Details

Time bar (total: 6.6s)

analyze1.0s (15.1%)

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
13.2%86.5%0.2%10
17%82.8%0.2%11
18.2%81.5%0.2%12
21.7%78.1%0.2%13
32.9%66.9%0.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample30.0ms (0.5%)

Algorithm
intervals
Results
9.0ms256×body128valid
1.0ms25×body128invalid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify173.0ms (2.6%)

Algorithm
egg-herbie
Rules
1133×div-sub_binary64
860×sub-neg_binary64
750×associate-/r/_binary64
699×cancel-sign-sub-inv_binary64
610×distribute-rgt-neg-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
12616
24916
38616
416616
529316
657016
7155916
8236616
9226816
10253216
11275316
12283916
13303416
14410916
15449516
16454316
17497316

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
11.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
11.7b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 48 to 30 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 x (*.f64 y z))
11.5b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

rewrite69.0ms (1%)

Algorithm
rewrite-expression-head
Error
11.6b
Rules
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
times-frac_binary64
add-exp-log_binary64 add-log-exp_binary64 add-cbrt-cube_binary64
flip3--_binary64 flip--_binary64 associate-/l*_binary64 associate-/r*_binary64
pow1_binary64 associate-/l/_binary64 associate-/r/_binary64
Counts
2 → 44
Calls

2 calls:

6.0ms
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
3.0ms
(-.f64 x (*.f64 y z))
Compiler

Compiled 941 to 165 computations (82.5% saved)

series163.0ms (2.5%)

Error
3.3b
Counts
2 → 52
Calls

2 calls:

116.0ms
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
27.0ms
(-.f64 x (*.f64 y z))
Compiler

Compiled 2338 to 1436 computations (38.6% saved)

simplify97.0ms (1.5%)

Algorithm
egg-herbie
Rules
474×associate-/l*_binary64
465×times-frac_binary64
295×associate-/r*_binary64
293×div-sub_binary64
256×cancel-sign-sub-inv_binary64
Counts
96 → 73
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01382083
14061978
213701900
346021891
451321891

prune67.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New601373
Fresh000
Picked101
Done000
Total611374
Error
3.2b
Counts
74 → 13
Alt Table
StatusErrorProgram
37.2b
(/.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (/.f64 (-.f64 t (*.f64 z a)) (sqrt.f64 (-.f64 x (*.f64 z y)))))
11.8b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
12.0b
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
32.6b
(/.f64 x (-.f64 t (*.f64 z a)))
34.6b
(/.f64 (/.f64 (-.f64 x (*.f64 z y)) (sqrt.f64 (-.f64 t (*.f64 z a)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
36.0b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y z) (*.f64 y z))) (*.f64 (-.f64 t (*.f64 z a)) (+.f64 (*.f64 z y) x)))
12.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))))
37.2b
(*.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (/.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (-.f64 t (*.f64 z a))))
34.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 z y))) (cbrt.f64 (-.f64 x (*.f64 z y)))) (sqrt.f64 (-.f64 t (*.f64 z a)))) (/.f64 (cbrt.f64 (-.f64 x (*.f64 z y))) (sqrt.f64 (-.f64 t (*.f64 z a)))))
37.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a))) 3))
35.6b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 z (*.f64 a a))) (-.f64 y (/.f64 x z))) (/.f64 x (*.f64 z a))))
37.5b
(*.f64 (/.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (*.f64 (cbrt.f64 (-.f64 t (*.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a))))) (/.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (cbrt.f64 (-.f64 t (*.f64 z a)))))
36.6b
(*.f64 (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))))
Compiler

Compiled 1679 to 538 computations (68% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 x (*.f64 y z))
0.5b
(/.f64 1 (-.f64 t (*.f64 z a)))
11.3b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

rewrite111.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
3.2b
Rules
26×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64 times-frac_binary64
19×add-cube-cbrt_binary64
16×add-exp-log_binary64
15×associate-*r*_binary64
Counts
3 → 87
Calls

3 calls:

11.0ms
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
5.0ms
(/.f64 1 (-.f64 t (*.f64 z a)))
3.0ms
(-.f64 x (*.f64 y z))
Compiler

Compiled 1898 to 576 computations (69.7% saved)

series197.0ms (3%)

Error
3.2b
Counts
3 → 69
Calls

3 calls:

115.0ms
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
37.0ms
(/.f64 1 (-.f64 t (*.f64 z a)))
27.0ms
(-.f64 x (*.f64 y z))
Compiler

Compiled 3150 to 2008 computations (36.3% saved)

simplify124.0ms (1.9%)

