Details

Time bar (total: 6.3s)

analyze1.1s (17.3%)

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
15.6%84.2%0.2%8
15.6%84.2%0.2%9
20.3%79.5%0.2%10
25.3%74.5%0.2%11
34.2%65.6%0.2%12
37.4%62%0.6%13
41.7%57.7%0.6%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample34.0ms (0.5%)

Algorithm
intervals
Results
15.0ms256×body128valid
5.0ms99×body128invalid
Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify338.0ms (5.4%)

Algorithm
egg-herbie
Rules
1775×cancel-sign-sub-inv_binary64
1670×distribute-rgt-in_binary64
1374×div-sub_binary64
1020×distribute-lft-in_binary64
922×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01222
12522
25822
310722
421522
540816
677316
7179716
8201916
9215016
10274116
11292516
12302616
13476816
14348416
15353816
16365916
17365516
18366216
19371016
20372916
21373016
22373016
23282016
24336416
25398816
26370216
27480016

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 2
Alt Table
StatusErrorProgram
2.7b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
4.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
Compiler

Compiled 83 to 56 computations (32.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
0.0b
(-.f64 y (/.f64 t y))
0.4b
(/.f64 -1/3 z)
2.6b
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))

rewrite188.0ms (3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
70×add-sqr-sqrt_binary64
66×times-frac_binary64
65×cancel-sign-sub-inv_binary64
59×*-un-lft-identity_binary64
55×add-cube-cbrt_binary64
Counts
4 → 160
Calls

4 calls:

12.0ms
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
7.0ms
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
6.0ms
(-.f64 y (/.f64 t y))
2.0ms
(/.f64 -1/3 z)
Compiler

Compiled 3251 to 1406 computations (56.8% saved)

series130.0ms (2.1%)

Error
0.0b
Counts
4 → 57
Calls

4 calls:

61.0ms
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
35.0ms
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
15.0ms
(-.f64 y (/.f64 t y))
4.0ms
(/.f64 -1/3 z)
Compiler

Compiled 1526 to 1020 computations (33.2% saved)

simplify136.0ms (2.2%)

Algorithm
egg-herbie
Rules
555×distribute-rgt-in_binary64
254×distribute-lft-neg-out_binary64
245×distribute-rgt-neg-out_binary64
200×associate-*l*_binary64
194×associate-*r*_binary64
Counts
217 → 147
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02393330
16893162
223532901
347402901
450022901

prune80.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1398147
Fresh011
Picked101
Done000
Total1409149
Error
0.0b
Counts
149 → 9
Alt Table
StatusErrorProgram
35.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
36.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
34.5b
(+.f64 x (*.f64 (/.f64 -1/3 z) (+.f64 y (/.f64 (/.f64 (neg.f64 t) (sqrt.f64 y)) (sqrt.f64 y)))))
30.2b
(+.f64 x (cbrt.f64 (*.f64 -1/27 (pow.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 3))))
23.0b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
29.3b
(+.f64 x (*.f64 (sqrt.f64 (/.f64 -1/3 z)) (*.f64 (-.f64 y (/.f64 t y)) (sqrt.f64 (/.f64 -1/3 z)))))
4.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.2b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 1/3 (/.f64 t (*.f64 y z)))))
2.8b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z)))
Compiler

Compiled 2010 to 961 computations (52.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (neg.f64 t) (/.f64 1 y))
0.3b
(*.f64 -1/3 (/.f64 y z))
0.4b
(/.f64 -1/3 z)
3.5b
(*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z))

rewrite184.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
55×add-exp-log_binary64
49×add-sqr-sqrt_binary64
39×times-frac_binary64
39×associate-*r*_binary64
38×*-un-lft-identity_binary64
Counts
4 → 149
Calls

4 calls:

8.0ms
(*.f64 -1/3 (/.f64 y z))
8.0ms
(*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z))
7.0ms
(*.f64 (neg.f64 t) (/.f64 1 y))
2.0ms
(/.f64 -1/3 z)
Compiler

Compiled 3492 to 1999 computations (42.8% saved)

series57.0ms (0.9%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

24.0ms
(*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z))
14.0ms
(*.f64 -1/3 (/.f64 y z))
11.0ms
(*.f64 (neg.f64 t) (/.f64 1 y))
4.0ms
(/.f64 -1/3 z)
Compiler

Compiled 1044 to 736 computations (29.5% saved)

simplify121.0ms (1.9%)

Algorithm
egg-herbie
Rules
381×distribute-lft-neg-out_binary64
355×times-frac_binary64
300×distribute-rgt-neg-out_binary64
298×associate-*l*_binary64
231×div-sub_binary64
Counts
173 → 110
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02042063
15101690
219231690
342291689
449951689
549661689

prune75.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1082110
Fresh358
Picked101
Done000
Total1127119
Error
0.0b
Counts
119 → 7
Alt Table
StatusErrorProgram
35.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
36.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
23.0b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
1.5b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (/.f64 (*.f64 1/3 t) z) y))
4.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.2b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 1/3 (/.f64 t (*.f64 y z)))))
2.8b
(+.f64 (+.f64 (/.f64 (*.f64 y -1/3) z) x) (*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z)))
Compiler

