Details

Time bar (total: 10.6s)

analyze1.6s (15.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
5.8%93.9%0.3%11
8.4%91.3%0.3%12
9.7%90%0.3%13
10.7%89%0.3%14
Compiler

Compiled 24 to 16 computations (33.3% saved)

sample30.0ms (0.3%)

Algorithm
intervals
Results
15.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
associate-/l*_binary64
associate-/r/_binary64
associate-+r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01625
12925
24125
34725
44925
54825

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
16.7b
Counts
1 → 1
Alt Table
StatusErrorProgram
16.7b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
Compiler

Compiled 46 to 30 computations (34.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (/.f64 (*.f64 y z) t))
3.8b
(/.f64 (*.f64 y b) t)
5.2b
(/.f64 (*.f64 y z) t)
13.1b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

rewrite151.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
12.2b
Rules
58×*-un-lft-identity_binary64
26×times-frac_binary64
22×distribute-lft-out_binary64
19×add-sqr-sqrt_binary64
19×add-cube-cbrt_binary64
Counts
4 → 101
Calls

4 calls:

12.0ms
(+.f64 x (/.f64 (*.f64 y z) t))
10.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
3.0ms
(/.f64 (*.f64 y b) t)
3.0ms
(/.f64 (*.f64 y z) t)
Compiler

Compiled 2332 to 739 computations (68.3% saved)

series287.0ms (2.7%)

Error
4.1b
Counts
4 → 81
Calls

4 calls:

184.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
39.0ms
(+.f64 x (/.f64 (*.f64 y z) t))
21.0ms
(/.f64 (*.f64 y b) t)
21.0ms
(/.f64 (*.f64 y z) t)
Compiler

Compiled 5204 to 3303 computations (36.5% saved)

simplify151.0ms (1.4%)

Algorithm
egg-herbie
Rules
624×distribute-rgt-in_binary64
378×cancel-sign-sub-inv_binary64
277×times-frac_binary64
270×associate-/l*_binary64
140×sub-neg_binary64
Counts
182 → 108
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02654270
17614127
229933989
348623989
450313989

prune63.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9810108
Fresh000
Picked101
Done000
Total9910109
Error
1.1b
Counts
109 → 10
Alt Table
StatusErrorProgram
16.8b
(*.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
28.9b
(+.f64 (/.f64 x (+.f64 1 a)) (*.f64 (/.f64 y t) (-.f64 (/.f64 z (+.f64 1 a)) (/.f64 (*.f64 b x) (pow.f64 (+.f64 1 a) 2)))))
17.5b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (*.f64 y (/.f64 b t))))
42.4b
(/.f64 (*.f64 y z) (*.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
41.8b
(-.f64 (+.f64 (/.f64 z b) (/.f64 x (/.f64 (*.f64 y b) t))) (*.f64 (/.f64 z (*.f64 b b)) (+.f64 (/.f64 t y) (/.f64 (*.f64 a t) y))))
33.6b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))) (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
16.3b
(/.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
16.8b
(/.f64 (+.f64 x (*.f64 y (/.f64 z t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
42.5b
(+.f64 (/.f64 z b) (-.f64 (*.f64 (/.f64 t y) (-.f64 (/.f64 x b) (/.f64 z (*.f64 b b)))) (+.f64 (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b))) (*.f64 (/.f64 x (*.f64 y (*.f64 b b))) (+.f64 (/.f64 (*.f64 t t) y) (/.f64 (*.f64 a (*.f64 t t)) y))))))
34.1b
(*.f64 (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (*.f64 (-.f64 a 1) (+.f64 (*.f64 t (+.f64 1 a)) (*.f64 y b)))) (*.f64 (-.f64 a 1) t))
Compiler

Compiled 2232 to 892 computations (60% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b
(/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
3.8b
(/.f64 (*.f64 y b) t)
5.3b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
13.1b
(/.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

rewrite149.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
0.8b
Rules
61×*-un-lft-identity_binary64
34×add-exp-log_binary64
33×times-frac_binary64
28×add-sqr-sqrt_binary64
26×add-cbrt-cube_binary64
Counts
4 → 128
Calls

4 calls:

10.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
8.0ms
(/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
6.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
3.0ms
(/.f64 (*.f64 y b) t)
Compiler

Compiled 3946 to 998 computations (74.7% saved)

series343.0ms (3.2%)

Error
1.1b
Counts
4 → 66
Calls

4 calls:

194.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
74.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
36.0ms
(/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
22.0ms
(/.f64 (*.f64 y b) t)
Compiler

Compiled 5286 to 3381 computations (36% saved)

simplify217.0ms (2%)

