Details

Time bar (total: 1.9min)

analyze129.0ms (0.1%)

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%68.7%6.3%6
25%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 32 to 22 computations (31.3% saved)

sample23.0ms (0%)

Algorithm
intervals
Results
16.0ms256×body128valid
Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify147.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02046
16146
215246
343846
4129746
5250846
6460546
7502946

prune7.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.1b
Counts
3 → 1
Compiler

Compiled 93 to 58 computations (37.6% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
0.1b
(*.f64 (*.f64 a a) (+.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.9b
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite38.0ms (0%)

Algorithm
rewrite-expression-head
Rules
15×add-exp-log_binary64_798 pow1_binary64_821
14×add-cbrt-cube_binary64_796
10×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
add-cube-cbrt_binary64_795
associate-*r*_binary64_700
prod-exp_binary64_809 add-log-exp_binary64_799 cbrt-unprod_binary64_793 pow-prod-down_binary64_831
distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710 associate-*r/_binary64_702
pow-unpow_binary64_837 unpow-prod-down_binary64_839
unswap-sqr_binary64_728 flip3-+_binary64_763 cancel-sign-sub-inv_binary64_726 flip-+_binary64_734 associate-+r+_binary64_692 associate-*l*_binary64_701 sub-neg_binary64_753 *-commutative_binary64_691
distribute-lft-out_binary64_711 unpow2_binary64_825 pow-exp_binary64_828 pow-to-exp_binary64_829 +-commutative_binary64_690 sum-log_binary64_851 sqr-pow_binary64_732 flip--_binary64_735 pow-pow_binary64_832 flip3--_binary64_764
Counts
4 → 80
Calls

4 calls:

9.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
8.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))
8.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

series659.0ms (0.6%)

Counts
4 → 48
Calls

4 calls:

378.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
121.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
109.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
51.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))
Compiler

Compiled 1986 to 1590 computations (19.9% saved)

simplify87.0ms (0.1%)

Algorithm
egg-herbie
Counts
128 → 315
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01892885
15302569
217562484
354542484

prune705.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3123315
Fresh000
Picked101
Done000
Total3133316
Error
0.0b
Counts
316 → 3
Compiler

Compiled 12398 to 6755 computations (45.5% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
0.1b
(*.f64 (*.f64 a a) (+.f64 1 a))
0.9b
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
1.4b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite66.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
32×associate-*r/_binary64_702
28×add-sqr-sqrt_binary64_782
26×add-exp-log_binary64_798
20×frac-add_binary64_768
18×unswap-sqr_binary64_728
16×add-cbrt-cube_binary64_796
15×prod-exp_binary64_809 associate-*r*_binary64_700
14×flip3-+_binary64_763 flip-+_binary64_734 pow1_binary64_821 unpow-prod-down_binary64_839
13×add-log-exp_binary64_799
12×*-un-lft-identity_binary64_760
10×unpow2_binary64_825 add-cube-cbrt_binary64_795 associate-*l*_binary64_701 sqr-pow_binary64_732
cbrt-unprod_binary64_793 pow-prod-down_binary64_831
pow-exp_binary64_828 pow-to-exp_binary64_829 sum-log_binary64_851
flip--_binary64_735 flip3--_binary64_764
distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
*-commutative_binary64_691
cancel-sign-sub-inv_binary64_726 associate-+r+_binary64_692 sub-neg_binary64_753
distribute-lft-out_binary64_711 associate-+l+_binary64_693 +-commutative_binary64_690
Counts
4 → 128
Calls

4 calls:

22.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
8.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))
8.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series651.0ms (0.6%)

Counts
4 → 42
Calls

4 calls:

388.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))
119.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
88.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
55.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))
Compiler

Compiled 2052 to 1704 computations (17% saved)

simplify161.0ms (0.1%)

Algorithm
egg-herbie
Counts
170 → 610
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03376173
110265783
247385759
349855759

prune4.3s (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New6100610
Fresh022
Picked011
Done000
Total6103613
Error
0.0b
Counts
613 → 3
Compiler

Compiled 44451 to 29196 computations (34.3% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) 3)
0.3b
(pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)
0.9b
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
25.0b
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) 3))

rewrite38.0ms (0%)

