Details

Time bar (total: 6.2s)

analyze800.0ms (13%)

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%93.6%6.4%7
3.1%84.2%12.7%8
12.5%67.1%20.5%9
16%63.5%20.5%10
17.9%57.7%24.4%11
22.6%48.7%28.7%12
28.7%37.8%33.6%13
30.4%35.9%33.7%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample45.0ms (0.7%)

Algorithm
intervals
Results
13.0ms256×body128valid
5.0ms104×body128nan
1.0ms23×body128invalid
Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11312
21512
31512

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
18.8b
Counts
1 → 1
Alt Table
StatusErrorProgram
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 24 to 16 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.4b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
6.9b
(/.f64 A (*.f64 V l))
13.8b
(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite128.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
9.4b
Rules
21×add-cube-cbrt_binary64
18×add-sqr-sqrt_binary64
16×add-exp-log_binary64
15×add-cbrt-cube_binary64
13×pow1_binary64
Counts
3 → 126
Calls

3 calls:

13.0ms
(/.f64 A (*.f64 V l))
12.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))
12.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
Compiler

Compiled 1389 to 359 computations (74.2% saved)

series65.0ms (1.1%)

Error
18.8b
Counts
3 → 30
Calls

3 calls:

30.0ms
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
17.0ms
(/.f64 A (*.f64 V l))
16.0ms
(sqrt.f64 (/.f64 A (*.f64 V l)))
Compiler

Compiled 1042 to 726 computations (30.3% saved)

simplify113.0ms (1.8%)

Algorithm
egg-herbie
Rules
586×associate-/l*_binary64
405×prod-exp_binary64
333×associate-*l/_binary64
296×associate-/r*_binary64
268×div-exp_binary64
Counts
156 → 57
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01291471
12781383
29961365
337051365
453541365

prune33.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New471057
Fresh000
Picked011
Done000
Total471158
Error
9.4b
Counts
58 → 11
Alt Table
StatusErrorProgram
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
41.3b
(/.f64 (*.f64 c0 (neg.f64 (sqrt.f64 A))) (neg.f64 (sqrt.f64 (*.f64 V l))))
19.5b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 c0)))
50.1b
(sqrt.f64 (*.f64 (/.f64 A (*.f64 V l)) (*.f64 c0 c0)))
40.0b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)))
43.0b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0) 3))
18.4b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
18.2b
(*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
21.3b
(*.f64 c0 (sqrt.f64 (exp.f64 (log.f64 (/.f64 A (*.f64 V l))))))
19.0b
(*.f64 c0 (*.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) (pow.f64 (/.f64 A (*.f64 V l)) 1/4)))
19.2b
(*.f64 c0 (*.f64 (cbrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))))
Compiler

Compiled 778 to 349 computations (55.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b
(*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.3b
(/.f64 V (/.f64 (cbrt.f64 A) l))
4.7b
(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
13.8b
(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite183.0ms (3%)

Algorithm
rewrite-expression-head
Error
8.3b
Rules
38×add-cube-cbrt_binary64
28×add-exp-log_binary64
22×add-sqr-sqrt_binary64
22×add-cbrt-cube_binary64
17×pow1_binary64
Counts
4 → 172
Calls

4 calls:

14.0ms
(/.f64 V (/.f64 (cbrt.f64 A) l))
14.0ms
(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
12.0ms
(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
12.0ms
(*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
Compiler

Compiled 3248 to 552 computations (83% saved)

series147.0ms (2.4%)

Error
9.4b
Counts
4 → 39
Calls

4 calls:

49.0ms
(/.f64 V (/.f64 (cbrt.f64 A) l))
38.0ms
(*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
25.0ms
(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
22.0ms
(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
Compiler

Compiled 1560 to 1085 computations (30.4% saved)

simplify85.0ms (1.4%)

