Details

Time bar (total: 2.4s)

analyze87.0ms (3.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
40.6%59.3%0.1%7
45.3%53.1%1.7%8
63.2%33.6%3.2%9
66%28.9%5.2%10
75.1%17.8%7.1%11
76.6%15%8.4%12
Compiler

Compiled 10 to 6 computations (40% saved)

sample1.8s (76.1%)

Results
1.7s8256×body256valid
57.0ms380×body256invalid

preprocess28.0ms (1.2%)

Algorithm
egg-herbie
Rules
associate-/r*_binary64
*-commutative_binary64
count-2_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0920
11320
21820
32220
022
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))
Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 x x))
(/.f64 (+.f64 x y) (+.f64 x x))
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.3%)

Algorithm
egg-herbie
Rules
associate-/r*_binary64
+-commutative_binary64
*-commutative_binary64
count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
1910
21210
31410
Stop Event
saturated
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
Outputs
(/.f64 (+.f64 x y) (+.f64 y y))

eval0.0ms (0%)

Compiler

Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(/.f64 (+.f64 x y) (+.f64 y y))
Compiler

Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 x y) (+.f64 y y))
Compiler

Compiled 17 to 5 computations (70.6% saved)

series4.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

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

rewrite57.0ms (2.4%)

Algorithm
batch-egg-rewrite
Rules
803×pow1_binary64
753×add-log-exp_binary64
752×log1p-expm1-u_binary64
752×expm1-log1p-u_binary64
737×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
114210
2237810
Stop Event
node limit
Counts
1 → 33
Calls
Call 1
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (+.f64 x y) (+.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x y) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y y) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 y y) (*.f64 (+.f64 x y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 x y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x y)) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (+.f64 x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (+.f64 y y)) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x y) (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x y) 0) 0)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (+.f64 x y) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) 2) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x y) 3) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 x y) (+.f64 y y))))))))

simplify13.0ms (0.6%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
fma-def_binary64
+-commutative_binary64
associate-/l*_binary64
associate-*r/_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07204
111168
220168
328168
432168
533168
Stop Event
saturated
Counts
57 → 38
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Outputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)

eval7.0ms (0.3%)

Compiler

Compiled 401 to 119 computations (70.3% saved)

prune6.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New35338
Fresh000
Picked101
Done000
Total36339
Error
0b
Counts
39 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
29.8b
(/.f64 x (/.f64 y 1/2))
0.2b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
34.0b
1/2
Compiler

Compiled 19 to 15 computations (21.1% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.2b
(*.f64 1/2 (/.f64 x y))
Compiler

Compiled 20 to 10 computations (50% saved)

series4.0ms (0.2%)

Counts
1 → 0
Calls

6 calls:

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

rewrite73.0ms (3.1%)

Algorithm
batch-egg-rewrite
Rules
653×pow1_binary64
606×add-log-exp_binary64
606×log1p-expm1-u_binary64
606×expm1-log1p-u_binary64
594×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11277
216097
Stop Event
node limit
Counts
1 → 20
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 y (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 1/2 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) 1/2) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (neg.f64 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (/.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))))))

simplify7.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
20 → 20
Calls
Call 1
Inputs
Outputs

localize6.0ms (0.2%)

Compiler

Compiled 13 to 8 computations (38.5% saved)

eval5.0ms (0.2%)

Compiler

Compiled 192 to 135 computations (29.7% saved)

prune4.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New20020
Fresh011
Picked011
Done011
Total20323
Error
0b
Counts
23 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
29.8b
(/.f64 x (/.f64 y 1/2))
0.2b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
34.0b
1/2
Compiler

Compiled 19 to 15 computations (21.1% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
29.8b
(/.f64 x (/.f64 y 1/2))
0.2b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
34.0b
1/2
Compiler

Compiled 19 to 15 computations (21.1% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune28.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done022
Total033
Error
0b
Counts
3 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
29.8b
(/.f64 x (/.f64 y 1/2))
0.2b
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
34.0b
1/2
Compiler

Compiled 19 to 15 computations (21.1% saved)

regimes13.0ms (0.6%)

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

3 calls:

4.0ms
y
4.0ms
x
3.0ms
(/.f64 (+.f64 x y) (+.f64 y y))
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(/.f64 (+.f64 x y) (+.f64 y y))
Compiler

Compiled 37 to 23 computations (37.8% saved)

regimes11.0ms (0.5%)

Counts
3 → 1
Calls
Call 1
Inputs
1/2
(/.f64 x (/.f64 y 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Outputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
Calls

2 calls:

6.0ms
x
4.0ms
y
Results
ErrorSegmentsBranch
0.2b1x
0.2b1y
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes89.0ms (3.8%)

Accuracy

Total -46.5b remaining (-307.7%)

Threshold costs -46.5b (-307.7%)

Counts
2 → 3
Calls
Call 1
Inputs
1/2
(/.f64 x (/.f64 y 1/2))
Outputs
1/2
(/.f64 x (/.f64 y 1/2))
1/2
Calls

2 calls:

76.0ms
x
12.0ms
y
Results
ErrorSegmentsBranch
15.3b7x
15.1b3y
Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch35.0ms (1.5%)

Algorithm
binary-search
Steps
TimeLeftRight
17.0ms
4.881831016229347e-34
4.763038762564546e-33
17.0ms
-3.3579252950480026e+100
-8.831723890999667e+97
Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01942
12242
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(if (<=.f64 y -33579252950480025910725680996624255687194282733483256155823069631948046698625611194275766667434786816) 1/2 (if (<=.f64 y 5707843218713581/11692013098647223345629478661730264157247460343808) (/.f64 x (/.f64 y 1/2)) 1/2))
1/2
Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(if (<=.f64 y -33579252950480025910725680996624255687194282733483256155823069631948046698625611194275766667434786816) 1/2 (if (<=.f64 y 5707843218713581/11692013098647223345629478661730264157247460343808) (/.f64 x (/.f64 y 1/2)) 1/2))
1/2
Compiler

Compiled 38 to 28 computations (26.3% saved)

soundness0.0ms (0%)

end59.0ms (2.5%)

Compiler

Compiled 32 to 22 computations (31.3% saved)

Profiling

Loading profile data...