Details

Time bar (total: 8.2s)

analyze898.0ms (11%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%68.6%6.4%7
31.2%62.4%6.4%8
36.7%54.6%8.7%9
38.2%48.4%13.4%10
42.7%42.3%15%11
47.8%34.1%18.1%12
49.1%30.3%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample59.0ms (0.7%)

Algorithm
intervals
Results
19.0ms162×body128valid
16.0ms50×body2048valid
7.0ms26×body1024valid
4.0ms10×body4096valid
1.0ms20×body128nan
1.0msbody512valid
1.0ms10×body128invalid
0.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify320.0ms (3.9%)

Algorithm
egg-herbie
Rules
904×div-sub_binary64
743×associate-/l*_binary64
567×times-frac_binary64
521×associate-/l/_binary64
427×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01326
12924
26224
312524
417524
528424
645624
775924
8118624
9163524
10191324
11186824
12191624
13198524
14202924
15159724
16158924
17158124
18158524
19158724
20158724
21180124
22190124
23183524
24184324
25186524
26187724
27188324
28188324
29192724
30198324
31193524
32193524
33174624

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
34.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
34.6b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
Compiler

Compiled 57 to 39 computations (31.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
0.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
0.2b
(*.f64 (*.f64 3 a) c)
24.6b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

rewrite128.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
34.4b
Rules
17×add-sqr-sqrt_binary64
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
12×*-un-lft-identity_binary64
10×pow1_binary64
Counts
4 → 75
Calls

4 calls:

9.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
8.0ms
(*.f64 (*.f64 3 a) c)
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
3.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
Compiler

Compiled 1824 to 1066 computations (41.6% saved)

series153.0ms (1.9%)

Error
5.1b
Counts
4 → 60
Calls

4 calls:

49.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
45.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
31.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
11.0ms
(*.f64 (*.f64 3 a) c)
Compiler

Compiled 2473 to 1765 computations (28.6% saved)

simplify79.0ms (1%)

Algorithm
egg-herbie
Rules
629×associate-/r*_binary64
624×associate-/l*_binary64
226×distribute-rgt-neg-in_binary64
222×cancel-sign-sub-inv_binary64
206×distribute-lft-neg-in_binary64
Counts
135 → 104
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02092671
15432465
218682461
353442461

prune73.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New9311104
Fresh000
Picked011
Done000
Total9312105
Error
8.5b
Counts
105 → 12
Alt Table
StatusErrorProgram
34.6b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
44.3b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
34.6b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
34.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
44.1b
(*.f64 (/.f64 b a) -2/3)
43.3b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))
48.7b
(+.f64 (*.f64 1/6 (/.f64 (*.f64 b b) (*.f64 a (sqrt.f64 (*.f64 c (*.f64 a -3)))))) (*.f64 1/3 (-.f64 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) a) (/.f64 b a))))
45.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) a))
50.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 3 a))
44.1b
(/.f64 (-.f64 (neg.f64 b) b) (*.f64 3 a))
36.2b
(/.f64 (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))))) b) (*.f64 3 a))
34.6b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
Compiler

Compiled 1907 to 1114 computations (41.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
0.2b
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))
0.2b
(*.f64 3 (*.f64 c a))
24.6b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))

rewrite224.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
8.5b
Rules
138×times-frac_binary64
118×add-sqr-sqrt_binary64
93×*-un-lft-identity_binary64
69×add-cube-cbrt_binary64
24×difference-of-squares_binary64
Counts
4 → 152
Calls

4 calls:

105.0ms
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
4.0ms
(*.f64 3 (*.f64 c a))
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))
3.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))
Compiler

Compiled 3924 to 2113 computations (46.2% saved)

series149.0ms (1.8%)

Error
8.5b
Counts
4 → 60
Calls

4 calls:

52.0ms
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
43.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))
30.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))
10.0ms
(*.f64 3 (*.f64 c a))
Compiler

Compiled 2473 to 1765 computations (28.6% saved)

simplify196.0ms (2.4%)

Algorithm
egg-herbie
Rules
619×associate-/l*_binary64
433×associate-/l/_binary64
425×div-sub_binary64
204×distribute-rgt-neg-in_binary64
195×cancel-sign-sub-inv_binary64
Counts
212 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03276470
17866264
222236263
347996263
456536263

prune52.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1043107
Fresh3710
Picked011
Done101
Total10811119
Error
8.5b
Counts
119 → 11
Alt Table
StatusErrorProgram
34.6b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
44.3b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
34.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) (/.f64 a 1/3))
43.3b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))
34.9b
(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) (sqrt.f64 3)) a))
50.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 3 a))
44.1b
(/.f64 (/.f64 (-.f64 (neg.f64 b) b) 3) a)
34.6b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
34.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
45.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) a))
44.1b
(/.f64 (-.f64 (neg.f64 b) b) (*.f64 3 a))
Compiler

Compiled 2002 to 1152 computations (42.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
0.2b
(*.f64 (*.f64 3 a) c)
0.3b
(/.f64 1/3 a)
24.6b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

rewrite88.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
8.5b
Rules
32×add-sqr-sqrt_binary64
24×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
19×times-frac_binary64
16×associate-*r*_binary64
Counts
4 → 99
Calls