Algorithm
egg-herbie
Rules
620×times-frac_binary64
278×distribute-rgt-in_binary64
270×distribute-lft-in_binary64
246×cancel-sign-sub-inv_binary64
190×neg-mul-1_binary64
Counts
156 → 111
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01773087
14692817
216912724
346092715
450432715

prune79.0ms (1.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1074111
Fresh3912
Picked011
Done000
Total11014124
Error
3.2b
Counts
124 → 14
Alt Table
StatusErrorProgram
11.8b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
12.0b
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
39.4b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (*.f64 z z)))) (/.f64 x (*.f64 z a))))
45.1b
(/.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (*.f64 z y) 3)) (-.f64 t (*.f64 z a))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z)))))
32.6b
(/.f64 x (-.f64 t (*.f64 z a)))
34.6b
(/.f64 (/.f64 (-.f64 x (*.f64 z y)) (sqrt.f64 (-.f64 t (*.f64 z a)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
12.6b
(*.f64 (-.f64 x (*.f64 y z)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 t (*.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a))))) (/.f64 1 (cbrt.f64 (-.f64 t (*.f64 z a))))))
12.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))))
37.2b
(*.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (/.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (-.f64 t (*.f64 z a))))
34.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 z y))) (cbrt.f64 (-.f64 x (*.f64 z y)))) (sqrt.f64 (-.f64 t (*.f64 z a)))) (/.f64 (cbrt.f64 (-.f64 x (*.f64 z y))) (sqrt.f64 (-.f64 t (*.f64 z a)))))
37.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a))) 3))
35.6b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 z (*.f64 a a))) (-.f64 y (/.f64 x z))) (/.f64 x (*.f64 z a))))
36.6b
(*.f64 (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))))
12.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 z y))) (cbrt.f64 (-.f64 x (*.f64 z y)))) (cbrt.f64 (-.f64 x (*.f64 z y)))) (/.f64 1 (-.f64 t (*.f64 z a))))
Compiler

Compiled 2071 to 726 computations (64.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 x (*.f64 z y))
0.5b
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
11.4b
(/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y)))

rewrite157.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
3.2b
Rules
90×times-frac_binary64
55×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
18×associate-/r*_binary64
16×add-exp-log_binary64
11×associate-/r/_binary64
Counts
3 → 128
Calls

3 calls:

9.0ms
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
6.0ms
(/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y)))
3.0ms
(-.f64 x (*.f64 z y))
Compiler

Compiled 3377 to 812 computations (76% saved)

series287.0ms (4.3%)

Error
3.2b
Counts
3 → 86
Calls

3 calls:

118.0ms
(/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y)))
115.0ms
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
27.0ms
(-.f64 x (*.f64 z y))
Compiler

Compiled 4424 to 2777 computations (37.2% saved)

simplify201.0ms (3%)

Algorithm
egg-herbie
Rules
422×cancel-sign-sub-inv_binary64
330×distribute-rgt-in_binary64
299×distribute-lft-in_binary64
167×sub-neg_binary64
158×times-frac_binary64
Counts
214 → 169
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02565911
16965570
225895375
348255375
449885375

prune123.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1618169
Fresh8412
Picked011
Done101
Total17013183
Error
2.5b
Counts
183 → 13
Alt Table
StatusErrorProgram
11.7b
(*.f64 1 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 a z))))
12.0b
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
34.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (-.f64 t (*.f64 a z)))) (/.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 (-.f64 t (*.f64 a z))) (-.f64 x (*.f64 z y)))))
39.4b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (*.f64 z z)))) (/.f64 x (*.f64 z a))))
37.4b
(/.f64 1 (/.f64 (-.f64 (*.f64 t t) (*.f64 (*.f64 z a) (*.f64 z a))) (*.f64 (-.f64 x (*.f64 z y)) (+.f64 (*.f64 a z) t))))
35.8b
(/.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 (*.f64 z y) x) 1) (/.f64 t x)) (*.f64 (/.f64 a x) (+.f64 z (/.f64 (*.f64 z (*.f64 z y)) x)))))
39.3b
(/.f64 1 (+.f64 (/.f64 a y) (-.f64 (*.f64 (/.f64 x (*.f64 y y)) (-.f64 (/.f64 a z) (/.f64 t (*.f64 z z)))) (/.f64 t (*.f64 z y)))))
36.6b
(/.f64 1 (+.f64 (/.f64 (*.f64 (*.f64 z y) t) (*.f64 x x)) (/.f64 (-.f64 t (*.f64 a z)) x)))
37.2b
(*.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (/.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (-.f64 t (*.f64 z a))))
35.6b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 z (*.f64 a a))) (-.f64 y (/.f64 x z))) (/.f64 x (*.f64 z a))))
35.2b
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 z y) (*.f64 z y))) (-.f64 t (*.f64 a z))) (/.f64 1 (+.f64 x (*.f64 z y))))
36.6b
(*.f64 (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))))
11.9b
(/.f64 (/.f64 1 (-.f64 t (*.f64 a z))) (/.f64 1 (-.f64 x (*.f64 z y))))
Compiler

