Details

Time bar (total: 6.0s)

analyze1.2s (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)

sample87.0ms (1.5%)

Algorithm
intervals
Results
11.0ms209×body128valid
2.0ms14×body1024valid
2.0ms17×body512valid
1.0ms16×body256valid
1.0ms19×body128invalid
Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify132.0ms (2.2%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
11.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.8b
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
17.1b
(-.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))
3.0b
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series67.0ms (1.1%)

Counts
2 → 96
Calls

2 calls:

46.0ms
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
21.0ms
(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (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:

6.0ms
(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms
(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify117.0ms (1.9%)

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

prune120.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1307137
Fresh101
Picked101
Done000
Total1327139
Error
0.0b
Counts
139 → 7
Alt Table
StatusErrorProgram
27.1b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
12.8b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
36.5b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 t z) (sqrt.f64 (-.f64 a t)))) (+.f64 x y))
36.8b
(fma.f64 y (*.f64 (sqrt.f64 (-.f64 t z)) (/.f64 (sqrt.f64 (-.f64 t z)) (-.f64 a t))) (+.f64 x y))
30.1b
(-.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))))
26.3b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
28.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 a y) t))
Compiler

Compiled 3630 to 1226 computations (66.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t z) (-.f64 a t))
1.6b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
2.7b
(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

series100.0ms (1.7%)

Counts
2 → 108
Calls

2 calls:

58.0ms
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
42.0ms
(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

rewrite24.0ms (0.4%)

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:

13.0ms
(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
4.0ms
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))

simplify154.0ms (2.6%)

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

prune184.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2441245
Fresh156
Picked011
Done000
Total2457252
Error
0.0b
Counts
252 → 7
Alt Table
StatusErrorProgram
27.1b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
12.8b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
36.5b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 t z) (sqrt.f64 (-.f64 a t)))) (+.f64 x y))
13.3b
(+.f64 y (+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))))
30.1b
(-.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))))
26.3b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
28.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 a y) t))
Compiler

Compiled 6816 to 2138 computations (68.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
0.6b
(cbrt.f64 (-.f64 a t))
7.0b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))
7.4b
(+.f64 y (+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))))

series161.0ms (2.7%)

Counts
4 → 156
Calls

4 calls:

54.0ms
(+.f64 y (+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))))
38.0ms
(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
37.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))
31.0ms
(cbrt.f64 (-.f64 a t))

rewrite73.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt_binary64
79×*-un-lft-identity_binary64
60×cbrt-prod_binary64
54×associate-*r*_binary64
50×times-frac_binary64
Counts
4 → 187
Calls

4 calls:

27.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))
13.0ms
(+.f64 y (+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))))
8.0ms
(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
2.0ms
(cbrt.f64 (-.f64 a t))

simplify202.0ms (3.4%)

Algorithm
egg-herbie
Rules
332×associate-*l*_binary64
297×times-frac_binary64
258×associate-/l*_binary64
236×associate-/r*_binary64
232×associate-*r/_binary64
Counts
343 → 366
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
057610846
116089621
248919621
349749621

prune381.0ms (6.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New4680468
Fresh055
Picked011
Done011
Total4687475
Error
0.0b
Counts
475 → 7
Alt Table
StatusErrorProgram
27.1b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
12.8b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
36.5b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 t z) (sqrt.f64 (-.f64 a t)))) (+.f64 x y))
13.3b
(+.f64 y (+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))))
30.1b
(-.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))))
26.3b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
28.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 a y) t))
Compiler

Compiled 17458 to 5650 computations (67.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
5.4b
(*.f64 (/.f64 y t) (-.f64 z a))

series50.0ms (0.8%)

Counts
2 → 108
Calls

2 calls:

32.0ms
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
19.0ms
(*.f64 (/.f64 y t) (-.f64 z a))

rewrite23.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
39×add-cube-cbrt_binary64
36×prod-diff_binary64
26×associate-+r+_binary64
Counts
2 → 108
Calls

2 calls:

8.0ms
(*.f64 (/.f64 y t) (-.f64 z a))
7.0ms
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

simplify128.0ms (2.1%)

Algorithm
egg-herbie
Rules
660×fma-def_binary64
488×distribute-rgt-in_binary64
459×distribute-lft-in_binary64
280×fma-neg_binary64
153×exp-prod_binary64
Counts
216 → 178
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02293204
14732592
215282538
346182538
450002538
549482538

prune131.0ms (2.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1744178
Fresh224
Picked011
Done022
Total1769185
Error
0b
Counts
185 → 9
Alt Table
StatusErrorProgram
26.9b
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) t) (-.f64 z a))))
27.2b
(+.f64 x (/.f64 (neg.f64 y) (/.f64 t (-.f64 a z))))
26.3b
(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
28.2b
(+.f64 x (/.f64 (*.f64 (-.f64 z a) y) t))
27.1b
(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
12.8b
(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
27.7b
(+.f64 x (*.f64 y (/.f64 (-.f64 z a) t)))
36.5b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 t z) (sqrt.f64 (-.f64 a t)))) (+.f64 x y))
13.3b
(+.f64 y (+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))))
Compiler

Compiled 3671 to 855 computations (76.7% saved)

regimes1.6s (25.9%)

Accuracy

Total 5.8b remaining (98.4%)

Threshold costs 0b (0%)

Counts
118 → 4
Compiler

Compiled 14124 to 8310 computations (41.2% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify18.0ms (0.3%)

Algorithm
egg-herbie
Rules
55×distribute-rgt-neg-in_binary64
48×cancel-sign-sub-inv_binary64
39×distribute-lft-neg-in_binary64
36×neg-sub0_binary64
36×neg-mul-1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042143
167141
293141
3119141
4134141
5146141
6160141
7170141
8191141
9212141
10238141
11272141
12303141
13320141
14331141
15335141
16336141
17332141

end1.0ms (0%)

Compiler

Compiled 101 to 37 computations (63.4% saved)

sample1.0s (17.2%)

Algorithm
intervals
Results
347.0ms6791×body128valid
70.0ms477×body512valid
59.0ms337×body1024valid
33.0ms712×body128invalid
32.0ms328×body256valid
14.0ms67×body2048valid
Compiler

Compiled 293 to 154 computations (47.4% saved)

Profiling

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