Details

analyze359.0ms (13.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5790	44
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample24.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify192.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (186.0ms)

Iter	Nodes	Cost
0	4979	22
1	4979	22

prune7.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

18.1b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
17.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_3094`
7×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
5×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
4×	`frac-times_binary64_3157` `*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
3×	`times-frac_binary64_3153` `flip--_binary64_3122` `flip3--_binary64_3151` `associate-/r*_binary64_3091`
2×	`associate-l/_binary64_3090` `pow1_binary64_3208` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `associate-/r/_binary64_3093` `associate-r/_binary64_3089`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `associate-/l*_binary64_3092` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

2 → 42

Calls

2 calls:

13.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series67.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

45.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
22.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify40.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5131	969

prune49.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Error

0.2b

Counts

49 → 5

Compiler

Compiled 1111 to 227 computations (79.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 y y) (.f64 x x))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
17.8b	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`times-frac_binary64_3153`
29×	`*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
15×	`distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
12×	`difference-of-squares_binary64_3116`
10×	`associate-/r*_binary64_3091`
7×	`add-log-exp_binary64_3186`
5×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `neg-mul-1_binary64_3143`
4×	`associate-/l*_binary64_3092`
3×	`pow1_binary64_3208`
2×	`flip--_binary64_3122` `distribute-neg-frac_binary64_3111` `flip-+_binary64_3121` `flip3--_binary64_3151` `flip3-+_binary64_3150` `associate-/l/_binary64_3094` `associate-/r/_binary64_3093`
1×	`clear-num_binary64_3146` `cancel-sign-sub-inv_binary64_3113` `frac-2neg_binary64_3158` `sub-neg_binary64_3140` `+-commutative_binary64_3077` `div-sub_binary64_3152` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

3 → 95

Calls

3 calls:

11.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(-.f64 (.f64 y y) (.f64 x x))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series86.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))
23.0ms	(-.f64 (.f64 y y) (.f64 x x))
20.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify84.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5746	3152

prune78.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Error

0.2b

Counts

109 → 5

Compiler

Compiled 2762 to 357 computations (87.1% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
17.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
17.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite82.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64_3169`
96×	`times-frac_binary64_3153`
95×	`*-un-lft-identity_binary64_3147`
57×	`add-cube-cbrt_binary64_3182` `sqrt-prod_binary64_3163`
36×	`associate-l_binary64_3088`
30×	`associate-r_binary64_3087`
18×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
13×	`distribute-lft-out--_binary64_3099` `difference-of-squares_binary64_3116`
10×	`sqrt-div_binary64_3164`
9×	`unswap-sqr_binary64_3115`
8×	`pow1_binary64_3208`
6×	`associate-/r*_binary64_3091` `distribute-lft-out_binary64_3098` `associate-/r/_binary64_3093`
5×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `associate-/l*_binary64_3092`
4×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186`
3×	`div-inv_binary64_3144`
2×	`associate-/l/_binary64_3094` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `flip--_binary64_3122` `clear-num_binary64_3146` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `flip3--_binary64_3151` `frac-2neg_binary64_3158` `div-sub_binary64_3152` `associate-*r/_binary64_3089`

Counts

4 → 183

Calls

4 calls:

40.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
11.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series157.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
49.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
29.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
23.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify104.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4974	5945
1	4974	5945

prune159.0ms (6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	195	5	200

Error

0.2b

Counts

200 → 5

Compiler

Compiled 6724 to 636 computations (90.5% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

0.2b

Counts

5 → 5

Compiler

Compiled 0 to 0 computations (0% saved)

regimes120.0ms (4.5%)

Accuracy

Total 4.4b remaining (90.9%)

Threshold costs 0b (0%)

Compiler

Compiled 708 to 392 computations (44.6% saved)

bsearch52.0ms (2%)

Steps

Iters	Range	Point
9	7.586904616848997e-174	3.3572392456160113e-167	3.320634432733052e-167
6	-8.103748395700428e-160	-1.5330813363921657e-160	-1.5591593595318052e-160
9	-6.608137513723582e+156	-2.922631786567919e+151	-1.3451366543625375e+154

Iters

Range

Point

7.586904616848997e-174

3.3572392456160113e-167

3.320634432733052e-167

-8.103748395700428e-160

-1.5330813363921657e-160

-1.5591593595318052e-160

-6.608137513723582e+156

-2.922631786567919e+151

-1.3451366543625375e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	69
1	67	69

end0.0ms (0%)

sample891.0ms (33.7%)

Algorithm

1×

intervals

Results

311.0ms	8000×	body	128	valid
175.0ms	8000×	pre	128	true

Compiler

Compiled 315 to 173 computations (45.1% saved)

Details

analyze359.0ms (13.6%)

sample24.0ms (0.9%)

simplify192.0ms (7.3%)

prune7.0ms (0.3%)

localize10.0ms (0.4%)

rewrite21.0ms (0.8%)

series67.0ms (2.5%)

simplify40.0ms (1.5%)

prune49.0ms (1.9%)

localize8.0ms (0.3%)

rewrite30.0ms (1.1%)

series86.0ms (3.2%)

simplify84.0ms (3.2%)

prune78.0ms (2.9%)

localize14.0ms (0.5%)

rewrite82.0ms (3.1%)

series157.0ms (5.9%)

simplify104.0ms (3.9%)

prune159.0ms (6%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.3%)

prune1.0ms (0%)

regimes120.0ms (4.5%)

bsearch52.0ms (2%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample891.0ms (33.7%)

Profiling