4 calls:

13.0ms
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
4.0ms
(*.f64 (*.f64 3 a) c)
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
2.0ms
(/.f64 1/3 a)
Compiler

Compiled 2378 to 1410 computations (40.7% saved)

series182.0ms (2.2%)

Error
8.4b
Counts
4 → 45
Calls

4 calls:

114.0ms
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
40.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
11.0ms
(*.f64 (*.f64 3 a) c)
4.0ms
(/.f64 1/3 a)
Compiler

Compiled 2096 to 1481 computations (29.3% saved)

simplify121.0ms (1.5%)

Algorithm
egg-herbie
Rules
549×associate-/l*_binary64
256×distribute-rgt-in_binary64
246×distribute-lft-in_binary64
235×distribute-rgt-neg-in_binary64
224×cancel-sign-sub-inv_binary64
Counts
144 → 92
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02482765
16122583
220962580
349802580

prune56.0ms (0.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New89392
Fresh279
Picked011
Done011
Total9112103
Error
8.5b
Counts
103 → 12
Alt Table
StatusErrorProgram
34.6b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
44.3b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
34.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) (/.f64 a 1/3))
43.3b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))
34.9b
(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) (sqrt.f64 3)) a))
45.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) a))
57.7b
(log.f64 (pow.f64 (exp.f64 (/.f64 1/3 a)) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b)))
34.6b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
34.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
50.0b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1/3 a)) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b)) (sqrt.f64 (/.f64 1/3 a)))
44.1b
(/.f64 (-.f64 (neg.f64 b) b) (*.f64 3 a))
44.1b
(*.f64 (-.f64 (neg.f64 b) b) (/.f64 1/3 a))
Compiler

Compiled 2036 to 1209 computations (40.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
0.2b
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))
0.2b
(*.f64 3 (*.f64 c a))
24.6b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))

rewrite336.0ms (4.1%)

Algorithm
rewrite-expression-head
Error
8.5b
Rules
693×times-frac_binary64
435×add-sqr-sqrt_binary64
362×*-un-lft-identity_binary64
290×add-cube-cbrt_binary64
72×difference-of-squares_binary64
Counts
4 → 357
Calls

4 calls:

20.0ms
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
4.0ms
(*.f64 3 (*.f64 c a))
3.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))
Compiler

Compiled 10963 to 6591 computations (39.9% saved)

series162.0ms (2%)

Error
8.4b
Counts
4 → 60
Calls

4 calls:

61.0ms
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
43.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a))))
33.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))
11.0ms
(*.f64 3 (*.f64 c a))
Compiler

Compiled 2633 to 1925 computations (26.9% saved)

simplify541.0ms (6.6%)

Algorithm
egg-herbie
Rules
314×associate-/r/_binary64
248×*-commutative_binary64
238×neg-mul-1_binary64
209×distribute-rgt-neg-in_binary64
198×cancel-sign-sub-inv_binary64
Counts
417 → 366
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041916804
194815973
2305115793
3466415792
4506015792

prune197.0ms (2.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New3651366
Fresh189
Picked011
Done022
Total36612378
Error
8.5b
Counts
378 → 12
Alt Table
StatusErrorProgram
34.6b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) a)))
44.3b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
43.3b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))
34.9b
(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) (sqrt.f64 3)) a))
45.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -3))) a))
57.7b
(log.f64 (pow.f64 (exp.f64 (/.f64 1/3 a)) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b)))
34.6b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) 3) a)
34.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
50.0b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1/3 a)) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b)) (sqrt.f64 (/.f64 1/3 a)))
44.1b
(/.f64 (-.f64 (neg.f64 b) b) (*.f64 3 a))
44.1b
(*.f64 (-.f64 (neg.f64 b) b) (/.f64 1/3 a))
34.6b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 c a)))) b) (/.f64 3 (/.f64 1 a)))
Compiler

Compiled 4790 to 2664 computations (44.4% saved)

regimes2.1s (26.1%)

Accuracy

Total 1.4b remaining (13.2%)

Threshold costs 0b (0%)

Compiler

Compiled 16562 to 11318 computations (31.7% saved)

bsearch70.0ms (0.9%)

Steps
ItersRangePoint
8
1.8638401907671574e-65
2.7664583564676636e-62
7.869053993413591e-64
9
-1.659795985055506e+78
-8.394355750031888e+72
-1.612020823558058e+78
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02855
14455
26455
37755
48955
59655
69955
710055
89855

end1.0ms (0%)

Compiler

Compiled 40 to 27 computations (32.5% saved)

sample1.9s (23.2%)

Algorithm
intervals
Results
484.0ms5209×body128valid
387.0ms1133×body2048valid
192.0ms742×body1024valid
171.0ms391×body4096valid
73.0ms657×body128nan
65.0ms347×body512valid
29.0ms420×body128invalid
25.0ms178×body256valid
Compiler

Compiled 284 to 203 computations (28.5% saved)

Profiling

Loading profile data...