Details

analyze182.0ms (4.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4920	34
1	4920	34
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	5×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.3b

Counts

2 → 1

Compiler

Compiled 24 to 17 computations (29.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
12.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite60.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
7×	`add-sqr-sqrt_binary64_3851`
6×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829`
5×	`add-log-exp_binary64_3868`
4×	`pow1_binary64_3890` `times-frac_binary64_3835` `associate-/l*_binary64_3774`
3×	`difference-of-squares_binary64_3798` `sqrt-prod_binary64_3845`
2×	`div-exp_binary64_3880` `cbrt-undiv_binary64_3863` `flip3--_binary64_3833` `associate-/l/_binary64_3776` `flip--_binary64_3804`
1×	`prod-exp_binary64_3878` `cbrt-unprod_binary64_3862` `frac-2neg_binary64_3840` `div-sub_binary64_3834` `clear-num_binary64_3828` `div-inv_binary64_3826` `associate-/r*_binary64_3773` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847` `rem-sqrt-square_binary64_3842` `diff-log_binary64_3921` `sub-neg_binary64_3822` `cancel-sign-sub-inv_binary64_3795`

Counts

3 → 52

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 1164 to 244 computations (79% saved)

series350.0ms (8.7%)

Error

0.5b

Counts

3 → 30

Calls

3 calls:

162.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
100.0ms	(-.f64 (.f64 a a) (.f64 b b))
67.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 870 to 747 computations (14.1% saved)

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4937	1189
1	4937	1189

prune63.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Error

Counts

83 → 3

Compiler

Compiled 1287 to 415 computations (67.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
0.0b	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
0.1b	(*.f64 b (/.f64 b a))

rewrite73.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-sqr-sqrt_binary64_3851`
20×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829`
19×	`times-frac_binary64_3835`
13×	`associate-r_binary64_3769`
10×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
6×	`pow1_binary64_3890`
3×	`add-log-exp_binary64_3868` `associate-l_binary64_3770` `associate-/l_binary64_3774` `associate-/r_binary64_3773` `sqrt-prod_binary64_3845`
2×	`div-exp_binary64_3880` `prod-exp_binary64_3878` `cbrt-unprod_binary64_3862` `cbrt-undiv_binary64_3863` `unswap-sqr_binary64_3797` `div-inv_binary64_3826` `associate-/l/_binary64_3776`
1×	`pow-prod-down_binary64_3900` `associate-r/_binary64_3771` `-commutative_binary64_3760` `frac-2neg_binary64_3840` `div-sub_binary64_3834` `clear-num_binary64_3828` `flip3--_binary64_3833` `flip--_binary64_3804` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847` `rem-sqrt-square_binary64_3842`

Counts

3 → 75

Calls

3 calls:

8.0ms	(*.f64 b (/.f64 b a))
5.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

Compiler

Compiled 1476 to 430 computations (70.9% saved)

series298.0ms (7.4%)

Error

Counts

3 → 24

Calls

3 calls:

154.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
65.0ms	(*.f64 b (/.f64 b a))
64.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

Compiler

Compiled 678 to 572 computations (15.6% saved)

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5079	1432

prune69.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

Counts

102 → 3

Compiler

Compiled 1581 to 534 computations (66.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))
0.0b	(/.f64 (+.f64 b a) a)
0.0b	(/.f64 (-.f64 a b) a)
0.0b	(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))

rewrite155.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

69×	`*-un-lft-identity_binary64_3829`
68×	`add-sqr-sqrt_binary64_3851`
58×	`times-frac_binary64_3835`
41×	`add-cube-cbrt_binary64_3864`
20×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
19×	`associate-r_binary64_3769`
16×	`associate-l_binary64_3770`
9×	`associate-/l*_binary64_3774`
7×	`pow1_binary64_3890` `distribute-lft-out_binary64_3780` `difference-of-squares_binary64_3798` `distribute-lft-out--_binary64_3781`
6×	`div-exp_binary64_3880` `cbrt-undiv_binary64_3863` `associate-/r*_binary64_3773`
4×	`prod-exp_binary64_3878` `add-log-exp_binary64_3868` `cbrt-unprod_binary64_3862` `unswap-sqr_binary64_3797` `div-inv_binary64_3826` `associate-/l/_binary64_3776`
3×	`sqrt-prod_binary64_3845`
2×	`frac-2neg_binary64_3840` `clear-num_binary64_3828`
1×	`pow-prod-down_binary64_3900` `frac-times_binary64_3839` `associate-l/_binary64_3772` `associate-r/_binary64_3771` `*-commutative_binary64_3760` `div-sub_binary64_3834` `flip3--_binary64_3833` `flip--_binary64_3804` `flip3-+_binary64_3832` `flip-+_binary64_3803` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847` `rem-sqrt-square_binary64_3842`

