Details

Time bar (total: 8.3s)

analyze1.9s (22.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
1.6%98.1%0.3%13
2.3%97.4%0.3%14
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.9s (22.3%)

Symmetry

(sort y z t)

(sort a b)

Results
1.2s8256×body128valid
440.0ms3001×body128invalid
Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify71.0ms (0.8%)

Algorithm
egg-herbie
Rules
712×fma-neg_binary64
641×fma-def_binary64
213×cancel-sign-sub-inv_binary64
172×distribute-rgt-neg-in_binary64
157×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01825
13923
211521
330821
455221
590221
6120121
7143321
8167221
9178721
10179121
11179121
12179121
13167421

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
1.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
3.4b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
Compiler

Compiled 126 to 90 computations (28.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
0.2b
(*.f64 (*.f64 y 9) z)
0.2b
(*.f64 (*.f64 a 27) b)
5.2b
(*.f64 (*.f64 (*.f64 y 9) z) t)

series55.0ms (0.7%)

Counts
4 → 156
Calls

4 calls:

31.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
10.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
9.0ms
(*.f64 (*.f64 a 27) b)
4.0ms
(*.f64 (*.f64 y 9) z)

rewrite29.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
23×pow1_binary64
12×cbrt-unprod_binary64
12×prod-exp_binary64
Counts
4 → 84
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
6.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
4.0ms
(*.f64 (*.f64 y 9) z)
3.0ms
(*.f64 (*.f64 a 27) b)

simplify114.0ms (1.4%)

Algorithm
egg-herbie
Rules
804×fma-neg_binary64
586×fma-def_binary64
359×associate-*l*_binary64
268×associate-*r*_binary64
268×exp-prod_binary64
Counts
240 → 138
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01633457
14153135
217363112
341473112
449573112

prune156.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1308138
Fresh101
Picked101
Done000
Total1328140
Error
0.0b
Counts
140 → 8
Alt Table
StatusErrorProgram
1.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
9.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (*.f64 (*.f64 a 27) b))
1.8b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 y 9) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))) (*.f64 (*.f64 a 27) b))
3.4b
(+.f64 (*.f64 x 2) (fma.f64 y (*.f64 (*.f64 t z) -9) (*.f64 27 (*.f64 a b))))
3.4b
(-.f64 (*.f64 x 2) (fma.f64 a (*.f64 b -27) (*.f64 9 (*.f64 y (*.f64 t z)))))
30.7b
(/.f64 (fma.f64 (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) -729)) (fma.f64 a (*.f64 b -27) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x))))
1.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
1.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b))))
Compiler

Compiled 3595 to 2204 computations (38.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
0.2b
(*.f64 y (*.f64 9 z))
0.2b
(*.f64 (*.f64 a 27) b)
5.2b
(*.f64 (*.f64 y (*.f64 9 z)) t)

series43.0ms (0.5%)

Counts
3 → 132
Calls

3 calls:

29.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
9.0ms
(*.f64 (*.f64 y (*.f64 9 z)) t)
4.0ms
(*.f64 y (*.f64 9 z))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
17×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
3 → 64
Calls

3 calls:

5.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
5.0ms
(*.f64 (*.f64 y (*.f64 9 z)) t)
3.0ms
(*.f64 y (*.f64 9 z))

simplify111.0ms (1.3%)

Algorithm
egg-herbie
Rules
751×fma-neg_binary64
540×fma-def_binary64
259×associate-*l*_binary64
254×exp-prod_binary64
238×log-prod_binary64
Counts
196 → 109
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01283145
13412792
214132769
335322769
449222769
550102769

prune157.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1381139
Fresh167
Picked011
Done000
Total1398147
Error
0.0b
Counts
147 → 8
Alt Table
StatusErrorProgram
3.4b
(fma.f64 y (*.f64 t (*.f64 z -9)) (fma.f64 27 (*.f64 a b) (+.f64 x x)))
3.4b
(-.f64 (*.f64 x 2) (fma.f64 a (*.f64 b -27) (*.f64 9 (*.f64 y (*.f64 t z)))))
1.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
9.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (*.f64 (*.f64 a 27) b))
3.4b
(+.f64 (*.f64 x 2) (fma.f64 y (*.f64 (*.f64 t z) -9) (*.f64 27 (*.f64 a b))))
30.7b
(/.f64 (fma.f64 (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) -729)) (fma.f64 a (*.f64 b -27) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x))))
1.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
1.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b))))
Compiler

Compiled 3559 to 2189 computations (38.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
0.2b
(*.f64 (*.f64 y 9) z)
0.3b
(*.f64 27 (*.f64 a b))
5.2b
(*.f64 (*.f64 (*.f64 y 9) z) t)

series34.0ms (0.4%)

