Details

Time bar (total: 6.4s)

analyze418.0ms (6.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 33 to 24 computations (27.3% saved)

sample46.0ms (0.7%)

Algorithm
intervals
Results
12.0ms123×body256valid
8.0ms290×pre128true
7.0ms53×body512valid
4.0ms80×body128valid
1.0ms34×body128nan
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify348.0ms (5.4%)

Algorithm
egg-herbie
Rules
1261×associate-/l*_binary64
1150×div-sub_binary64
772×distribute-rgt-in_binary64
702×distribute-lft-in_binary64
619×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13224
26524
312824
417824
528724
646024
775424
8112024
9114224
10179924
11216224
12195324
13204124
14210524
15213124
16284324
17260324
18284124
19295124
20307124
21311324
22318324
23317124
24317124
25219124
26214124
27210524
28210724
29210724
30210724
31210724
32183424

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
52.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
52.3b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
25.3b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite128.0ms (2%)

Algorithm
rewrite-expression-head
Error
49.1b
Rules
21×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
add-cube-cbrt_binary64
Counts
4 → 74
Calls

4 calls:

11.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1903 to 1105 computations (41.9% saved)

series206.0ms (3.2%)

Error
0.4b
Counts
4 → 72
Calls

4 calls:

60.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
48.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
38.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
37.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2658 to 1932 computations (27.3% saved)

simplify130.0ms (2%)

Algorithm
egg-herbie
Rules
794×times-frac_binary64
230×distribute-rgt-in_binary64
199×distribute-lft-in_binary64
182×cancel-sign-sub-inv_binary64
181×div-sub_binary64
Counts
146 → 122
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02063603
15503323
218583272
347533272
452093272

prune77.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1157122
Fresh000
Picked101
Done000
Total1167123
Error
0.3b
Counts
123 → 7
Alt Table
StatusErrorProgram
52.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))) (*.f64 a 2))
52.0b
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
1.6b
(+.f64 (-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (*.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
1.8b
(/.f64 (+.f64 (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)) (*.f64 (/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (*.f64 a 2))
52.4b
(-.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) (*.f64 a 2)) (/.f64 b (*.f64 a 2)))
52.3b
(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (*.f64 (+.f64 (*.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) b)) (*.f64 a (*.f64 c -4))) (*.f64 a 2)))
52.3b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
Compiler

Compiled 2168 to 1217 computations (43.9% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
0.4b
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
0.4b
(*.f64 (*.f64 a a) (pow.f64 c 3))
0.4b
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))

rewrite332.0ms (5.2%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
109×add-exp-log_binary64
54×prod-exp_binary64
42×add-sqr-sqrt_binary64
30×div-exp_binary64
29×unpow-prod-down_binary64
Counts
4 → 178
Calls

4 calls:

10.0ms
(/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
9.0ms
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
9.0ms
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
9.0ms
(*.f64 (*.f64 a a) (pow.f64 c 3))
Compiler

Compiled 6758 to 4045 computations (40.1% saved)

series170.0ms (2.7%)

Error
0.3b
Counts
4 → 30
Calls

4 calls:

59.0ms
(/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
51.0ms
(/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))
28.0ms
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
26.0ms
(*.f64 (*.f64 a a) (pow.f64 c 3))
Compiler

Compiled 2766 to 1992 computations (28% saved)

simplify142.0ms (2.2%)

Algorithm
egg-herbie
Rules
615×log-prod_binary64
398×associate-*l*_binary64
325×associate-*r*_binary64
324×times-frac_binary64
316×associate-/l*_binary64
Counts
208 → 156
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02633437
15723061
233832982
346572982
454432982

prune101.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1560156
Fresh066
Picked011
Done000
Total1567163
Error
0.3b
Counts
163 → 7
Alt Table
StatusErrorProgram
52.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))) (*.f64 a 2))
52.0b
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
1.6b
(+.f64 (-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (*.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
1.8b
(/.f64 (+.f64 (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)) (*.f64 (/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (*.f64 a 2))
52.4b
(-.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) (*.f64 a 2)) (/.f64 b (*.f64 a 2)))
52.3b
(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (*.f64 (+.f64 (*.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) b)) (*.f64 a (*.f64 c -4))) (*.f64 a 2)))
52.3b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
Compiler

Compiled 2634 to 1566 computations (40.5% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.4b
(/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))
0.4b
(*.f64 (*.f64 a c) (*.f64 a c))
0.6b
(pow.f64 (*.f64 a c) 3)

rewrite369.0ms (5.8%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
98×add-exp-log_binary64
63×times-frac_binary64
46×pow1_binary64
42×div-exp_binary64
42×unpow-prod-down_binary64
Counts
4 → 207
Calls

