Details

Time bar (total: 8.1s)

analyze628.0ms (7.8%)

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)

sample41.0ms (0.5%)

Algorithm
intervals
Results
9.0ms171×body128valid
8.0ms34×body2048valid
5.0ms24×body1024valid
4.0ms12×body4096valid
2.0ms12×body512valid
1.0ms18×body128nan
1.0ms13×body128invalid
0.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify330.0ms (4.1%)

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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
33.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
33.4b
(/.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)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
0.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b)
2.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
21.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

rewrite168.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
33.2b
Rules
21×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64 add-cube-cbrt_binary64
sqrt-prod_binary64 difference-of-squares_binary64 times-frac_binary64 associate-/l*_binary64
Counts
4 → 74
Calls

4 calls:

12.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
Compiler

Compiled 1903 to 1105 computations (41.9% saved)

series214.0ms (2.7%)

Error
5.4b
Counts
4 → 62
Calls

4 calls:

66.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (*.f64 3 a))
42.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
41.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b)
38.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
Compiler

Compiled 2488 to 1789 computations (28.1% saved)

simplify131.0ms (1.6%)

Algorithm
egg-herbie
Rules
588×times-frac_binary64
414×associate-/l*_binary64
351×associate-/r*_binary64
316×div-sub_binary64
177×distribute-rgt-in_binary64
Counts
136 → 109
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02002848
15112611
215182604
347052604
455382604

prune100.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New9712109
Fresh000
Picked101
Done000
Total9812110
Error
7.1b
Counts
110 → 12
Alt Table
StatusErrorProgram
33.3b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) a)))
41.6b
(*.f64 (/.f64 b a) -2/3)
46.3b
(/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) (*.f64 3 a))
46.6b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))))
48.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 3 a))
33.4b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
48.0b
(+.f64 (*.f64 1/3 (-.f64 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) a) (/.f64 b a))) (*.f64 (/.f64 (*.f64 b b) (sqrt.f64 (*.f64 a (*.f64 c -3)))) (/.f64 1/6 a)))
33.2b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) 3) a)
33.9b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (*.f64 3 a))
41.6b
(/.f64 (*.f64 b -2) (*.f64 3 a))
41.8b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
47.7b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b) -3/2) (*.f64 3 a))
Compiler

Compiled 2056 to 1180 computations (42.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 3 (*.f64 a c))
0.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)
2.8b
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))
21.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c))))

rewrite80.0ms (1%)

Algorithm
rewrite-expression-head
Error
7.1b
Rules
12×add-sqr-sqrt_binary64
10×pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64
Counts
4 → 62
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)
5.0ms
(*.f64 3 (*.f64 a c))
4.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c))))
Compiler

Compiled 1452 to 762 computations (47.5% saved)

series173.0ms (2.1%)

Error
7.0b
Counts
4 → 52
Calls

4 calls:

61.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)
43.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))
38.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c))))
16.0ms
(*.f64 3 (*.f64 a c))
Compiler

Compiled 1999 to 1420 computations (29% saved)

simplify106.0ms (1.3%)

Algorithm
egg-herbie
Rules
362×distribute-rgt-neg-in_binary64
348×distribute-lft-neg-in_binary64
312×distribute-rgt-in_binary64
293×times-frac_binary64
284×cancel-sign-sub-inv_binary64
Counts
114 → 61
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01451692
13231610
29311607
326961595
446781595
548961595

prune50.0ms (0.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New58361
Fresh2911
Picked011
Done000
Total601373
Error
7.0b
Counts
73 → 13
Alt Table
StatusErrorProgram
33.3b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) a)))
46.3b
(/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) (*.f64 3 a))
46.6b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))))
48.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 3 a))
33.4b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
48.0b
(+.f64 (*.f64 1/3 (-.f64 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) a) (/.f64 b a))) (*.f64 (/.f64 (*.f64 b b) (sqrt.f64 (*.f64 a (*.f64 c -3)))) (/.f64 1/6 a)))
33.2b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) 3) a)
35.0b
(/.f64 (/.f64 (/.f64 (*.f64 a (*.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))))) 3) a)
33.9b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (*.f64 3 a))
41.6b
(/.f64 (/.f64 (*.f64 b -2) 3) a)
41.8b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
47.7b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b) -3/2) (*.f64 3 a))
47.7b
(/.f64 (/.f64 (*.f64 (/.f64 (*.f64 a c) b) -3/2) 3) a)
Compiler

Compiled 1170 to 723 computations (38.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 3 (*.f64 a c))
0.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)
2.8b
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))
21.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c))))

rewrite85.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
7.0b
Rules
12×add-sqr-sqrt_binary64
10×pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64
Counts
4 → 62
Calls

4 calls:

10.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)
5.0ms
(*.f64 3 (*.f64 a c))
4.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c))))
Compiler

Compiled 1564 to 874 computations (44.1% saved)

series154.0ms (1.9%)

Error
7.0b
Counts
4 → 52
Calls

4 calls:

43.0ms
(-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))
40.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)
38.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c))))
17.0ms
(*.f64 3 (*.f64 a c))
Compiler

Compiled 2201 to 1622 computations (26.3% saved)

simplify109.0ms (1.3%)

Algorithm
egg-herbie
Rules
362×distribute-rgt-neg-in_binary64
348×distribute-lft-neg-in_binary64
312×distribute-rgt-in_binary64
293×times-frac_binary64
284×cancel-sign-sub-inv_binary64
Counts
114 → 61
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01451692
13231610
29311607
326961595
446781595
548961595

prune50.0ms (0.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New58361
Fresh3811
Picked011
Done011
Total611374
Error
7.0b
Counts
74 → 13
Alt Table
StatusErrorProgram
33.3b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) a)))
46.3b
(/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) (*.f64 3 a))
46.6b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))))
48.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 3 a))
41.6b
(/.f64 1 (/.f64 3 (/.f64 (*.f64 b -2) a)))
47.8b
(/.f64 1 (/.f64 3 (/.f64 (*.f64 (/.f64 (*.f64 a c) b) -3/2) a)))
33.4b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
33.2b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) 3) a)
35.0b
(/.f64 (/.f64 (/.f64 (*.f64 a (*.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))))) 3) a)
46.1b
(/.f64 1 (/.f64 3 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) a)))
33.9b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (*.f64 3 a))
41.6b
(/.f64 (/.f64 (*.f64 b -2) 3) a)
41.8b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
Compiler

Compiled 1179 to 756 computations (35.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (*.f64 3 a) c)
0.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b)
2.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
21.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

rewrite85.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
7.0b
Rules
12×add-sqr-sqrt_binary64
10×pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
add-cube-cbrt_binary64
Counts
4 → 62
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b)
5.0ms
(*.f64 (*.f64 3 a) c)
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
Compiler

Compiled 1470 to 856 computations (41.8% saved)

series149.0ms (1.9%)

Error
7.0b
Counts
4 → 52
Calls

4 calls:

40.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b)
40.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
37.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
15.0ms
(*.f64 (*.f64 3 a) c)
Compiler

Compiled 1999 to 1420 computations (29% saved)

simplify110.0ms (1.4%)

Algorithm
egg-herbie
Rules
408×distribute-rgt-neg-in_binary64
382×distribute-lft-neg-in_binary64
353×distribute-rgt-in_binary64
314×cancel-sign-sub-inv_binary64
294×*-commutative_binary64
Counts
114 → 82
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01501694
13431612
210201609
327271603
447881603
548871603

prune59.0ms (0.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New81182
Fresh01010
Picked011
Done022
Total811495
Error
7.0b
Counts
95 → 14
Alt Table
StatusErrorProgram
33.3b
(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) a)))
46.3b
(/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) (*.f64 3 a))
46.6b
(-.f64 (*.f64 -1/2 (/.f64 c b)) (*.f64 3/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))))
48.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b b)) b) (*.f64 3 a))
41.6b
(/.f64 1 (/.f64 3 (/.f64 (*.f64 b -2) a)))
47.8b
(/.f64 1 (/.f64 3 (/.f64 (*.f64 (/.f64 (*.f64 a c) b) -3/2) a)))
33.4b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))) b) (/.f64 1/3 a))
33.2b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b) 3) a)
35.0b
(/.f64 (/.f64 (/.f64 (*.f64 a (*.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))))) 3) a)
46.1b
(/.f64 1 (/.f64 3 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -3))) a)))
33.9b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 3 (*.f64 a c)))) b))) (*.f64 3 a))
41.6b
(*.f64 (*.f64 b -2) (/.f64 1/3 a))
41.6b
(/.f64 (/.f64 (*.f64 b -2) 3) a)
41.8b
(+.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 (/.f64 b a) -2/3))
Compiler

Compiled 1324 to 776 computations (41.4% saved)

regimes3.6s (44.3%)

Accuracy

Total 3.0b remaining (28.8%)

Threshold costs 0b (0%)

Compiler

Compiled 21258 to 14548 computations (31.6% saved)

bsearch65.0ms (0.8%)

Steps
ItersRangePoint
10
4.8670834147901665e-32
1.5137431237819256e-21
2.1387839641340222e-29
9
-1.8193489604909258e+95
-6.124186158538392e+85
-1.3691570764324218e+95
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
sub-neg_binary64 +-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64
distribute-frac-neg_binary64
distribute-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02955
14055
24555
35055
45655
56155
66455
76555
86555

end2.0ms (0%)

Compiler

Compiled 40 to 27 computations (32.5% saved)

sample1.5s (19.2%)

Algorithm
intervals
Results
287.0ms1128×body2048valid
282.0ms5223×body128valid
139.0ms720×body1024valid
114.0ms376×body4096valid
56.0ms368×body512valid
42.0ms680×body128nan
23.0ms428×body128invalid
21.0ms185×body256valid
Compiler

Compiled 319 to 224 computations (29.8% saved)

Profiling

Loading profile data...