Details

analyze39.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample14.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify308.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

Iter	Nodes	Cost
0	2142	13
1	2142	13

prune6.0ms (0.1%)

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

0.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_20197`
40×	`add-sqr-sqrt_binary64_20219`
30×	`times-frac_binary64_20203`
19×	`distribute-lft-out--_binary64_20149`
14×	`add-cube-cbrt_binary64_20232`
13×	`difference-of-squares_binary64_20166`
6×	`associate-/r*_binary64_20141` `distribute-lft-out_binary64_20148`
5×	`associate-/l*_binary64_20142`
3×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
2×	`flip3--_binary64_20201` `associate-/r/_binary64_20143` `associate-/l/_binary64_20144` `flip--_binary64_20172`
1×	`div-sub_binary64_20202` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `add-log-exp_binary64_20236` `div-inv_binary64_20194` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `pow1_binary64_20258`

Counts

1 → 58

Calls

1 calls:

11.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series128.0ms (2.7%)

Counts

1 → 19

Calls

1 calls:

128.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 632 to 526 computations (16.8% saved)

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5320	1923

prune73.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Error

Counts

78 → 5

Compiler

Compiled 1506 to 718 computations (52.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
0.1b	(pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) 3)
7.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) 3))

rewrite76.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`*-un-lft-identity_binary64_20197`
180×	`add-sqr-sqrt_binary64_20219`
150×	`times-frac_binary64_20203`
83×	`distribute-lft-out--_binary64_20149`
78×	`cbrt-prod_binary64_20228`
72×	`unpow-prod-down_binary64_20276` `cube-prod_binary64_20225`
66×	`add-cube-cbrt_binary64_20232`
57×	`difference-of-squares_binary64_20166`
26×	`distribute-lft-out_binary64_20148`
10×	`associate-/r/_binary64_20143`
8×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
6×	`flip3--_binary64_20201` `associate-/r*_binary64_20141` `flip--_binary64_20172`
5×	`div-inv_binary64_20194` `associate-/l*_binary64_20142`
4×	`pow1_binary64_20258`
3×	`pow-unpow_binary64_20274` `add-log-exp_binary64_20236`
2×	`rem-cube-cbrt_binary64_20220` `cube-div_binary64_20226` `unpow3_binary64_20263` `div-exp_binary64_20248` `sqr-pow_binary64_20169` `associate-/l/_binary64_20144` `pow-exp_binary64_20265` `cube-mult_binary64_20227` `cbrt-undiv_binary64_20231`
1×	`div-sub_binary64_20202` `pow1/3_binary64_20279` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `pow-pow_binary64_20269` `rem-cbrt-cube_binary64_20221` `pow-to-exp_binary64_20266` `cbrt-div_binary64_20229`

Counts

3 → 238

Calls

3 calls:

16.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) 3))
14.0ms	(pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) 3)
11.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series626.0ms (13.4%)

Counts

3 → 58

Calls

3 calls:

330.0ms	(pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) 3)
157.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) 3))
139.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 2291 to 1933 computations (15.6% saved)

simplify122.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4940	8667
1	4940	8667

prune325.0ms (7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	296	5	301

Error

Counts

301 → 5

Compiler

Compiled 6676 to 3416 computations (48.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
0.1b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

rewrite158.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

667×	`*-un-lft-identity_binary64_20197`
341×	`add-sqr-sqrt_binary64_20219`
327×	`times-frac_binary64_20203`
302×	`sqrt-prod_binary64_20213`
218×	`distribute-lft-out--_binary64_20149`
110×	`add-cube-cbrt_binary64_20232`
97×	`difference-of-squares_binary64_20166`
95×	`swap-sqr_binary64_20164`
69×	`distribute-lft-out_binary64_20148`
39×	`associate-l_binary64_20138` `associate-r_binary64_20137`
20×	`pow1_binary64_20258`
14×	`associate-/r/_binary64_20143`
12×	`associate-/r*_binary64_20141`
10×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233` `associate-/l*_binary64_20142`
9×	`flip3--_binary64_20201` `sqrt-pow1_binary64_20215` `pow1/2_binary64_20277` `unswap-sqr_binary64_20165` `flip--_binary64_20172`
7×	`div-inv_binary64_20194`
6×	`rem-sqrt-square_binary64_20210`
5×	`pow-prod-up_binary64_20267` `sqrt-div_binary64_20214`
4×	`add-log-exp_binary64_20236` `associate-/l/_binary64_20144`
3×	`pow-sqr_binary64_20170` `pow-prod-down_binary64_20268`
2×	`div-sub_binary64_20202` `sqr-abs_binary64_20212` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231`
1×	`sqrt-unprod_binary64_20217` `rem-square-sqrt_binary64_20209` `frac-times_binary64_20207` `cbrt-unprod_binary64_20230` `pow-plus_binary64_20260` `pow2_binary64_20278` `prod-exp_binary64_20246` `-commutative_binary64_20128` `associate-r/_binary64_20139` `associate-*l/_binary64_20140`

