Details

Time bar (total: 6.2s)

analyze870.0ms (14%)

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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample42.0ms (0.7%)

Algorithm
intervals
Results
8.0ms174×body128valid
8.0ms37×body2048valid
3.0ms19×body1024valid
2.0ms16×body512valid
1.0msbody4096valid
1.0ms25×body128nan
0.0ms12×body128invalid
0.0msbody256valid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify73.0ms (1.2%)

Algorithm
egg-herbie
Rules
518×div-sub_binary64
246×associate-/l*_binary64
183×times-frac_binary64
166×associate-/l/_binary64
154×distribute-rgt-in_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
12620
25220
310620
415820
524120
632720
737220
843020
965220
10149320
1177420
1275820
1376620
1477420
1577420
1678220
1781820
1882020
1971420

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
32.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
32.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
Compiler

Compiled 32 to 20 computations (37.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
0.7b
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
20.2b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite181.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
31.8b
Rules
40×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
21×times-frac_binary64
19×add-cube-cbrt_binary64
11×sqrt-prod_binary64
Counts
4 → 96
Calls

4 calls:

11.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
9.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 1965 to 333 computations (83.1% saved)

series177.0ms (2.8%)

Error
6.6b
Counts
4 → 56
Calls

4 calls:

41.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
37.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
36.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
35.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 2005 to 1303 computations (35% saved)

simplify131.0ms (2.1%)

Algorithm
egg-herbie
Rules
530×associate-/l*_binary64
440×associate-/r*_binary64
162×distribute-rgt-neg-in_binary64
156×distribute-rgt-in_binary64
144×cancel-sign-sub-inv_binary64
Counts
152 → 88
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02093278
15233128
215223108
347623108
449393108

prune51.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New80888
Fresh000
Picked011
Done000
Total80989
Error
8.0b
Counts
89 → 9
Alt Table
StatusErrorProgram
47.8b
(/.f64 (*.f64 b_2 -2) a)
58.0b
(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
50.1b
(*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (neg.f64 b_2))) (/.f64 (-.f64 (sqrt.f64 (neg.f64 b_2)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) a))
29.8b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
46.8b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
57.2b
(*.f64 (/.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (neg.f64 b_2))) (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (neg.f64 b_2)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) (sqrt.f64 a)))
32.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
44.8b
(/.f64 (-.f64 (*.f64 (neg.f64 b_2) (neg.f64 b_2)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) (*.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
46.7b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b_2) -1/2) a)
Compiler

Compiled 1370 to 460 computations (66.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
3.4b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.1b
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
20.2b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite136.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
7.6b
Rules
66×times-frac_binary64
58×add-sqr-sqrt_binary64
43×*-un-lft-identity_binary64
29×add-cube-cbrt_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
Counts
4 → 129
Calls

4 calls:

13.0ms
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.0ms
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
7.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
Compiler

Compiled 3475 to 488 computations (86% saved)

series238.0ms (3.8%)

Error
8.0b
Counts
4 → 69
Calls

4 calls:

59.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
55.0ms
(/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
48.0ms
(/.f64 (/.f64 (*.f64 a c) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
48.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
Compiler

Compiled 3436 to 2046 computations (40.5% saved)

simplify149.0ms (2.4%)

Algorithm
egg-herbie
Rules
568×associate-/r/_binary64
200×times-frac_binary64
198×associate-/l*_binary64
196×cancel-sign-sub-inv_binary64
192×distribute-rgt-neg-in_binary64
Counts
198 → 118
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03035859
17735457
227895355
350455355

prune74.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1144118
Fresh347
Picked101
Done011
Total1189127
Error
7.6b
Counts
127 → 9
Alt Table
StatusErrorProgram
47.8b
(/.f64 (*.f64 b_2 -2) a)
44.7b
(exp.f64 (log.f64 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))
58.0b
(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
26.8b
(*.f64 1 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
46.8b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
34.2b
(*.f64 (*.f64 a c) (/.f64 (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
32.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
29.8b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2)) a)
46.7b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b_2) -1/2) a)
Compiler

Compiled 2340 to 672 computations (71.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
20.2b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite89.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
7.6b
Rules
38×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
18×times-frac_binary64
17×add-cube-cbrt_binary64
10×difference-of-squares_binary64
Counts
4 → 85
Calls

4 calls:

9.0ms
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 1881 to 457 computations (75.7% saved)

series215.0ms (3.5%)

Error
6.4b
Counts
4 → 74
Calls

4 calls:

60.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
48.0ms
(/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
45.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
34.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 3091 to 2089 computations (32.4% saved)

simplify102.0ms (1.6%)

Algorithm
egg-herbie
Rules
743×associate-/l*_binary64
540×associate-/r*_binary64
252×associate-*l/_binary64
187×cancel-sign-sub-inv_binary64
168×associate-/r/_binary64
Counts
159 → 83
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02183532
15163377
215583374
349733374

prune46.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh347
Picked011
Done011
Total85792
Error
6.4b
Counts
92 → 7
Alt Table
StatusErrorProgram
47.8b
(/.f64 (*.f64 b_2 -2) a)
41.6b
(*.f64 1 (/.f64 c (*.f64 b_2 -2)))
26.8b
(*.f64 1 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
46.8b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
34.2b
(*.f64 (*.f64 a c) (/.f64 (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
32.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
29.8b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2)) a)
Compiler

Compiled 1236 to 540 computations (56.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.5b
(-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2)
10.0b
(/.f64 (*.f64 a c) (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2))
21.0b
(cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
21.0b
(cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite86.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
6.4b
Rules
add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 cbrt-prod_binary64
pow1_binary64 flip3--_binary64 cbrt-div_binary64 flip--_binary64
times-frac_binary64 associate-/r*_binary64 cancel-sign-sub-inv_binary64
pow1/3_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-/r/_binary64
Counts
4 → 63
Calls

4 calls:

16.0ms
(/.f64 (*.f64 a c) (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2))
13.0ms
(-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2)
4.0ms
(cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
Compiler

Compiled 2765 to 371 computations (86.6% saved)

series519.0ms (8.3%)

Error
6.4b
Counts
4 → 68
Calls

4 calls:

204.0ms
(/.f64 (*.f64 a c) (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2))
113.0ms
(-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2)
74.0ms
(cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
74.0ms
(cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
Compiler

Compiled 8300 to 5426 computations (34.6% saved)

simplify164.0ms (2.6%)

Algorithm
egg-herbie
Rules
360×cancel-sign-sub-inv_binary64
310×unswap-sqr_binary64
258×associate-*r*_binary64
243×times-frac_binary64
215×associate-/l*_binary64
Counts
131 → 112
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02985333
18694213
234224139
349874139
450014139

prune74.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1120112
Fresh044
Picked011
Done022
Total1127119
Error
6.4b
Counts
119 → 7
Alt Table
StatusErrorProgram
47.8b
(/.f64 (*.f64 b_2 -2) a)
41.6b
(*.f64 1 (/.f64 c (*.f64 b_2 -2)))
26.8b
(*.f64 1 (/.f64 c (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
46.8b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
34.2b
(*.f64 (*.f64 a c) (/.f64 (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
32.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
29.8b
(/.f64 (/.f64 (*.f64 a c) (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) b_2)) a)
Compiler

Compiled 3217 to 1139 computations (64.6% saved)

regimes1.5s (23.4%)

Accuracy

Total 1.3b remaining (18.7%)

Threshold costs 0b (0%)

Compiler

Compiled 12569 to 6265 computations (50.2% saved)

bsearch47.0ms (0.8%)

Steps
ItersRangePoint
5
2.002342733126003e+38
5.9818136131662096e+38
5.897751866039278e+38
6
-8.21531726165022e-305
-8.611236947236464e-306
-8.757693797729915e-306
2
-5.470603890992672e+158
-2.985535089321315e+152
-1.0928129976042705e+154
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64
*-lft-identity_binary64 cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
1-exp_binary64 distribute-neg-frac_binary64 distribute-lft-neg-out_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03273
14873
26473
37573
48273
58473
68373

end2.0ms (0%)

Compiler

Compiled 52 to 28 computations (46.2% saved)

sample1.2s (20%)

Algorithm
intervals
Results
237.0ms1106×body2048valid
231.0ms5200×body128valid
123.0ms762×body1024valid
100.0ms401×body4096valid
44.0ms371×body512valid
31.0ms791×body128nan
13.0ms160×body256valid
10.0ms249×body128invalid
Compiler

Compiled 194 to 116 computations (40.2% saved)

Profiling

Loading profile data...