Algorithm
egg-herbie
Rules
704×associate-*l/_binary64
514×associate-/r/_binary64
456×associate-/l/_binary64
270×unswap-sqr_binary64
150×times-frac_binary64
Counts
211 → 113
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01953334
14642180
217472119
352032119

prune63.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1094113
Fresh099
Picked101
Done011
Total11014124
Error
8.3b
Counts
124 → 14
Alt Table
StatusErrorProgram
19.5b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 c0)))
20.5b
(*.f64 c0 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))))
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
41.3b
(/.f64 (*.f64 c0 (neg.f64 (sqrt.f64 A))) (neg.f64 (sqrt.f64 (*.f64 V l))))
15.3b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))))
21.3b
(*.f64 c0 (sqrt.f64 (exp.f64 (log.f64 (/.f64 A (*.f64 V l))))))
17.6b
(/.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 A))) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l))))
50.1b
(sqrt.f64 (*.f64 (/.f64 A (*.f64 V l)) (*.f64 c0 c0)))
40.0b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)))
43.0b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0) 3))
18.4b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
15.3b
(/.f64 c0 (/.f64 (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l))) (fabs.f64 (cbrt.f64 A))))
19.0b
(*.f64 c0 (*.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) (pow.f64 (/.f64 A (*.f64 V l)) 1/4)))
19.2b
(*.f64 c0 (*.f64 (cbrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))))
Compiler

Compiled 1603 to 597 computations (62.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 A)
1.4b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.3b
(/.f64 V (/.f64 (cbrt.f64 A) l))
15.5b
(sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))

rewrite166.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
7.3b
Rules
34×add-cube-cbrt_binary64
22×add-sqr-sqrt_binary64
21×pow1_binary64
20×add-exp-log_binary64
16×add-cbrt-cube_binary64
Counts
4 → 160
Calls

4 calls:

14.0ms
(/.f64 V (/.f64 (cbrt.f64 A) l))
14.0ms
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))))
11.0ms
(cbrt.f64 A)
11.0ms
(sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))
Compiler

Compiled 2412 to 547 computations (77.3% saved)

series189.0ms (3.1%)

Error
6.9b
Counts
4 → 33
Calls

4 calls:

80.0ms
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))))
48.0ms
(/.f64 V (/.f64 (cbrt.f64 A) l))
41.0ms
(sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))
11.0ms
(cbrt.f64 A)
Compiler

Compiled 1734 to 1294 computations (25.4% saved)

simplify113.0ms (1.8%)

Algorithm
egg-herbie
Rules
881×associate-/l*_binary64
626×associate-/r*_binary64
214×associate-/r/_binary64
192×associate-/l/_binary64
170×associate-*l*_binary64
Counts
193 → 89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02072469
14592154
216112101
350022101

prune61.0ms (1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New86389
Fresh01212
Picked011
Done011
Total8617103
Error
7.0b
Counts
103 → 17
Alt Table
StatusErrorProgram
19.5b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 c0)))
20.5b
(*.f64 c0 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l)))))))
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
41.3b
(/.f64 (*.f64 c0 (neg.f64 (sqrt.f64 A))) (neg.f64 (sqrt.f64 (*.f64 V l))))
15.3b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)))))
21.3b
(*.f64 c0 (sqrt.f64 (exp.f64 (log.f64 (/.f64 A (*.f64 V l))))))
17.6b
(/.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 A))) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l))))
19.0b
(*.f64 c0 (*.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) (pow.f64 (/.f64 A (*.f64 V l)) 1/4)))
15.0b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))))
15.3b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (*.f64 (pow.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)) 1/4) (pow.f64 (/.f64 V (/.f64 (cbrt.f64 A) l)) 1/4))))
50.1b
(sqrt.f64 (*.f64 (/.f64 A (*.f64 V l)) (*.f64 c0 c0)))
40.0b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)))
43.0b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0) 3))
18.4b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
15.3b
(/.f64 c0 (/.f64 (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l))) (fabs.f64 (cbrt.f64 A))))
19.2b
(*.f64 c0 (*.f64 (cbrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))))
40.4b
(*.f64 (pow.f64 (neg.f64 A) 1/6) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 -1) (*.f64 V l))) (*.f64 c0 (fabs.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 A)))))))
Compiler

Compiled 1483 to 628 computations (57.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 A)
1.4b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))))
2.5b
(*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l))
15.5b
(sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))

rewrite187.0ms (3%)