Counts

4 → 376

Calls

4 calls:

58.0ms	(*.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
11.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
11.0ms	(sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
11.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series767.0ms (16.4%)

Counts

4 → 70

Calls

4 calls:

321.0ms	(sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
154.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
150.0ms	(*.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
141.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 3500 to 2785 computations (20.4% saved)

simplify154.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

446 → 446

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5171	11552

prune610.0ms (13.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	446	0	446
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	446	5	451

Error

Counts

451 → 5

Compiler

Compiled 11922 to 5493 computations (53.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (/.f64 2 y))
0.0b	(*.f64 2 (/.f64 x y))
0.0b	(-.f64 (+.f64 1 (/.f64 2 y)) (*.f64 2 (/.f64 x y)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_20219`
13×	`-un-lft-identity_binary64_20197` `associate-r*_binary64_20137`
11×	`add-cube-cbrt_binary64_20232`
10×	`add-log-exp_binary64_20236` `times-frac_binary64_20203`
8×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
5×	`pow1_binary64_20258`
3×	`associate-l_binary64_20138` `associate-*r/_binary64_20139`
2×	`frac-sub_binary64_20206` `cbrt-unprod_binary64_20230` `unswap-sqr_binary64_20165` `sum-log_binary64_20288` `prod-exp_binary64_20246` `flip3-+_binary64_20200` `diff-log_binary64_20289` `flip-+_binary64_20171`
1×	`sub-neg_binary64_20190` `flip3--_binary64_20201` `associate--l+_binary64_20134` `div-inv_binary64_20194` `div-exp_binary64_20248` `distribute-lft-out_binary64_20148` `+-commutative_binary64_20127` `*-commutative_binary64_20128` `pow-prod-down_binary64_20268` `cbrt-undiv_binary64_20231` `cancel-sign-sub-inv_binary64_20163` `flip--_binary64_20172`

Counts

3 → 60

Calls

3 calls:

9.0ms	(-.f64 (+.f64 1 (/.f64 2 y)) (*.f64 2 (/.f64 x y)))
7.0ms	(*.f64 2 (/.f64 x y))
6.0ms	(+.f64 1 (/.f64 2 y))

series213.0ms (4.6%)

Counts

3 → 24

Calls

3 calls:

134.0ms	(-.f64 (+.f64 1 (/.f64 2 y)) (*.f64 2 (/.f64 x y)))
51.0ms	(*.f64 2 (/.f64 x y))
28.0ms	(+.f64 1 (/.f64 2 y))

Compiler

Compiled 415 to 389 computations (6.3% saved)

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5115	991

prune67.0ms (1.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	84	5	89

Error

Counts

89 → 5

Compiler

Compiled 1198 to 807 computations (32.6% saved)

regimes88.0ms (1.9%)

Accuracy

Total 0.0b remaining (87.7%)

Threshold costs 0.0b (87.7%)

Compiler

Compiled 679 to 553 computations (18.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	13
1	37	13

end0.0ms (0%)

sample677.0ms (14.5%)

Algorithm

1×

intervals

Results

224.0ms	7997×	body	128	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 253 to 204 computations (19.4% saved)

Details

analyze39.0ms (0.8%)

sample14.0ms (0.3%)

simplify308.0ms (6.6%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series128.0ms (2.7%)

simplify66.0ms (1.4%)

prune73.0ms (1.6%)

localize8.0ms (0.2%)

rewrite76.0ms (1.6%)

series626.0ms (13.4%)

simplify122.0ms (2.6%)

prune325.0ms (7%)

localize8.0ms (0.2%)

rewrite158.0ms (3.4%)

series767.0ms (16.4%)

simplify154.0ms (3.3%)

prune610.0ms (13.1%)

localize7.0ms (0.1%)

rewrite26.0ms (0.6%)

series213.0ms (4.6%)

simplify75.0ms (1.6%)

prune67.0ms (1.4%)

regimes88.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample677.0ms (14.5%)

Profiling