Details

Time bar (total: 8.4s)

analyze1.3s (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
6.2%93.6%0.2%9
9.4%90.4%0.2%10
14%83.4%2.5%11
18.7%78.2%3.1%12
28.1%65.5%6.4%13
30.7%59.4%9.9%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample52.0ms (0.6%)

Algorithm
intervals
Results
20.0ms256×body128valid
13.0ms221×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify16.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
12522
24322
35122
44922
54922

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
35.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
35.1b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 38 to 22 computations (42.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
21.2b
(/.f64 (*.f64 z z) (*.f64 t t))
25.0b
(/.f64 (*.f64 x x) (*.f64 y y))

rewrite74.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
8.1b
Rules
27×add-cbrt-cube_binary64
27×add-exp-log_binary64
cbrt-unprod_binary64
cbrt-undiv_binary64
div-exp_binary64
Counts
3 → 55
Calls

3 calls:

8.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
7.0ms
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
4.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
Compiler

Compiled 1291 to 211 computations (83.7% saved)

series106.0ms (1.3%)

Error
30.2b
Counts
3 → 36
Calls

3 calls:

67.0ms
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z z) (*.f64 t t)))
19.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
13.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 1107 to 823 computations (25.7% saved)

simplify80.0ms (1%)

Algorithm
egg-herbie
Rules
738×associate-/l*_binary64
645×associate-*l/_binary64
471×associate-*r/_binary64
384×associate-/r*_binary64
342×unswap-sqr_binary64
Counts
91 → 68
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01141508
13271369
211681274
342241249
449761249

prune26.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New61768
Fresh000
Picked101
Done000
Total62769
Error
8.1b
Counts
69 → 7
Alt Table
StatusErrorProgram
26.3b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
26.6b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
23.7b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
23.4b
(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (/.f64 (*.f64 z z) (*.f64 t t)))
21.7b
(+.f64 (/.f64 x (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
19.7b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
38.9b
(+.f64 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y)))) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 590 to 236 computations (60% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
0.3b
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
21.2b
(/.f64 (*.f64 z z) (*.f64 t t))

rewrite127.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
117×add-sqr-sqrt_binary64
72×fabs-mul_binary64
61×times-frac_binary64
35×*-un-lft-identity_binary64
35×add-cube-cbrt_binary64
Counts
3 → 134
Calls

3 calls:

12.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
8.0ms
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
5.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
Compiler

Compiled 3465 to 545 computations (84.3% saved)

series79.0ms (0.9%)

Error
3.6b
Counts
3 → 30
Calls

3 calls:

48.0ms
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
15.0ms
(/.f64 (*.f64 z z) (*.f64 t t))
11.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
Compiler

Compiled 1025 to 721 computations (29.7% saved)

simplify164.0ms (2%)

Algorithm
egg-herbie
Rules
695×times-frac_binary64
663×associate-/l*_binary64
459×*-commutative_binary64
242×associate-/r*_binary64
187×associate-*l*_binary64
Counts
164 → 149
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02253207
14892564
216822419
342122328
448012328
549502328

prune69.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1445149
Fresh336
Picked101
Done000
Total1488156
Error
0.1b
Counts
156 → 8
Alt Table
StatusErrorProgram
44.5b
(/.f64 (-.f64 (pow.f64 (/.f64 x y) 4) (pow.f64 (/.f64 z t) 4)) (-.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (*.f64 z z) (*.f64 t t))))
0.4b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
23.4b
(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (/.f64 (*.f64 z z) (*.f64 t t)))
41.0b
(+.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
4.2b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 z (/.f64 t (/.f64 z t))))
26.3b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
21.7b
(+.f64 (/.f64 x (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
20.1b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (/.f64 (*.f64 z z) (*.f64 t t)))
Compiler

Compiled 2054 to 606 computations (70.5% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
0.3b
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
0.3b
(*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t)))

rewrite261.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
231×add-sqr-sqrt_binary64
144×fabs-mul_binary64
120×times-frac_binary64
67×*-un-lft-identity_binary64
67×add-cube-cbrt_binary64
Counts
3 → 218
Calls

3 calls:

11.0ms
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
11.0ms
(*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t)))
11.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
Compiler

Compiled 6032 to 892 computations (85.2% saved)

series56.0ms (0.7%)

Error
0.1b
Counts
3 → 24
Calls

3 calls:

33.0ms
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
11.0ms
(*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t)))
10.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
Compiler

Compiled 937 to 621 computations (33.7% saved)

simplify214.0ms (2.5%)