Algorithm
egg-herbie
Rules
436×times-frac_binary64
366×associate-/l*_binary64
263×associate-/r*_binary64
223×associate-*l*_binary64
187×associate-*r*_binary64
Counts
194 → 139
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03476073
19654624
243614608
348094608
449974608
549434608

prune76.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1354139
Fresh369
Picked101
Done000
Total13910149
Error
0.8b
Counts
149 → 10
Alt Table
StatusErrorProgram
41.8b
(-.f64 (+.f64 (/.f64 z b) (/.f64 x (/.f64 (*.f64 y b) t))) (*.f64 (/.f64 z (*.f64 b b)) (+.f64 (/.f64 t y) (/.f64 (*.f64 a t) y))))
16.8b
(*.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
42.4b
(/.f64 (*.f64 y z) (*.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
33.6b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))) (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
16.4b
(*.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
16.5b
(/.f64 (+.f64 x (/.f64 1 (/.f64 (/.f64 t y) z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
30.3b
(-.f64 (/.f64 x (+.f64 1 a)) (+.f64 (/.f64 (*.f64 y (*.f64 b x)) (*.f64 t (pow.f64 (+.f64 1 a) 2))) (*.f64 (/.f64 y (-.f64 -1 a)) (/.f64 z t))))
16.9b
(/.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1) (*.f64 y (/.f64 b t))))
42.5b
(+.f64 (/.f64 z b) (-.f64 (*.f64 (/.f64 t y) (-.f64 (/.f64 x b) (/.f64 z (*.f64 b b)))) (+.f64 (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b))) (*.f64 (/.f64 x (*.f64 y (*.f64 b b))) (+.f64 (/.f64 (*.f64 t t) y) (/.f64 (*.f64 a (*.f64 t t)) y))))))
34.1b
(*.f64 (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (*.f64 (-.f64 a 1) (+.f64 (*.f64 t (+.f64 1 a)) (*.f64 y b)))) (*.f64 (-.f64 a 1) t))
Compiler

Compiled 3152 to 1170 computations (62.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b
(/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
3.8b
(/.f64 (*.f64 y b) t)
5.3b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
12.5b
(*.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))

rewrite163.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.8b
Rules
41×*-un-lft-identity_binary64
41×add-exp-log_binary64
34×add-sqr-sqrt_binary64
30×times-frac_binary64
29×add-cbrt-cube_binary64
Counts
4 → 130
Calls

4 calls:

16.0ms
(*.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
9.0ms
(/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
7.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
4.0ms
(/.f64 (*.f64 y b) t)
Compiler

Compiled 4439 to 1199 computations (73% saved)

series377.0ms (3.6%)

Error
0.8b
Counts
4 → 66
Calls

4 calls:

225.0ms
(*.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
78.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
32.0ms
(/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
22.0ms
(/.f64 (*.f64 y b) t)
Compiler

Compiled 5404 to 3494 computations (35.3% saved)

simplify164.0ms (1.6%)

Algorithm
egg-herbie
Rules
422×times-frac_binary64
359×associate-/l*_binary64
257×associate-/r*_binary64
249×associate-*l*_binary64
207×associate-*r*_binary64
Counts
196 → 147
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03415565
19814261
243504261
347944187
449534187

prune95.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1461147
Fresh189
Picked101
Done000
Total1489157
Error
0.8b
Counts
157 → 9
Alt Table
StatusErrorProgram
16.9b
(*.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (/.f64 1 (+.f64 1 (+.f64 a (*.f64 y (/.f64 b t))))))
33.6b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))) (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
41.8b
(-.f64 (+.f64 (/.f64 z b) (/.f64 x (/.f64 (*.f64 y b) t))) (*.f64 (/.f64 z (*.f64 b b)) (+.f64 (/.f64 t y) (/.f64 (*.f64 a t) y))))
16.8b
(*.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
42.4b
(/.f64 (*.f64 y z) (*.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
16.5b
(/.f64 (+.f64 x (/.f64 1 (/.f64 (/.f64 t y) z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
30.3b
(-.f64 (/.f64 x (+.f64 1 a)) (+.f64 (/.f64 (*.f64 y (*.f64 b x)) (*.f64 t (pow.f64 (+.f64 1 a) 2))) (*.f64 (/.f64 y (-.f64 -1 a)) (/.f64 z t))))
42.5b
(+.f64 (/.f64 z b) (-.f64 (*.f64 (/.f64 t y) (-.f64 (/.f64 x b) (/.f64 z (*.f64 b b)))) (+.f64 (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b))) (*.f64 (/.f64 x (*.f64 y (*.f64 b b))) (+.f64 (/.f64 (*.f64 t t) y) (/.f64 (*.f64 a (*.f64 t t)) y))))))
34.1b
(*.f64 (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (*.f64 (-.f64 a 1) (+.f64 (*.f64 t (+.f64 1 a)) (*.f64 y b)))) (*.f64 (-.f64 a 1) t))
Compiler