Counts

4 → 143

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
6.0ms	(/.f64 (-.f64 a b) a)
5.0ms	(/.f64 (+.f64 b a) a)
1.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 3107 to 760 computations (75.5% saved)

series433.0ms (10.8%)

Error

Counts

4 → 42

Calls

4 calls:

172.0ms	(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
79.0ms	(/.f64 (+.f64 b a) a)
79.0ms	(/.f64 (-.f64 a b) a)
76.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))))

Compiler

Compiled 1242 to 881 computations (29.1% saved)

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4998	2730
1	4998	2730

prune128.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	185	3	188

Error

Counts

188 → 3

Compiler

Compiled 3307 to 912 computations (72.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
0.1b	(*.f64 b (/.f64 b a))
0.2b	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))

rewrite112.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`add-sqr-sqrt_binary64_3851`
21×	`*-un-lft-identity_binary64_3829` `times-frac_binary64_3835`
20×	`add-cube-cbrt_binary64_3864`
17×	`add-exp-log_binary64_3867`
16×	`associate-l_binary64_3770` `associate-r_binary64_3769`
13×	`add-cbrt-cube_binary64_3865`
8×	`pow1_binary64_3890`
6×	`prod-exp_binary64_3878`
5×	`unswap-sqr_binary64_3797`
4×	`cbrt-unprod_binary64_3862`
3×	`div-exp_binary64_3880` `add-log-exp_binary64_3868` `associate-*r/_binary64_3771` `sqrt-prod_binary64_3845`
2×	`pow-prod-down_binary64_3900` `cbrt-undiv_binary64_3863` `flip3--_binary64_3833` `frac-times_binary64_3839` `flip--_binary64_3804` `sub-neg_binary64_3822` `distribute-rgt-in_binary64_3779` `cancel-sign-sub-inv_binary64_3795` `distribute-lft-in_binary64_3778` `div-inv_binary64_3826` `*-commutative_binary64_3760`
1×	`1-exp_binary64_3873` `rec-exp_binary64_3879` `associate-*l/_binary64_3772` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847` `rem-sqrt-square_binary64_3842`

Counts

3 → 88

Calls

3 calls:

9.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
7.0ms	(*.f64 b (/.f64 b a))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))

Compiler

Compiled 1921 to 845 computations (56% saved)

series306.0ms (7.6%)

Error

Counts

3 → 24

Calls

3 calls:

159.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
69.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
62.0ms	(*.f64 b (/.f64 b a))

Compiler

Compiled 714 to 608 computations (14.8% saved)

simplify82.0ms (2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4949	1562
1	4949	1562

prune88.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	112	3	115

Error

Counts

115 → 3

Compiler

Compiled 1847 to 788 computations (57.3% saved)

regimes155.0ms (3.8%)

Accuracy

Total 0.0b remaining (82.3%)

Threshold costs 0.0b (82.3%)

Compiler

Compiled 1250 to 931 computations (25.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms (0%)

sample1.1s (27.8%)

Algorithm

1×

intervals

Results

359.0ms	8000×	pre	128	true
283.0ms	8000×	body	128	valid
2.0ms	133×	pre	128	false

Compiler

Compiled 161 to 120 computations (25.5% saved)

Details

analyze182.0ms (4.5%)

sample29.0ms (0.7%)

simplify76.0ms (1.9%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

rewrite60.0ms (1.5%)

series350.0ms (8.7%)

simplify56.0ms (1.4%)

prune63.0ms (1.6%)

localize7.0ms (0.2%)

rewrite73.0ms (1.8%)

series298.0ms (7.4%)

simplify74.0ms (1.8%)

prune69.0ms (1.7%)

localize8.0ms (0.2%)

rewrite155.0ms (3.9%)

series433.0ms (10.8%)

simplify72.0ms (1.8%)

prune128.0ms (3.2%)

localize9.0ms (0.2%)

rewrite112.0ms (2.8%)

series306.0ms (7.6%)

simplify82.0ms (2%)

prune88.0ms (2.2%)

regimes155.0ms (3.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (27.8%)

Profiling