Details

Time bar (total: 6.3s)

analyze1.3s (20.1%)

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
3.5%96.2%0.2%10
9.8%89.9%0.2%11
14.1%85.7%0.2%12
22.6%77.1%0.2%13
23.7%76%0.2%14
Compiler

Compiled 19 to 12 computations (36.8% saved)

sample85.0ms (1.4%)

Algorithm
intervals
Results
10.0ms212×body128valid
3.0msbody1024valid
2.0ms31×body128invalid
2.0ms15×body512valid
2.0ms18×body256valid
0.0msbody2048valid
Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify133.0ms (2.1%)

Algorithm
egg-herbie
Rules
1303×div-sub_binary64
658×fma-def_binary64
640×sub-neg_binary64
569×unsub-neg_binary64
393×neg-mul-1_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01219
12319
25819
314317
434417
596717
6228217
7364617
8370017
9409717
10425317
11454317
12471917
13547817

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
11.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.9b
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
18.4b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t z) (-.f64 a t))
3.8b
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series63.0ms (1%)

Counts
2 → 96
Calls

2 calls:

44.0ms
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
18.0ms
(/.f64 (-.f64 t z) (-.f64 a t))

rewrite15.0ms (0.2%)

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:

10.0ms
(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify140.0ms (2.2%)

Algorithm
egg-herbie
Rules
671×times-frac_binary64
644×fma-neg_binary64
523×cancel-sign-sub-inv_binary64
397×sub-neg_binary64
195×div-sub_binary64
Counts
160 → 137
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02734255
17404157
224803550
344303531
451673531

prune129.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1289137
Fresh101
Picked101
Done000
Total1309139
Error
0.0b
Counts
139 → 9
Alt Table
StatusErrorProgram
12.9b
(fma.f64 y (*.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
25.5b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
23.9b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
23.4b
(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))
12.9b
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
31.8b
(-.f64 (+.f64 x (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 (*.f64 y z) t))) (*.f64 y (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
40.2b
(fma.f64 y (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (sqrt.f64 (-.f64 a t))) (/.f64 (cbrt.f64 (-.f64 t z)) (sqrt.f64 (-.f64 a t)))) (+.f64 x y))
40.3b
(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
12.9b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
Compiler

Compiled 3728 to 1274 computations (65.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t z) (-.f64 a t))
2.1b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
2.6b
(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

series79.0ms (1.2%)

Counts
2 → 108
Calls

2 calls:

47.0ms
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
32.0ms
(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

rewrite21.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
37×*-un-lft-identity_binary64
31×associate-*r*_binary64
26×times-frac_binary64
15×add-cube-cbrt_binary64
Counts
2 → 71
Calls

2 calls:

10.0ms
(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
4.0ms
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))

simplify157.0ms (2.5%)

Algorithm
egg-herbie
Rules
726×cancel-sign-sub-inv_binary64
429×sub-neg_binary64
380×fma-neg_binary64
179×associate-/l*_binary64
178×associate--r+_binary64
Counts
179 → 164
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02964775
18164523
231614173
348364173
449934173
549724173

prune227.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2414245
Fresh358
Picked101
Done000
Total2459254
Error
0.0b
Counts
254 → 9
Alt Table
StatusErrorProgram
11.3b
(+.f64 y (+.f64 x (*.f64 (*.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 a t))))))
12.9b
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
25.5b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
45.7b
(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)) 3))
13.0b
(+.f64 y (+.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (/.f64 (-.f64 t z) (-.f64 a t))))))
31.8b
(-.f64 (+.f64 x (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 (*.f64 y z) t))) (*.f64 y (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
23.9b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
40.3b
(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
16.5b
(+.f64 y (+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t)))))
Compiler

Compiled 6936 to 2207 computations (68.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
0.6b
(cbrt.f64 (-.f64 t z))
0.6b
(cbrt.f64 (-.f64 a t))
2.1b
(+.f64 y (+.f64 x (*.f64 (*.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 a t))))))

series163.0ms (2.6%)

Counts
4 → 132
Calls

4 calls:

64.0ms
(+.f64 y (+.f64 x (*.f64 (*.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 a t))))))
38.0ms
(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
31.0ms
(cbrt.f64 (-.f64 a t))
29.0ms
(cbrt.f64 (-.f64 t z))

rewrite27.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod_binary64
35×*-un-lft-identity_binary64
35×add-sqr-sqrt_binary64
16×cbrt-div_binary64
15×add-cube-cbrt_binary64
Counts
4 → 111
Calls