Compiled 3436 to 1381 computations (59.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(/.f64 1 (/.f64 (/.f64 t y) z))
3.8b
(/.f64 (*.f64 y b) t)
4.6b
(/.f64 (/.f64 t y) z)
13.1b
(/.f64 (+.f64 x (/.f64 1 (/.f64 (/.f64 t y) z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

rewrite411.0ms (3.9%)

Algorithm
rewrite-expression-head
Error
0.8b
Rules
496×times-frac_binary64
292×*-un-lft-identity_binary64
244×add-sqr-sqrt_binary64
244×add-cube-cbrt_binary64
54×associate-/r*_binary64
Counts
4 → 344
Calls

4 calls:

39.0ms
(/.f64 (+.f64 x (/.f64 1 (/.f64 (/.f64 t y) z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
9.0ms
(/.f64 1 (/.f64 (/.f64 t y) z))
6.0ms
(/.f64 (/.f64 t y) z)
5.0ms
(/.f64 (*.f64 y b) t)
Compiler

Compiled 10143 to 4043 computations (60.1% saved)

series307.0ms (2.9%)

Error
0.8b
Counts
4 → 66
Calls

4 calls:

175.0ms
(/.f64 (+.f64 x (/.f64 1 (/.f64 (/.f64 t y) z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
78.0ms
(/.f64 1 (/.f64 (/.f64 t y) z))
22.0ms
(/.f64 (/.f64 t y) z)
19.0ms
(/.f64 (*.f64 y b) t)
Compiler

Compiled 4905 to 3134 computations (36.1% saved)

simplify329.0ms (3.1%)

Algorithm
egg-herbie
Rules
423×cancel-sign-sub-inv_binary64
342×associate-/r/_binary64
295×associate-/l*_binary64
293×times-frac_binary64
259×associate-/l/_binary64
Counts
410 → 322
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04619876
111478819
240468729
349828729
449838729

prune158.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3211322
Fresh178
Picked011
Done000
Total3229331
Error
0.8b
Counts
331 → 9
Alt Table
StatusErrorProgram
16.9b
(*.f64 (+.f64 x (/.f64 (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (/.f64 1 (+.f64 1 (+.f64 a (*.f64 y (/.f64 b t))))))
33.6b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))) (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (sqrt.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
41.8b
(-.f64 (+.f64 (/.f64 z b) (/.f64 x (/.f64 (*.f64 y b) t))) (*.f64 (/.f64 z (*.f64 b b)) (+.f64 (/.f64 t y) (/.f64 (*.f64 a t) y))))
42.4b
(/.f64 (*.f64 y z) (*.f64 t (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
16.5b
(/.f64 (+.f64 x (/.f64 1 (/.f64 (/.f64 t y) z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
30.3b
(-.f64 (/.f64 x (+.f64 1 a)) (+.f64 (/.f64 (*.f64 y (*.f64 b x)) (*.f64 t (pow.f64 (+.f64 1 a) 2))) (*.f64 (/.f64 y (-.f64 -1 a)) (/.f64 z t))))
42.5b
(+.f64 (/.f64 z b) (-.f64 (*.f64 (/.f64 t y) (-.f64 (/.f64 x b) (/.f64 z (*.f64 b b)))) (+.f64 (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b))) (*.f64 (/.f64 x (*.f64 y (*.f64 b b))) (+.f64 (/.f64 (*.f64 t t) y) (/.f64 (*.f64 a (*.f64 t t)) y))))))
34.1b
(*.f64 (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (*.f64 (-.f64 a 1) (+.f64 (*.f64 t (+.f64 1 a)) (*.f64 y b)))) (*.f64 (-.f64 a 1) t))
17.1b
(/.f64 (+.f64 x (/.f64 (/.f64 y t) (/.f64 1 z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
Compiler

Compiled 4893 to 1635 computations (66.6% saved)

regimes4.3s (40.9%)

Accuracy

Total 8.5b remaining (90.1%)

Threshold costs 0b (0%)

Compiler

Compiled 67895 to 40928 computations (39.7% saved)

bsearch15.0ms (0.1%)

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
049156
168156
278156
396156
4117156
5137156
6150156
7157156
8159156
9158156

end1.0ms (0%)

Compiler

Compiled 109 to 56 computations (48.6% saved)

sample1.1s (10.3%)

Algorithm
intervals
Results
535.0ms8000×body128valid
16.0ms270×body128invalid
Compiler

Compiled 437 to 260 computations (40.5% saved)

Profiling

Loading profile data...