Counts
2 → 72
Calls

2 calls:

30.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
4.0ms
(*.f64 27 (*.f64 a b))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-log-exp_binary64
add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
Counts
2 → 41
Calls

2 calls:

6.0ms
(*.f64 27 (*.f64 a b))
5.0ms
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))

simplify99.0ms (1.2%)

Algorithm
egg-herbie
Rules
759×fma-neg_binary64
701×associate-*r*_binary64
456×fma-def_binary64
295×exp-prod_binary64
204×distribute-rgt-in_binary64
Counts
113 → 66
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0972183
12521974
28131960
331471960
446161960
548621960

prune151.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh066
Picked011
Done011
Total1298137
Error
0.0b
Counts
137 → 8
Alt Table
StatusErrorProgram
3.4b
(fma.f64 y (*.f64 t (*.f64 z -9)) (fma.f64 27 (*.f64 a b) (+.f64 x x)))
3.4b
(-.f64 (*.f64 x 2) (fma.f64 a (*.f64 b -27) (*.f64 9 (*.f64 y (*.f64 t z)))))
1.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
9.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (*.f64 (*.f64 a 27) b))
3.4b
(+.f64 (*.f64 x 2) (fma.f64 y (*.f64 (*.f64 t z) -9) (*.f64 27 (*.f64 a b))))
30.7b
(/.f64 (fma.f64 (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) -729)) (fma.f64 a (*.f64 b -27) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x))))
1.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
1.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b))))
Compiler

Compiled 3324 to 1914 computations (42.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b)))
0.5b
(*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b)))
5.2b
(*.f64 (*.f64 (*.f64 y 9) z) t)
6.9b
(cbrt.f64 (*.f64 (*.f64 a 27) b))

series908.0ms (10.9%)

Counts
3 → 72
Calls

3 calls:

524.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b)))
361.0ms
(cbrt.f64 (*.f64 (*.f64 a 27) b))
22.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b)))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
16×pow1/3_binary64
11×pow-prod-up_binary64
11×add-sqr-sqrt_binary64
10×add-exp-log_binary64
Counts
3 → 79
Calls

3 calls:

6.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b)))
4.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b)))
2.0ms
(cbrt.f64 (*.f64 (*.f64 a 27) b))

simplify106.0ms (1.3%)

Algorithm
egg-herbie
Rules
750×fma-neg_binary64
365×exp-sum_binary64
307×exp-prod_binary64
285×unswap-sqr_binary64
266×*-commutative_binary64
Counts
151 → 125
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01402322
12802085
26931804
314471548
435711430
549381430
649501430

prune264.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2080208
Fresh055
Picked011
Done022
Total2088216
Error
0.0b
Counts
216 → 8
Alt Table
StatusErrorProgram
3.4b
(fma.f64 y (*.f64 t (*.f64 z -9)) (fma.f64 27 (*.f64 a b) (+.f64 x x)))
3.4b
(-.f64 (*.f64 x 2) (fma.f64 a (*.f64 b -27) (*.f64 9 (*.f64 y (*.f64 t z)))))
1.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
9.6b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 (*.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (*.f64 (*.f64 a 27) b))
3.4b
(+.f64 (*.f64 x 2) (fma.f64 y (*.f64 (*.f64 t z) -9) (*.f64 27 (*.f64 a b))))
30.7b
(/.f64 (fma.f64 (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x)) (*.f64 (*.f64 (*.f64 a b) (*.f64 a b)) -729)) (fma.f64 a (*.f64 b -27) (fma.f64 (*.f64 y (*.f64 t z)) -9 (+.f64 x x))))
1.5b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
1.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a 27) b)) (cbrt.f64 (*.f64 (*.f64 a 27) b))) (cbrt.f64 (*.f64 (*.f64 a 27) b))))
Compiler

Compiled 7604 to 5238 computations (31.1% saved)

regimes1.5s (17.4%)

Accuracy

Total 0.6b remaining (97.2%)

Threshold costs 0.6b (97.2%)

Counts
61 → 2
Compiler

Compiled 25540 to 18821 computations (26.3% saved)

bsearch47.0ms (0.6%)

Steps
ItersRangePoint
8
9.33344817713355e-112
7.915445538876157e-109
9.395682275617862e-111
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
17×*-commutative_binary64
10×+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02954
14754
26754
38354
49454
510054
610254
710154

end726.0ms (8.7%)

Remove

(sort a b)

Compiler

Compiled 572 to 391 computations (31.6% saved)

Profiling

Loading profile data...