Details

Time bar (total: 12.8s)

analyze306.0ms (2.4%)

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
49.9%49.9%0.2%6
49.9%49.9%0.2%7
49.9%49.9%0.2%8
49.9%49.9%0.2%9
49.9%49.9%0.2%10
74.8%24.9%0.2%11
74.8%24.9%0.2%12
74.8%24.9%0.2%13
74.8%24.9%0.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample873.0ms (6.8%)

Infinites
8.2% of outputs are infinite.
Results
790.0ms8256×body128valid
Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (0.9%)

Algorithm
egg-herbie
Rules
1894×fma-neg_binary64
843×div-sub_binary64
750×fma-def_binary64
582×times-frac_binary64
397×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01116
11816
23714
37814
416314
529514
664514
7155414
8304014
9322814
10346914
11337014
12336314
13339814
14494914

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
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
9.1b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 z t) (-.f64 a t))
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series59.0ms (0.5%)

Counts
2 → 96
Calls

2 calls:

40.0ms
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
20.0ms
(/.f64 (-.f64 z t) (-.f64 a t))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity_binary64
38×add-sqr-sqrt_binary64
25×times-frac_binary64
14×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
Counts
2 → 64
Calls

2 calls:

8.0ms
(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify111.0ms (0.9%)

Algorithm
egg-herbie
Rules
690×cancel-sign-sub-inv_binary64
647×times-frac_binary64
542×fma-neg_binary64
354×sub-neg_binary64
188×neg-mul-1_binary64
Counts
160 → 138
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02674118
17404035
224343427
342313410
449643410

prune101.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1344138
Fresh011
Picked011
Done000
Total1346140
Error
0.0b
Counts
140 → 6
Alt Table
StatusErrorProgram
26.9b
(fma.f64 y (/.f64 (-.f64 (*.f64 z z) (*.f64 t t)) (*.f64 (-.f64 a t) (+.f64 z t))) x)
2.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
2.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
3.3b
(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
9.1b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
Compiler

Compiled 3473 to 1154 computations (66.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
0.4b
(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
1.7b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
4.8b
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

series778.0ms (6.1%)

Counts
4 → 168
Calls

4 calls:

494.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
196.0ms
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
53.0ms
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
33.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite124.0ms (1%)

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity_binary64
248×cbrt-prod_binary64
247×add-sqr-sqrt_binary64
205×times-frac_binary64
96×distribute-lft-out--_binary64
Counts
4 → 284
Calls

4 calls:

30.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
28.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
9.0ms
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
0.0ms
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)

simplify351.0ms (2.7%)

Algorithm
egg-herbie
Rules
623×*-commutative_binary64
236×associate-*r*_binary64
222×associate-+r+_binary64
218×fma-def_binary64
150×associate-/l*_binary64
Counts
452 → 482
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158024416
1498624416
2500124416

prune857.0ms (6.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New6800680
Fresh044
Picked011
Done011
Total6806686
Error
0.0b
Counts
686 → 6
Alt Table
StatusErrorProgram
26.9b
(fma.f64 y (/.f64 (-.f64 (*.f64 z z) (*.f64 t t)) (*.f64 (-.f64 a t) (+.f64 z t))) x)
2.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
2.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
3.3b
(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
9.1b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
Compiler

Compiled 49387 to 20834 computations (57.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
0.5b
(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
4.3b
(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))

series4.2s (33%)

Counts
3 → 180
Calls

3 calls:

3.6s
(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
572.0ms
(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))
43.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))

rewrite23.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
5.0ms
(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
1.0ms
(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))

simplify567.0ms (4.4%)

Algorithm
egg-herbie
Rules
968×fma-def_binary64
48×unpow1/3_binary64
log-div_binary64
log-prod_binary64
log-rec_binary64
Counts
273 → 297
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0399564620
1502264620

prune2.6s (20.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New6820682
Fresh033
Picked011
Done022
Total6826688
Error
0.0b
Counts
688 → 6
Alt Table
StatusErrorProgram
26.9b
(fma.f64 y (/.f64 (-.f64 (*.f64 z z) (*.f64 t t)) (*.f64 (-.f64 a t) (+.f64 z t))) x)
2.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
2.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
3.3b
(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
9.1b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
Compiler

Compiled 137036 to 72439 computations (47.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
0.0b
(/.f64 y (-.f64 a t))
8.5b
(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series93.0ms (0.7%)

Counts
3 → 132
Calls

3 calls:

44.0ms
(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
32.0ms
(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
16.0ms
(/.f64 y (-.f64 a t))

rewrite35.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt_binary64
68×*-un-lft-identity_binary64
52×add-cube-cbrt_binary64
36×prod-diff_binary64
31×times-frac_binary64
Counts
3 → 155
Calls

3 calls:

12.0ms
(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
4.0ms
(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
4.0ms
(/.f64 y (-.f64 a t))

simplify204.0ms (1.6%)

Algorithm
egg-herbie
Rules
422×sub-neg_binary64
404×fma-neg_binary64
222×associate--l+_binary64
218×+-commutative_binary64
182×associate-*l*_binary64
Counts
287 → 308
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04436869
110786148
239776052
347076051
449946051
549426051

prune248.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New3062308
Fresh022
Picked101
Done123
Total3086314
Error
0b
Counts
314 → 6
Alt Table
StatusErrorProgram
26.9b
(fma.f64 y (/.f64 (-.f64 (*.f64 z z) (*.f64 t t)) (*.f64 (-.f64 a t) (+.f64 z t))) x)
2.0b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
3.7b
(+.f64 x (*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))) (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))))
3.3b
(fma.f64 (-.f64 z t) (/.f64 y (-.f64 a t)) x)
1.7b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
9.1b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
Compiler

Compiled 8030 to 2049 computations (74.5% saved)

regimes944.0ms (7.4%)

Accuracy

Total 0.6b remaining (98.3%)

Threshold costs 0.6b (98.3%)

Counts
99 → 3
Compiler

Compiled 16816 to 8871 computations (47.2% saved)

bsearch5.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02891
13991
25091
36191
46791
57091
67191
77191

end94.0ms (0.7%)

Compiler

Compiled 276 to 118 computations (57.2% saved)

Profiling

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