Algorithm
egg-herbie
Rules
614×associate-/l*_binary64
309×associate-*l*_binary64
302×associate-*r*_binary64
237×associate-*l/_binary64
233×associate-*r/_binary64
Counts
242 → 229
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03405245
16684033
222833813
343653753
449123753
549813753

prune140.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2218229
Fresh257
Picked101
Done000
Total22413237
Error
0.0b
Counts
237 → 13
Alt Table
StatusErrorProgram
26.3b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
21.6b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (fabs.f64 z) (/.f64 z (*.f64 t t))))
23.4b
(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (/.f64 (*.f64 z z) (*.f64 t t)))
41.0b
(+.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
21.7b
(+.f64 (/.f64 x (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.1b
(+.f64 (*.f64 (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (/.f64 x (pow.f64 (cbrt.f64 y) 3))) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
1.0b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (*.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 t)) (/.f64 z (pow.f64 (cbrt.f64 t) 3))) (/.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))))
4.2b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 z (/.f64 t (/.f64 z t))))
39.9b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (*.f64 (/.f64 z t) (sqrt.f64 z)) (fabs.f64 (/.f64 (sqrt.f64 z) t))))
14.3b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (*.f64 (/.f64 z t) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (fabs.f64 (/.f64 (cbrt.f64 z) t))))
14.8b
(+.f64 (/.f64 (*.f64 x (/.f64 x y)) (fabs.f64 y)) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
34.2b
(/.f64 (-.f64 (pow.f64 (/.f64 x y) 4) (pow.f64 (/.f64 z t) 4)) (-.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2)))
0.8b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
Compiler

Compiled 3874 to 1066 computations (72.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2)))
17.9b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
17.9b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
17.9b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))

rewrite575.0ms (6.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
186×cbrt-prod_binary64
124×add-sqr-sqrt_binary64
115×unpow-prod-down_binary64
75×times-frac_binary64
64×*-un-lft-identity_binary64
Counts
4 → 195
Calls

4 calls:

19.0ms
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2)))
3.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
3.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
3.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
Compiler

Compiled 7691 to 3383 computations (56% saved)

series164.0ms (1.9%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

36.0ms
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2)))
36.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
35.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
34.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
Compiler

Compiled 2830 to 1850 computations (34.6% saved)

simplify273.0ms (3.2%)

Algorithm
egg-herbie
Rules
709×unswap-sqr_binary64
466×exp-prod_binary64
328×log-pow_binary64
299×log-prod_binary64
215×*-commutative_binary64
Counts
219 → 200
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
02605966
14804358
210783989
321043840
442973606
547733606
646463439
749593439
849843439

prune153.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1973200
Fresh01212
Picked101
Done000
Total19815213
Error
0.0b
Counts
213 → 15
Alt Table
StatusErrorProgram
0.9b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
4.2b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 z (/.f64 t (/.f64 z t))))
39.9b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (*.f64 (/.f64 z t) (sqrt.f64 z)) (fabs.f64 (/.f64 (sqrt.f64 z) t))))
4.1b
(+.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (/.f64 (/.f64 x y) y))) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
14.3b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (*.f64 (/.f64 z t) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (fabs.f64 (/.f64 (cbrt.f64 z) t))))
14.1b
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 4)) (cbrt.f64 (pow.f64 (/.f64 x y) 2))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
26.3b
(+.f64 (/.f64 (*.f64 x x) (*.f64 y y)) (/.f64 (*.f64 z (/.f64 z t)) t))
21.6b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (fabs.f64 z) (/.f64 z (*.f64 t t))))
23.4b
(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (/.f64 (*.f64 z z) (*.f64 t t)))
41.0b
(+.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
21.7b
(+.f64 (/.f64 x (/.f64 y (/.f64 x y))) (/.f64 (*.f64 z z) (*.f64 t t)))
1.1b
(+.f64 (*.f64 (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (/.f64 x (pow.f64 (cbrt.f64 y) 3))) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
1.0b
(+.f64 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (*.f64 (*.f64 (/.f64 (cbrt.f64 z) (cbrt.f64 t)) (/.f64 z (pow.f64 (cbrt.f64 t) 3))) (/.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))))
14.8b
(+.f64 (/.f64 (*.f64 x (/.f64 x y)) (fabs.f64 y)) (*.f64 (fabs.f64 (/.f64 z t)) (fabs.f64 (/.f64 z t))))
34.2b
(/.f64 (-.f64 (pow.f64 (/.f64 x y) 4) (pow.f64 (/.f64 z t) 4)) (-.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2)))
Compiler

Compiled 4055 to 1712 computations (57.8% saved)

regimes2.9s (34.3%)

Accuracy

Total 0.3b remaining (80.9%)

Threshold costs 0.3b (80.9%)

Compiler

Compiled 66470 to 36877 computations (44.5% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
*-lft-identity_binary64
sqr-abs_binary64
fabs-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01519
12319
22119

end0.0ms (0%)

Compiler

Compiled 17 to 10 computations (41.2% saved)

sample1.6s (18.7%)

Algorithm
intervals
Results
481.0ms8000×body128valid
367.0ms5925×body128invalid
Compiler

Compiled 453 to 255 computations (43.7% saved)

Profiling

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