Details

Time bar (total: 1.0s)

analyze3.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%25%25%4
62.5%12.5%25%5
68.7%6.2%25%6
71.8%3.1%25%7
73.4%1.6%25%8
74.2%0.8%25%9
74.6%0.4%25%10
74.8%0.2%25%11
74.9%0.1%25%12
74.9%0%25.1%13
74.9%0%25.1%14
Compiler

Compiled 7 to 5 computations (28.6% saved)

sample647.0ms (63.7%)

Results
635.0ms8256×body128valid
0.0msbody128invalid
Compiler

Compiled 14 to 10 computations (28.6% saved)

preprocess17.0ms (1.6%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*l*_binary64
associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
187
2117
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 (*.f64 x 3) x)
Outputs
(*.f64 (*.f64 x 3) x)
(*.f64 x (*.f64 x 3))
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify7.0ms (0.7%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*l*_binary64
associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
187
2117
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (*.f64 x 3) x)
Outputs
(*.f64 (*.f64 x 3) x)
(*.f64 x (*.f64 x 3))

prune2.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.2b
(*.f64 (*.f64 x 3) x)
Compiler

Compiled 23 to 15 computations (34.8% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 x 3) x)

series3.0ms (0.3%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 (*.f64 x 3) x)
1.0ms
x
@0
(*.f64 (*.f64 x 3) x)
0.0ms
x
@-inf
(*.f64 (*.f64 x 3) x)

rewrite31.0ms (3.1%)

Algorithm
batch-egg-rewrite
Rules
446×pow1_binary64
412×add-log-exp_binary64
412×log1p-expm1-u_binary64
412×expm1-log1p-u_binary64
404×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11017
211327
Stop Event
node limit
Counts
1 → 13
Calls
Call 1
Inputs
(*.f64 (*.f64 x 3) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 x 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 x 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x 3) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 3))))))))

simplify56.0ms (5.5%)

Algorithm
egg-herbie
Rules
609×sqr-pow_binary64
451×associate-*l*_binary64
434×unswap-sqr_binary64
281×cube-prod_binary64
271×fabs-mul_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410684
531584
6123584
7211684
8228084
9246484
10267284
11296384
12335684
13383484
14439584
Stop Event
node limit
Counts
25 → 15
Calls
Call 1
Inputs
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
Outputs
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))

prune10.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New12315
Fresh000
Picked011
Done000
Total12416
Error
0.0b
Counts
16 → 4
Alt Table
StatusErrorProgram
26.9b
(cbrt.f64 (pow.f64 (*.f64 x (*.f64 x 3)) 3))
0.9b
(pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 3))) 3)
0.2b
(*.f64 3 (pow.f64 x 2))
0.2b
(*.f64 (*.f64 x 3) x)
Compiler

Compiled 170 to 129 computations (24.1% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.2b
(*.f64 3 (pow.f64 x 2))

series1.0ms (0.1%)

Counts
1 → 0
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(*.f64 3 (pow.f64 x 2))
0.0ms
x
@0
(*.f64 3 (pow.f64 x 2))
0.0ms
x
@-inf
(*.f64 3 (pow.f64 x 2))

rewrite31.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
469×pow1_binary64
435×add-log-exp_binary64
434×log1p-expm1-u_binary64
434×expm1-log1p-u_binary64
426×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11247
212657
Stop Event
node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 3 (pow.f64 x 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 3 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 3 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 3 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 3 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 3 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 3 (*.f64 x x))))))))

simplify7.0ms (0.7%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
11 → 11
Calls
Call 1
Inputs
Outputs

prune7.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New10111
Fresh202
Picked011
Done011
Total12315
Error
0.0b
Counts
15 → 3
Alt Table
StatusErrorProgram
0.2b
(*.f64 3 (pow.f64 x 2))
0.2b
(*.f64 (*.f64 x 3) x)
21.2b
(sqrt.f64 (*.f64 (pow.f64 x 4) 9))
Compiler

Compiled 108 to 75 computations (30.6% saved)

localize4.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (pow.f64 x 4) 9)
20.5b
(sqrt.f64 (*.f64 (pow.f64 x 4) 9))

series4.0ms (0.4%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(*.f64 (pow.f64 x 4) 9)
1.0ms
x
@0
(*.f64 (pow.f64 x 4) 9)
1.0ms
x
@0
(sqrt.f64 (*.f64 (pow.f64 x 4) 9))
0.0ms
x
@inf
(sqrt.f64 (*.f64 (pow.f64 x 4) 9))
0.0ms
x
@-inf
(*.f64 (pow.f64 x 4) 9)

rewrite36.0ms (3.5%)

Algorithm
batch-egg-rewrite
Rules
574×pow1_binary64
538×add-log-exp_binary64
538×log1p-expm1-u_binary64
538×expm1-log1p-u_binary64
525×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0716
114814
2155614
Stop Event
node limit
Counts
2 → 36
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (pow.f64 x 4) 9))
(*.f64 (pow.f64 x 4) 9)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (*.f64 x x) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (pow.f64 9 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 9)) (cbrt.f64 (*.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x x) 3)) (cbrt.f64 (*.f64 (pow.f64 x 4) 9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 3)) (*.f64 x (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 81 (pow.f64 x 8)))) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 9))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 9 1/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 81 (pow.f64 x 8))) 1/2) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 9)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 9) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) 9) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) 3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) 9) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) 3)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x 4) 9)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 9) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 3) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 81 (pow.f64 x 8)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) 9) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 9)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 81 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 9) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) 9) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) 9)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) 9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) 9)))))))

simplify69.0ms (6.8%)

Algorithm
egg-herbie
Rules
616×sqr-pow_binary64
402×associate-*l*_binary64
342×unswap-sqr_binary64
327×pow-sqr_binary64
299×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010168
119168
239168
389168
4281168
51160168
61908168
72032168
82200168
92399168
102670168
113027168
123476168
134000168
144626168
Stop Event
node limit
Counts
60 → 39
Calls
Call 1
Inputs
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
Outputs
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (*.f64 x x))
(*.f64 x (*.f64 3 x))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))
(*.f64 9 (pow.f64 x 4))

prune21.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New39039
Fresh000
Picked011
Done022
Total39342
Error
0.0b
Counts
42 → 3
Alt Table
StatusErrorProgram
0.2b
(*.f64 3 (pow.f64 x 2))
0.2b
(*.f64 (*.f64 x 3) x)
21.2b
(sqrt.f64 (*.f64 (pow.f64 x 4) 9))
Compiler

Compiled 339 to 255 computations (24.8% saved)

regimes9.0ms (0.8%)

Accuracy

Total 0.1b remaining (79%)

Threshold costs 0.1b (79%)

Counts
5 → 1
Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
177
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 x 3) x)
Outputs
(*.f64 (*.f64 x 3) x)
(*.f64 x (*.f64 x 3))

end45.0ms (4.4%)

Stop Event
done
Compiler

Compiled 31 to 23 computations (25.8% saved)

Profiling

Loading profile data...