1/2 binary64))
✓50.2%
(*.f64 x #s(literal 1/2 binary64))
Compiler

Compiled 37 to 24 computations (35.1% saved)

regimes7.0ms (0.3%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Outputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
Calls

3 calls:

2.0ms
(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
2.0ms
y
2.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.5%)

Counts
2 → 2
Calls
Call 1
Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 y #s(literal 1/2 binary64))
Outputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 y #s(literal 1/2 binary64))
Calls

2 calls:

10.0ms
y
2.0ms
x
Results
AccuracySegmentsBranch
83.9%2x
80.8%2y
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 x #s(literal 1/2 binary64))
Outputs
(*.f64 x #s(literal 1/2 binary64))
Calls

2 calls:

1.0ms
y
1.0ms
x
Results
AccuracySegmentsBranch
50.2%1y
50.2%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch11.0ms (0.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
-1.104744372406942e-94
-3.35257989342735e-98
Results
6.0ms128×0valid
Compiler

Compiled 110 to 90 computations (18.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sub: 1.0ms (38.2% of total)
ival-div: 1.0ms (38.2% of total)
ival-add: 1.0ms (38.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×*-commutative
1×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01861
12261
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(if (<=.f64 x #s(literal -8266869891363893/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) (*.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
Outputs
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(if (<=.f64 x #s(literal -8266869891363893/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) (*.f64 x #s(literal 1/2 binary64)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))

soundness563.0ms (22%)

Rules
2980×fmm-def
653×fma-define
518×sub-neg
365×distribute-lft-out
349×+-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025220
156196
2161196
3463133
4845133
51493133
62939133
73539133
83564133
93582133
103582133
115283133
126297133
136523133
146588133
156652133
166652133
176675133
186683133
196683133
Stop Event
1×done
1×node limit
Compiler

Compiled 215 to 71 computations (67% saved)

preprocess41.0ms (1.6%)

Remove

(sort x y)

Compiler

Compiled 114 to 72 computations (36.8% saved)

end0.0ms (0%)

Profiling

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