Algorithm
rewrite-expression-head
Rules
31×unpow-prod-down_binary64_839
22×cbrt-prod_binary64_791
18×add-sqr-sqrt_binary64_782
17×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
16×cube-prod_binary64_788
12×add-exp-log_binary64_798
10×add-cbrt-cube_binary64_796 pow1_binary64_821
sqr-pow_binary64_732
pow-unpow_binary64_837
unpow2_binary64_825 pow-exp_binary64_828
add-log-exp_binary64_799
prod-exp_binary64_809 pow-to-exp_binary64_829 associate-*r*_binary64_700 cbrt-unprod_binary64_793 pow-prod-down_binary64_831
cube-mult_binary64_790 unpow3_binary64_826 cancel-sign-sub-inv_binary64_726 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710 associate-*r/_binary64_702 sub-neg_binary64_753 pow-pow_binary64_832
pow1/3_binary64_842 rem-cbrt-cube_binary64_784 unswap-sqr_binary64_728 rem-cube-cbrt_binary64_783 associate-*l*_binary64_701 *-commutative_binary64_691 flip--_binary64_735 flip3--_binary64_764
Counts
4 → 109
Calls

4 calls:

8.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) 3))
6.0ms
(pow.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) 3)
5.0ms
(pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)

series326.0ms (0.3%)

Counts
4 → 33
Calls

4 calls:

123.0ms
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) 3))
111.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
49.0ms
(pow.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) 3)
42.0ms
(pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)
Compiler

Compiled 1874 to 1485 computations (20.8% saved)

simplify138.0ms (0.1%)

Algorithm
egg-herbie
Counts
142 → 476
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01492566
13252274
29992203
329672203
449072203
551282203

prune1.2s (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New4760476
Fresh011
Picked011
Done011
Total4763479
Error
0.0b
Counts
479 → 3
Compiler

Compiled 20163 to 10594 computations (47.5% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

2.3b
(-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))))
2.8b
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))) (*.f64 (*.f64 a a) (+.f64 1 a)))) 3))
4.4b
(+.f64 (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) (-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))))
41.5b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))) (*.f64 (*.f64 a a) (+.f64 1 a)))) 3)) (+.f64 (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) (-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))))))

rewrite450.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
2246×associate-*r/_binary64_702
544×frac-add_binary64_768
412×flip3-+_binary64_763 flip-+_binary64_734
288×frac-sub_binary64_769
273×flip--_binary64_735 flip3--_binary64_764
216×frac-times_binary64_770
42×associate-*l/_binary64_703
23×*-un-lft-identity_binary64_760
13×add-cube-cbrt_binary64_795 add-log-exp_binary64_799 add-sqr-sqrt_binary64_782
12×distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710 sub-div_binary64_767 times-frac_binary64_766
associate--l+_binary64_697
add-exp-log_binary64_798 add-cbrt-cube_binary64_796 associate-+r+_binary64_692
distribute-lft-out_binary64_711
associate-/l*_binary64_705 associate--r+_binary64_696 pow1_binary64_821
associate-/r*_binary64_704 sum-log_binary64_851
diff-log_binary64_852 associate-/r/_binary64_706 associate-/l/_binary64_707 cancel-sign-sub-inv_binary64_726 +-commutative_binary64_690 sub-neg_binary64_753
frac-2neg_binary64_771 cbrt-undiv_binary64_794 div-inv_binary64_757 div-exp_binary64_811 clear-num_binary64_759 distribute-rgt-out--_binary64_714 associate-+r-_binary64_694
Counts
4 → 387
Calls

4 calls:

58.0ms
(-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))))
44.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))) (*.f64 (*.f64 a a) (+.f64 1 a)))) 3)) (+.f64 (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) (-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))))))
32.0ms
(+.f64 (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) (-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))))
11.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))) (*.f64 (*.f64 a a) (+.f64 1 a)))) 3))

series5.9s (5.3%)

Counts
4 → 73
Calls

4 calls:

4.6s
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))) (*.f64 (*.f64 a a) (+.f64 1 a)))) 3)) (+.f64 (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) (-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))))))
548.0ms
(+.f64 (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) (-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))))))
524.0ms
(-.f64 (*.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) (*.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))))
209.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a))) (*.f64 (*.f64 a a) (+.f64 1 a)))) 3))
Compiler

Compiled 11074 to 8342 computations (24.7% saved)

simplify1.1s (1%)

Algorithm
egg-herbie
Counts
460 → 1469
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01897114949
15295114949

prune1.6min (84%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New146901469
Fresh000
Picked011
Done022
Total146931472
Error
0.0b
Counts
1472 → 3
Compiler

Compiled 394973 to 237897 computations (39.8% saved)

regimes297.0ms (0.3%)

Accuracy

Total 0.0b remaining (65.3%)

Threshold costs 0.0b (65.3%)

Compiler

Compiled 5092 to 3433 computations (32.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02658
14658
25858
36658
48358
58458
68558
78158

end0.0ms (0%)

sample1.2s (1.1%)

Algorithm
intervals
Results
483.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 897 to 615 computations (31.4% saved)

Profiling

Loading profile data...