Details

Time bar (total: 6.4s)

analyze419.0ms (6.6%)

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)

sample44.0ms (0.7%)

Algorithm
intervals
Results
11.0ms123×body256valid
8.0ms285×pre128true
5.0ms38×body512valid
4.0ms95×body128valid
1.0ms29×body128nan
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify373.0ms (5.8%)

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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
52.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
52.8b
(/.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)))
0.1b
(/.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))
28.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite129.0ms (2%)

Algorithm
rewrite-expression-head
Error
49.7b
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:

12.0ms
(/.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)
5.0ms
(-.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)

series211.0ms (3.3%)

Error
0.2b
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)

simplify134.0ms (2.1%)

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

prune71.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1175122
Fresh000
Picked011
Done000
Total1176123
Error
0.1b
Counts
123 → 6
Alt Table
StatusErrorProgram
52.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) 3) (pow.f64 b 3)) (+.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))
1.4b
(+.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))
52.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
52.5b
(/.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 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))
52.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
Compiler

Compiled 2099 to 1170 computations (44.3% 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))
0.3b
(*.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))

rewrite384.0ms (6%)

Algorithm
rewrite-expression-head
Error
0.1b
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))
8.0ms
(*.f64 (*.f64 a a) (pow.f64 c 3))
8.0ms
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
Compiler

Compiled 6758 to 4045 computations (40.1% saved)

series173.0ms (2.7%)

Error
0.1b
Counts
4 → 30
Calls

4 calls:

60.0ms
(/.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))
29.0ms
(*.f64 (pow.f64 a 3) (pow.f64 c 4))
27.0ms
(*.f64 (*.f64 a a) (pow.f64 c 3))
Compiler

Compiled 2766 to 1992 computations (28% saved)

simplify143.0ms (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

prune97.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1560156
Fresh044
Picked011
Done011
Total1566162
Error
0.1b
Counts
162 → 6
Alt Table
StatusErrorProgram
52.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) 3) (pow.f64 b 3)) (+.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))
1.4b
(+.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))
52.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
52.5b
(/.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 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))
52.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
Compiler

Compiled 2565 to 1519 computations (40.8% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (pow.f64 a 4) (pow.f64 c 4))
0.4b
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.5b
(*.f64 (*.f64 a c) (*.f64 a c))
0.7b
(pow.f64 (*.f64 a c) 3)

rewrite369.0ms (5.8%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
56×times-frac_binary64
51×add-exp-log_binary64
48×unpow-prod-down_binary64
47×add-sqr-sqrt_binary64
46×pow1_binary64
Counts
4 → 192
Calls

4 calls:

7.0ms
(*.f64 (pow.f64 a 4) (pow.f64 c 4))
7.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
6.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
4.0ms
(pow.f64 (*.f64 a c) 3)
Compiler

Compiled 8988 to 5208 computations (42.1% saved)

series154.0ms (2.4%)

Error
0.1b
Counts
4 → 27
Calls

4 calls:

68.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
28.0ms
(pow.f64 (*.f64 a c) 3)
28.0ms
(*.f64 (pow.f64 a 4) (pow.f64 c 4))
25.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
Compiler

Compiled 3020 to 2072 computations (31.4% saved)

simplify146.0ms (2.3%)

Algorithm
egg-herbie
Rules
766×associate-/r/_binary64
507×log-prod_binary64
476×unswap-sqr_binary64
271×associate-/l*_binary64
206×associate-*l*_binary64
Counts
219 → 174
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02433381
14293084
222952936
346132936
452702936

prune122.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1740174
Fresh033
Picked011
Done022
Total1746180
Error
0.1b
Counts
180 → 6
Alt Table
StatusErrorProgram
52.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) 3) (pow.f64 b 3)) (+.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))
1.4b
(+.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))
52.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
52.5b
(/.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 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))
52.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) b)) 2)))
Compiler

Compiled 3542 to 2063 computations (41.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))
0.1b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
28.2b
(-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b))

rewrite137.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
54×times-frac_binary64
38×*-un-lft-identity_binary64
31×add-sqr-sqrt_binary64
22×associate-/l*_binary64
22×add-cube-cbrt_binary64
Counts
4 → 106
Calls

4 calls:

16.0ms
(/.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))
7.0ms
(-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
Compiler

Compiled 4850 to 2218 computations (54.3% saved)

series187.0ms (2.9%)

Error
0.0b
Counts
4 → 63
Calls

4 calls:

70.0ms
(/.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))
41.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
41.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
25.0ms
(-.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) (*.f64 b b))
Compiler

Compiled 3043 to 1906 computations (37.4% saved)

simplify145.0ms (2.3%)

Algorithm
egg-herbie
Rules
636×associate-/l/_binary64
309×div-sub_binary64
293×distribute-rgt-in_binary64
258×distribute-lft-in_binary64
162×cancel-sign-sub-inv_binary64
Counts
169 → 139
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02446060
16535529
222354548
350474548

prune92.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1363139
Fresh202
Picked101
Done123
Total1405145
Error
0b
Counts
145 → 5
Alt Table
StatusErrorProgram
1.4b
(+.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))
1.4b
(/.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 -4 (*.f64 a c))) (cbrt.f64 (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (*.f64 -4 (*.f64 a c)))) (+.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 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))
0.4b
(*.f64 (/.f64 (/.f64 (*.f64 -4 (*.f64 a c)) a) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b))) 3))) (/.f64 (+.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b)) (*.f64 b (-.f64 b (sqrt.f64 (+.f64 (*.f64 -4 (*.f64 a c)) (*.f64 b b)))))) 2))
0.3b
(*.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 3485 to 1756 computations (49.6% saved)

regimes1.1s (18%)

Accuracy

Total 0.4b remaining (94.4%)

Threshold costs 0.4b (94.4%)

Compiler

Compiled 25864 to 16758 computations (35.2% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01533
12033
22033

end1.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

sample1.6s (25.4%)

Algorithm
intervals
Results
384.0ms3803×body256valid
258.0ms8799×pre128true
215.0ms1475×body512valid
134.0ms2722×body128valid
44.0ms799×body128nan
Compiler

Compiled 276 to 180 computations (34.8% saved)

Profiling

Loading profile data...