Compiled 3257 to 972 computations (70.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 x (*.f64 z y))
11.5b
(/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 a z)))

rewrite56.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
2.5b
Rules
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
times-frac_binary64
add-exp-log_binary64 add-log-exp_binary64 add-cbrt-cube_binary64
flip3--_binary64 flip--_binary64 associate-/l*_binary64 associate-/r*_binary64
pow1_binary64 associate-/l/_binary64 associate-/r/_binary64
Counts
2 → 44
Calls

2 calls:

6.0ms
(/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 a z)))
3.0ms
(-.f64 x (*.f64 z y))
Compiler

Compiled 1027 to 251 computations (75.6% saved)

series162.0ms (2.4%)

Error
2.5b
Counts
2 → 52
Calls

2 calls:

116.0ms
(/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 a z)))
28.0ms
(-.f64 x (*.f64 z y))
Compiler

Compiled 2520 to 1618 computations (35.8% saved)

simplify108.0ms (1.6%)

Algorithm
egg-herbie
Rules
475×associate-/l*_binary64
467×times-frac_binary64
294×associate-/r*_binary64
293×div-sub_binary64
258×cancel-sign-sub-inv_binary64
Counts
96 → 68
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01352083
13961978
213691900
346171891
451571891

prune58.0ms (0.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New67168
Fresh11011
Picked011
Done011
Total681381
Error
2.5b
Counts
81 → 13
Alt Table
StatusErrorProgram
11.7b
(*.f64 1 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 a z))))
12.0b
(/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) (-.f64 x (*.f64 z y))))
39.4b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (*.f64 z z)))) (/.f64 x (*.f64 z a))))
37.4b
(/.f64 1 (/.f64 (-.f64 (*.f64 t t) (*.f64 (*.f64 z a) (*.f64 z a))) (*.f64 (-.f64 x (*.f64 z y)) (+.f64 (*.f64 a z) t))))
35.8b
(/.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 (*.f64 z y) x) 1) (/.f64 t x)) (*.f64 (/.f64 a x) (+.f64 z (/.f64 (*.f64 z (*.f64 z y)) x)))))
39.3b
(/.f64 1 (+.f64 (/.f64 a y) (-.f64 (*.f64 (/.f64 x (*.f64 y y)) (-.f64 (/.f64 a z) (/.f64 t (*.f64 z z)))) (/.f64 t (*.f64 z y)))))
36.6b
(/.f64 1 (+.f64 (/.f64 (*.f64 (*.f64 z y) t) (*.f64 x x)) (/.f64 (-.f64 t (*.f64 a z)) x)))
37.2b
(*.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (/.f64 (sqrt.f64 (-.f64 x (*.f64 z y))) (-.f64 t (*.f64 z a))))
35.6b
(+.f64 (/.f64 y a) (-.f64 (*.f64 (/.f64 t (*.f64 z (*.f64 a a))) (-.f64 y (/.f64 x z))) (/.f64 x (*.f64 z a))))
35.2b
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 z y) (*.f64 z y))) (-.f64 t (*.f64 a z))) (/.f64 1 (+.f64 x (*.f64 z y))))
36.6b
(*.f64 (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (*.f64 z y)) (-.f64 t (*.f64 z a)))))
34.6b
(*.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (-.f64 t (*.f64 z a)))) (/.f64 (-.f64 x (*.f64 z y)) (sqrt.f64 (-.f64 t (*.f64 z a))))))
11.9b
(/.f64 (/.f64 1 (-.f64 t (*.f64 a z))) (/.f64 1 (-.f64 x (*.f64 z y))))
Compiler

Compiled 1359 to 463 computations (65.9% saved)

regimes2.4s (35.7%)

Accuracy

Total 4.5b remaining (67%)

Threshold costs 0b (0%)

Compiler

Compiled 29990 to 16686 computations (44.4% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
sub-neg_binary64 +-commutative_binary64
*-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64
cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
not-or if-if-or-not_binary64 distribute-lft-neg-out_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
026119
14296
26596
38094
48794
58994
68994

end1.0ms (0%)

Compiler

Compiled 68 to 24 computations (64.7% saved)

sample946.0ms (14.3%)

Algorithm
intervals
Results
313.0ms8000×body128valid
26.0ms768×body128invalid
Compiler

Compiled 434 to 237 computations (45.4% saved)

Profiling

Loading profile data...