Algorithm
rewrite-expression-head
Error
7.0b
Rules
26×add-sqr-sqrt_binary64
22×pow1_binary64
21×add-cube-cbrt_binary64
20×add-exp-log_binary64
13×add-cbrt-cube_binary64
Counts
4 → 155
Calls

4 calls:

16.0ms
(*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l))
14.0ms
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))))
13.0ms
(sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))
11.0ms
(cbrt.f64 A)
Compiler

Compiled 2562 to 1372 computations (46.4% saved)

series197.0ms (3.2%)

Error
6.9b
Counts
4 → 33
Calls

4 calls:

83.0ms
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))))
54.0ms
(*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l))
39.0ms
(sqrt.f64 (*.f64 (cbrt.f64 (/.f64 1 A)) (*.f64 V l)))
12.0ms
(cbrt.f64 A)
Compiler

Compiled 1756 to 1322 computations (24.7% saved)

simplify111.0ms (1.8%)

Algorithm
egg-herbie
Rules
532×associate-/l*_binary64
430×associate-/r*_binary64
355×associate-*l/_binary64
291×unswap-sqr_binary64
256×fma-def_binary64
Counts
188 → 114
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02012613
14432290
216552240
348122240
450222240

prune80.0ms (1.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1113114
Fresh31114
Picked101
Done112
Total11615131
Error
7.0b
Counts
131 → 15
Alt Table
StatusErrorProgram
18.8b
(*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))
41.3b
(/.f64 (*.f64 c0 (neg.f64 (sqrt.f64 A))) (neg.f64 (sqrt.f64 (*.f64 V l))))
50.1b
(sqrt.f64 (*.f64 (/.f64 A (*.f64 V l)) (*.f64 c0 c0)))
35.9b
(/.f64 c0 (/.f64 (sqrt.f64 (*.f64 (*.f64 V l) (cbrt.f64 (/.f64 1 A)))) (cbrt.f64 A)))
43.0b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0) 3))
14.2b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (*.f64 (*.f64 V (cbrt.f64 (/.f64 1 A))) l))))
19.5b
(*.f64 (*.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 c0)))
40.0b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 A (*.f64 V l))) c0)))
15.3b
(*.f64 c0 (/.f64 (fabs.f64 (cbrt.f64 A)) (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 1 A))) (cbrt.f64 (cbrt.f64 (/.f64 1 A)))) (*.f64 (*.f64 V l) (cbrt.f64 (cbrt.f64 (/.f64 1 A))))))))
18.4b
(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
17.6b
(/.f64 (*.f64 c0 (fabs.f64 (cbrt.f64 A))) (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l))))
15.3b
(/.f64 c0 (/.f64 (sqrt.f64 (/.f64 V (/.f64 (cbrt.f64 A) l))) (fabs.f64 (cbrt.f64 A))))
19.0b
(*.f64 c0 (*.f64 (pow.f64 (/.f64 A (*.f64 V l)) 1/4) (pow.f64 (/.f64 A (*.f64 V l)) 1/4)))
19.2b
(*.f64 c0 (*.f64 (cbrt.f64 (/.f64 A (*.f64 V l))) (cbrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))))
40.4b
(*.f64 (pow.f64 (neg.f64 A) 1/6) (*.f64 (sqrt.f64 (/.f64 (cbrt.f64 -1) (*.f64 V l))) (*.f64 c0 (fabs.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (neg.f64 A)))))))
Compiler

Compiled 1654 to 947 computations (42.7% saved)

regimes2.1s (34.4%)

Accuracy

Total 1.7b remaining (19.9%)

Threshold costs 0b (0%)

Compiler

Compiled 28072 to 17552 computations (37.5% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
if-if-or-not_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036100
146100
245100

end9.0ms (0.1%)

Remove

(sort V l)

Compiler

Compiled 207 to 105 computations (49.3% saved)

sample1.2s (19.6%)

Algorithm
intervals
Results
400.0ms8000×body128valid
153.0ms3026×body128nan
44.0ms869×body128invalid
Compiler

Compiled 366 to 233 computations (36.3% saved)

Profiling

Loading profile data...