4 calls:

12.0ms
(/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))
8.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
7.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
4.0ms
(pow.f64 (*.f64 a c) 3)
Compiler

Compiled 9006 to 5208 computations (42.2% saved)

series196.0ms (3.1%)

Error
0.3b
Counts
4 → 30
Calls

4 calls:

69.0ms
(/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7))
65.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
30.0ms
(pow.f64 (*.f64 a c) 3)
27.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
Compiler

Compiled 3332 to 2276 computations (31.7% saved)

simplify160.0ms (2.5%)

Algorithm
egg-herbie
Rules
440×unswap-sqr_binary64
397×log-prod_binary64
349×associate-/l*_binary64
261×times-frac_binary64
204×log-div_binary64
Counts
237 → 191
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02634040
14803621
225953473
344143473
449483473

prune119.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1910191
Fresh055
Picked011
Done011
Total1917198
Error
0.3b
Counts
198 → 7
Alt Table
StatusErrorProgram
52.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b))) (*.f64 a 2))
52.0b
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
1.6b
(+.f64 (-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (*.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
1.8b
(/.f64 (+.f64 (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)) (*.f64 (/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10)) (*.f64 a 2))
52.4b
(-.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) (*.f64 a 2)) (/.f64 b (*.f64 a 2)))
52.3b
(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (*.f64 (+.f64 (*.f64 b (+.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) b)) (*.f64 a (*.f64 c -4))) (*.f64 a 2)))
52.3b
(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b) 2)))
Compiler

Compiled 3498 to 2045 computations (41.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
0.1b
(/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
0.1b
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
25.4b
(-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b))

rewrite189.0ms (3%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
70×times-frac_binary64
60×*-un-lft-identity_binary64
46×add-sqr-sqrt_binary64
32×add-cube-cbrt_binary64
26×associate-/l*_binary64
Counts
4 → 135
Calls

4 calls:

17.0ms
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
14.0ms
(/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
7.0ms
(-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b))
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
Compiler

Compiled 6256 to 2868 computations (54.2% saved)

series227.0ms (3.5%)

Error
0.0b
Counts
4 → 63
Calls

4 calls:

75.0ms
(/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
67.0ms
(/.f64 (/.f64 (-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))
44.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
24.0ms
(-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b))
Compiler

Compiled 3241 to 2156 computations (33.5% saved)

simplify235.0ms (3.7%)

Algorithm
egg-herbie
Rules
1132×div-sub_binary64
393×distribute-rgt-in_binary64
175×associate-/l*_binary64
171×sub-neg_binary64
155×cancel-sign-sub-inv_binary64
Counts
198 → 172
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02788966
17528210
226176703
344886703
461236703

prune129.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1684172
Fresh404
Picked101
Done112
Total1745179
Error
0b
Counts
179 → 5
Alt Table
StatusErrorProgram
1.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 -4 (*.f64 a c)) (+.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b)))))) (cbrt.f64 (/.f64 (*.f64 -4 (*.f64 a c)) (+.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b))))))) a) (/.f64 (cbrt.f64 (/.f64 (*.f64 -4 (*.f64 a c)) (+.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b)))))) 2))
0.3b
(/.f64 (/.f64 (*.f64 (*.f64 a c) 4) (+.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b))))) (*.f64 a -2))
1.6b
(+.f64 (-.f64 (-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b 3))) (/.f64 c b)) (*.f64 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -5))
0.6b
(/.f64 (/.f64 (/.f64 (*.f64 -4 (*.f64 a c)) (sqrt.f64 (+.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b)))))) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 a 2))
0.4b
(*.f64 (/.f64 (*.f64 -4 (*.f64 a c)) a) (/.f64 1/2 (+.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b))))))
Compiler

Compiled 4709 to 2376 computations (49.5% saved)

regimes1.0s (16.3%)

Accuracy

Total 0.4b remaining (95.5%)

Threshold costs 0.4b (95.5%)

Compiler

Compiled 24936 to 15002 computations (39.8% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01733
12333
22333

end1.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

sample1.5s (24.1%)

Algorithm
intervals
Results
353.0ms3803×body256valid
251.0ms8792×pre128true
201.0ms1474×body512valid
144.0ms2723×body128valid
37.0ms792×body128nan
Compiler

Compiled 261 to 167 computations (36% saved)

Profiling

Loading profile data...