4 calls:

10.0ms
(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
5.0ms
(+.f64 y (+.f64 x (*.f64 (*.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 a t))))))
2.0ms
(cbrt.f64 (-.f64 a t))
2.0ms
(cbrt.f64 (-.f64 t z))

simplify163.0ms (2.6%)

Algorithm
egg-herbie
Rules
402×fma-neg_binary64
377×associate-*r*_binary64
270×associate-*l*_binary64
228×*-commutative_binary64
212×fma-def_binary64
Counts
243 → 257
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04897224
113586953
247116953
350186953

prune481.0ms (7.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4590459
Fresh088
Picked011
Done000
Total4599468
Error
0.0b
Counts
468 → 9
Alt Table
StatusErrorProgram
11.3b
(+.f64 y (+.f64 x (*.f64 (*.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 a t))))))
12.9b
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
25.5b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
45.7b
(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)) 3))
13.0b
(+.f64 y (+.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (/.f64 (-.f64 t z) (-.f64 a t))))))
31.8b
(-.f64 (+.f64 x (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 (*.f64 y z) t))) (*.f64 y (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
23.9b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
40.3b
(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
16.5b
(+.f64 y (+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t)))))
Compiler

Compiled 22927 to 7563 computations (67% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 a t) (-.f64 t z))
0.2b
(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
3.8b
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

series78.0ms (1.2%)

Counts
3 → 132
Calls

3 calls:

40.0ms
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
19.0ms
(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
19.0ms
(/.f64 (-.f64 a t) (-.f64 t z))

rewrite40.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
218×times-frac_binary64
195×*-un-lft-identity_binary64
195×add-sqr-sqrt_binary64
91×add-cube-cbrt_binary64
52×distribute-lft-out--_binary64
Counts
3 → 214
Calls

3 calls:

9.0ms
(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
8.0ms
(/.f64 (-.f64 a t) (-.f64 t z))
0.0ms
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

simplify187.0ms (3%)

Algorithm
egg-herbie
Rules
672×cancel-sign-sub-inv_binary64
565×sub-neg_binary64
292×fma-neg_binary64
225×+-commutative_binary64
218×associate--r+_binary64
Counts
346 → 344
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03988897
110398416
236808214
354598214

prune296.0ms (4.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3440344
Fresh077
Picked011
Done011
Total3449353
Error
0.0b
Counts
353 → 9
Alt Table
StatusErrorProgram
11.3b
(+.f64 y (+.f64 x (*.f64 (*.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))) (/.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 a t))))))
12.9b
(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
25.5b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
45.7b
(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)) 3))
13.0b
(+.f64 y (+.f64 x (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (/.f64 (-.f64 t z) (-.f64 a t))))))
31.8b
(-.f64 (+.f64 x (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 (*.f64 y z) t))) (*.f64 y (*.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
23.9b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
40.3b
(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
16.5b
(+.f64 y (+.f64 x (neg.f64 (/.f64 (*.f64 y z) (-.f64 a t)))))
Compiler

Compiled 9405 to 2842 computations (69.8% saved)

regimes1.4s (22.3%)

Accuracy

Total 5.5b remaining (99.1%)

Threshold costs 0b (0%)

Counts
115 → 4
Compiler

Compiled 14790 to 8520 computations (42.4% saved)

bsearch6.0ms (0.1%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify13.0ms (0.2%)

Algorithm
egg-herbie
Rules
27×+-commutative_binary64
24×*-commutative_binary64
19×sub-neg_binary64
15×neg-sub0_binary64
15×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052199
185199
2109199
3136199
4159199
5174199
6183199
7188199
8193199
9196199
10197199
11193199

end1.0ms (0%)

Compiler

Compiled 137 to 53 computations (61.3% saved)

sample1.1s (17.1%)

Algorithm
intervals
Results
336.0ms6727×body128valid
78.0ms380×body1024valid
65.0ms477×body512valid
34.0ms740×body128invalid
31.0ms345×body256valid
18.0ms71×body2048valid
Compiler

Compiled 362 to 185 computations (48.9% saved)

Profiling

Loading profile data...