Details

Time bar (total: 8.2s)

analyze1.5s (19%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
9.4%90.4%0.2%11
9.4%90.4%0.2%12
10.1%89.6%0.2%13
20.8%78.9%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.6s (19.9%)

Symmetry

(sort x y)

(sort z t)

Results
1.1s8256×body128valid
450.0ms3309×body128invalid
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify208.0ms (2.6%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.3b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
6.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series52.0ms (0.6%)

Counts
2 → 108
Calls

2 calls:

42.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
10.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

7.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify104.0ms (1.3%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune93.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New761288
Fresh011
Picked101
Done000
Total771390
Error
6.9b
Counts
90 → 13
Alt Table
StatusErrorProgram
8.2b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
8.3b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
36.1b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
36.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))
8.1b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)))) (*.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
7.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
29.8b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
36.0b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
29.7b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
7.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
36.2b
(*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
8.2b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
Compiler

Compiled 2248 to 1246 computations (44.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
0.2b
(*.f64 9/2 (/.f64 (*.f64 t z) a))
4.3b
(/.f64 (*.f64 t z) a)
5.1b
(/.f64 (*.f64 y x) a)

series76.0ms (0.9%)

Counts
4 → 24
Calls

4 calls:

37.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
14.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
14.0ms
(/.f64 (*.f64 y x) a)
11.0ms
(/.f64 (*.f64 t z) a)

rewrite21.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
4 → 93
Calls

4 calls:

5.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
5.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
4.0ms
(/.f64 (*.f64 y x) a)
3.0ms
(/.f64 (*.f64 t z) a)

simplify73.0ms (0.9%)

Algorithm
egg-herbie
Rules
676×times-frac_binary64
581×fma-def_binary64
359×*-commutative_binary64
335×associate-/l/_binary64
254×associate-/r*_binary64
Counts
117 → 134
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01681744
14231541
215231530
341621530
449411530

prune138.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1268134
Fresh9312
Picked101
Done000
Total13611147
Error
0.3b
Counts
147 → 11
Alt Table
StatusErrorProgram
9.2b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
36.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))
7.2b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
7.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
9.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
34.9b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (/.f64 t (sqrt.f64 a))) (/.f64 z (sqrt.f64 a))))
29.7b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
9.4b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
35.6b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 z (/.f64 t (sqrt.f64 a))) (sqrt.f64 a))))
8.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
7.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a)))
Compiler

Compiled 3274 to 1442 computations (56% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
0.5b
(cbrt.f64 a)
3.5b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))
4.3b
(/.f64 (*.f64 t z) a)

series118.0ms (1.4%)

Counts
3 → 60
Calls

3 calls:

41.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
40.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))
36.0ms
(cbrt.f64 a)

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt_binary64
30×cbrt-prod_binary64
28×associate-*r*_binary64
28×times-frac_binary64
27×*-un-lft-identity_binary64
Counts
3 → 116
Calls

3 calls:

11.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))
4.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms
(cbrt.f64 a)

simplify102.0ms (1.3%)

Algorithm
egg-herbie
Rules
847×fma-neg_binary64
438×associate-/r/_binary64
425×*-commutative_binary64
328×unswap-sqr_binary64
160×associate-*r/_binary64
Counts
176 → 177
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01642580
14051795
218111738
325121684
445641684
552511684

prune191.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2383241
Fresh2810
Picked101
Done000
Total24111252
Error
0.0b
Counts
252 → 11
Alt Table
StatusErrorProgram
35.0b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 z (/.f64 t (sqrt.f64 a))) (sqrt.f64 a))))
29.7b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
9.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
34.9b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (/.f64 t (sqrt.f64 a))) (/.f64 z (sqrt.f64 a))))
7.4b
(-.f64 (*.f64 1/2 (*.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (*.f64 (cbrt.f64 (/.f64 x (cbrt.f64 a))) (cbrt.f64 (/.f64 x (cbrt.f64 a))))) (cbrt.f64 (/.f64 x (cbrt.f64 a))))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
9.2b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
9.4b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
22.5b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (cbrt.f64 (pow.f64 (/.f64 (*.f64 t z) a) 3))))
7.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
7.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a)))
Compiler

Compiled 7168 to 2588 computations (63.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a)))
0.2b
(*.f64 9/2 (*.f64 t z))
4.3b
(*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a))
5.1b
(/.f64 (*.f64 y x) a)

series56.0ms (0.7%)

Counts
3 → 96
Calls

3 calls:

36.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a)))
15.0ms
(*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a))
4.0ms
(*.f64 9/2 (*.f64 t z))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
47×add-exp-log_binary64
29×add-cbrt-cube_binary64
27×prod-exp_binary64
17×pow1_binary64
15×cbrt-unprod_binary64
Counts
3 → 87
Calls

3 calls:

7.0ms
(*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a))
6.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a)))
5.0ms
(*.f64 9/2 (*.f64 t z))

simplify94.0ms (1.2%)

Algorithm
egg-herbie
Rules
972×fma-def_binary64
454×associate-*l/_binary64
426×associate-*r/_binary64
319×associate-/l*_binary64
227×associate-*l*_binary64
Counts
183 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01512611
13802507
214162491
345962489
450592489

prune144.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1472149
Fresh2810
Picked011
Done000
Total14911160
Error
0.0b
Counts
160 → 11
Alt Table
StatusErrorProgram
35.0b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 z (/.f64 t (sqrt.f64 a))) (sqrt.f64 a))))
29.7b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
22.8b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (cbrt.f64 (*.f64 729/8 (pow.f64 (/.f64 (*.f64 t z) a) 3))))
7.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
9.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
7.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 (sqrt.f64 9/2) (*.f64 (sqrt.f64 9/2) (*.f64 t z))) (/.f64 1 a)))
7.4b
(-.f64 (*.f64 1/2 (*.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (*.f64 (cbrt.f64 (/.f64 x (cbrt.f64 a))) (cbrt.f64 (/.f64 x (cbrt.f64 a))))) (cbrt.f64 (/.f64 x (cbrt.f64 a))))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
9.2b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
9.4b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
7.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 9/2 (*.f64 t z)) (/.f64 1 a)))
Compiler

Compiled 3680 to 1874 computations (49.1% saved)

regimes2.8s (34.3%)

Accuracy

Total 0.4b remaining (53.7%)

Threshold costs 0.4b (53.7%)

Counts
127 → 3
Compiler

Compiled 34038 to 23496 computations (31% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
24×*-commutative_binary64
16×+-commutative_binary64
16×sub-neg_binary64
14×distribute-rgt-neg-in_binary64
13×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044126
176126
2110126
3139126
4163126
5172126
6174126
7171126

end598.0ms (7.3%)

Compiler

Compiled 783 to 455 computations (41.9% saved)

Profiling

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