Compiled 1725 to 932 computations (46% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (*.f64 1/3 t) z)
0.3b
(*.f64 -1/3 (/.f64 y z))
0.4b
(*.f64 1/3 t)
3.6b
(/.f64 (/.f64 (*.f64 1/3 t) z) y)

rewrite141.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
46×times-frac_binary64
39×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64
32×add-cube-cbrt_binary64
25×add-cbrt-cube_binary64
Counts
4 → 119
Calls

4 calls:

5.0ms
(*.f64 -1/3 (/.f64 y z))
5.0ms
(/.f64 (/.f64 (*.f64 1/3 t) z) y)
3.0ms
(/.f64 (*.f64 1/3 t) z)
3.0ms
(*.f64 1/3 t)
Compiler

Compiled 2495 to 1356 computations (45.7% saved)

series55.0ms (0.9%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

23.0ms
(/.f64 (/.f64 (*.f64 1/3 t) z) y)
13.0ms
(*.f64 -1/3 (/.f64 y z))
11.0ms
(/.f64 (*.f64 1/3 t) z)
4.0ms
(*.f64 1/3 t)
Compiler

Compiled 961 to 653 computations (32% saved)

simplify141.0ms (2.3%)

Algorithm
egg-herbie
Rules
659×associate-*l/_binary64
484×associate-*l*_binary64
470×associate-*r/_binary64
458×associate-/r*_binary64
350×associate-/r/_binary64
Counts
143 → 73
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01931792
14481615
214031612
339231612
443031612
547881612
649331612

prune70.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New71273
Fresh156
Picked011
Done000
Total72880
Error
0b
Counts
80 → 8
Alt Table
StatusErrorProgram
1.8b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (/.f64 1/3 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 t z) (cbrt.f64 y))))
23.0b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
1.5b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (/.f64 (*.f64 1/3 t) z) y))
1.4b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y)))
35.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
36.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
4.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
2.8b
(+.f64 (+.f64 (/.f64 (*.f64 y -1/3) z) x) (*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z)))
Compiler

Compiled 1488 to 805 computations (45.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y)))
0.3b
(*.f64 -1/3 (/.f64 t z))
0.3b
(*.f64 -1/3 (/.f64 y z))
3.6b
(/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y))

rewrite149.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
36×add-sqr-sqrt_binary64
30×times-frac_binary64
28×*-un-lft-identity_binary64
26×associate-*r*_binary64
26×add-cube-cbrt_binary64
Counts
4 → 118
Calls

4 calls:

9.0ms
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y)))
5.0ms
(/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y))
5.0ms
(*.f64 -1/3 (/.f64 y z))
5.0ms
(*.f64 -1/3 (/.f64 t z))
Compiler

Compiled 2691 to 1267 computations (52.9% saved)

series111.0ms (1.8%)

Error
0b
Counts
4 → 48
Calls

4 calls:

59.0ms
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y)))
23.0ms
(/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y))
13.0ms
(*.f64 -1/3 (/.f64 y z))
11.0ms
(*.f64 -1/3 (/.f64 t z))
Compiler

Compiled 1530 to 1042 computations (31.9% saved)

simplify103.0ms (1.7%)

Algorithm
egg-herbie
Rules
444×associate-/r/_binary64
356×distribute-rgt-in_binary64
336×distribute-lft-in_binary64
162×cancel-sign-sub-inv_binary64
148×associate-/l*_binary64
Counts
166 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02302438
16282133
220582108
349452108
449342108

prune58.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New90191
Fresh156
Picked011
Done101
Total92799
Error
0b
Counts
99 → 7
Alt Table
StatusErrorProgram
35.5b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
36.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
23.0b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
1.4b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 (*.f64 -1/3 (/.f64 t z)) (neg.f64 y)))
4.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
2.8b
(+.f64 (+.f64 (/.f64 (*.f64 y -1/3) z) x) (*.f64 (*.f64 (neg.f64 t) (/.f64 1 y)) (/.f64 -1/3 z)))
1.5b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (/.f64 1 (*.f64 3 (/.f64 y (/.f64 t z)))))
Compiler

Compiled 1307 to 642 computations (50.9% saved)

regimes1.8s (28.9%)

Accuracy

Total 1.4b remaining (98.1%)

Threshold costs 0b (0%)

Compiler

Compiled 28378 to 18963 computations (33.2% saved)

bsearch9.0ms (0.1%)

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

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
03288
14688
24888
34988
44988

end1.0ms (0%)

Compiler

Compiled 63 to 40 computations (36.5% saved)

sample1.1s (18.2%)

Algorithm
intervals
Results
457.0ms8000×body128valid
165.0ms3175×body128invalid
Compiler

Compiled 251 to 161 computations (35.9% saved)

Profiling

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