Details

Time bar (total: 1.8s)

analyze5.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
25%0%75%13
25%0%75%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample19.0ms (1%)

Algorithm
intervals
Results
14.0ms256×body128valid
Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify264.0ms (14.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
0557420

prune5.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1
Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

rewrite43.0ms (2.4%)

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity_binary64_751
37×times-frac_binary64_757
34×add-sqr-sqrt_binary64_772
28×sqrt-prod_binary64_766
25×add-cube-cbrt_binary64_783
10×difference-of-squares_binary64_720
distribute-lft-out_binary64_704 associate-/l*_binary64_698
div-inv_binary64_748
add-log-exp_binary64_787 add-cbrt-cube_binary64_784 add-exp-log_binary64_786
pow1_binary64_809 sqrt-div_binary64_767
associate-/r*_binary64_697 distribute-rgt-out_binary64_706
associate-/l/_binary64_700 flip--_binary64_726 flip3--_binary64_755
+-commutative_binary64_683 flip3-+_binary64_754 distribute-rgt1-in_binary64_709 rem-sqrt-square_binary64_764 pow1/2_binary64_828 cbrt-undiv_binary64_782 sum-log_binary64_839 frac-2neg_binary64_762 clear-num_binary64_750 sqrt-pow1_binary64_768 frac-add_binary64_759 flip-+_binary64_725 div-exp_binary64_799
Counts
3 → 90
Calls

3 calls:

24.0ms
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
7.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))

series184.0ms (10.1%)

Counts
3 → 9
Calls

3 calls:

85.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
55.0ms
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
44.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify68.0ms (3.7%)

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
051291925

prune107.0ms (5.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New97299
Fresh000
Picked101
Done000
Total982100

Merged error: 0b

Counts
100 → 2
Compiler

Compiled 2010 to 1304 computations (35.1% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 1 x))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite33.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64_772
20×*-un-lft-identity_binary64_751
13×associate-*r*_binary64_693
12×add-cube-cbrt_binary64_783 add-exp-log_binary64_786
11×times-frac_binary64_757
add-cbrt-cube_binary64_784
sqrt-prod_binary64_766
pow1_binary64_809
add-log-exp_binary64_787 associate-*l*_binary64_694
prod-exp_binary64_797 distribute-lft-out_binary64_704
unswap-sqr_binary64_719 flip3-+_binary64_754 flip-+_binary64_725
frac-times_binary64_761 sqrt-div_binary64_767 cbrt-unprod_binary64_781 associate-*l/_binary64_696 difference-of-squares_binary64_720 div-exp_binary64_799
1-exp_binary64_792 +-commutative_binary64_683 rec-exp_binary64_798 rem-sqrt-square_binary64_764 pow1/2_binary64_828 flip--_binary64_726 un-div-inv_binary64_749 pow-prod-down_binary64_819 *-commutative_binary64_684 div-inv_binary64_748 associate-*r/_binary64_695 cbrt-undiv_binary64_782 sum-log_binary64_839 sqrt-pow1_binary64_768 flip3--_binary64_755
Counts
3 → 72
Calls

3 calls:

17.0ms
(*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 1 x))
6.0ms
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))

series124.0ms (6.8%)

Counts
3 → 9
Calls

3 calls:

49.0ms
(*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 1 x))
43.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
31.0ms
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify68.0ms (3.7%)

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
054381423

prune84.0ms (4.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New81081
Fresh011
Picked011
Done000
Total81283

Merged error: 0b

Counts
83 → 2
Compiler

Compiled 1504 to 1064 computations (29.3% saved)

localize11.0ms (0.6%)

Local error

Found 1 expressions with local error:

0.0b
(-.f64 (/.f64 2 x) (+.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) 1/8)))

rewrite14.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_787 add-sqr-sqrt_binary64_772
*-un-lft-identity_binary64_751
frac-sub_binary64_760 diff-log_binary64_840 difference-of-squares_binary64_720
distribute-lft-out--_binary64_705 flip3-+_binary64_754 add-cube-cbrt_binary64_783 pow1_binary64_809 flip--_binary64_726 times-frac_binary64_757 add-cbrt-cube_binary64_784 sum-log_binary64_839 add-exp-log_binary64_786 associate--r+_binary64_689 sub-neg_binary64_744 flip3--_binary64_755 flip-+_binary64_725
Counts
1 → 18
Calls

1 calls:

12.0ms
(-.f64 (/.f64 2 x) (+.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) 1/8)))

series52.0ms (2.9%)

Counts
1 → 3
Calls

1 calls:

52.0ms
(-.f64 (/.f64 2 x) (+.f64 (*.f64 x 1/2) (*.f64 (pow.f64 x 3) 1/8)))

simplify73.0ms (4%)

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
05039653

prune28.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New21021
Fresh000
Picked011
Done011
Total21223

Merged error: 0b

Counts
23 → 2
Compiler

Compiled 514 to 408 computations (20.6% saved)

regimes8.0ms (0.4%)

Compiler

Compiled 29 to 25 computations (13.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03020
13020

end0.0ms (0%)

sample611.0ms (33.5%)

Algorithm
intervals
Results
431.0ms8000×body128valid
0.0msbody128nan
Compiler

Compiled 54 to 46 computations (14.8% saved)

Profiling

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