Details

analyze772.0ms (8.1%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample56.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	174×	body	128	valid
9.0ms	34×	body	1024	valid
7.0ms	26×	body	1024	nan
6.0ms	29×	body	512	valid
4.0ms	53×	body	128	nan
3.0ms	14×	body	512	nan
3.0ms	19×	body	256	valid
2.0ms	14×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify158.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5192	41

prune3.0ms (0%)

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

42.6b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t))))
0.4b	(*.f64 (sqrt.f64 2) t)
12.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.3b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite70.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
40×	`associate-l_binary64_19`
29×	`times-frac_binary64_84`
21×	`add-cube-cbrt_binary64_113`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
9×	`pow1_binary64_139`
8×	`difference-of-squares_binary64_47`
7×	`sqrt-prod_binary64_94` `distribute-lft-out_binary64_29`
6×	`add-log-exp_binary64_117` `associate-r_binary64_18`
4×	`distribute-lft-out--_binary64_30` `unswap-sqr_binary64_46` `difference-of-sqr-1_binary64_48`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `flip--_binary64_53`
2×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `flip-+_binary64_52` `distribute-rgt-in_binary64_28` `associate--l+_binary64_15` `frac-times_binary64_88` `pow-prod-down_binary64_149` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `associate-r/_binary64_20` `flip3-+_binary64_81`
1×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `div-inv_binary64_75` `associate-*l/_binary64_21` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 110

Calls

4 calls:

18.0ms	(.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t))))
15.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

series1.1s (11.6%)

Counts

4 → 12

Calls

4 calls:

817.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
164.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
98.0ms	(.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t))))
23.0ms	(*.f64 (sqrt.f64 2) t)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5396	3391

prune261.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	9	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Error

5.5b

Counts

123 → 9

Compiler

Compiled 4817 to 2891 computations (40% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
6.7b	(/.f64 (*.f64 l l) x)
9.0b	(/.f64 (*.f64 t t) x)
26.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`associate-*r/_binary64_20`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`frac-add_binary64_86` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`sqrt-prod_binary64_94`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-+r+_binary64_10` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

series168.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
47.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
16.0ms	(/.f64 (*.f64 t t) x)
13.0ms	(/.f64 (*.f64 l l) x)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4990	1973
1	4990	1973

prune138.0ms (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	80	15	95

Error

3.6b

Counts

95 → 15

Compiler

Compiled 3407 to 1611 computations (52.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
9.0b	(/.f64 (*.f64 t t) x)
26.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-+r+_binary64_10` `sum-log_binary64_169`
1×	`distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
5.0ms	(/.f64 (*.f64 t t) x)
4.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))

series188.0ms (2%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
51.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
29.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
16.0ms	(/.f64 (*.f64 t t) x)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4966	2011
1	4966	2011

prune115.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	76	15	91

Error

3.6b

Counts

91 → 15

Compiler

Compiled 3148 to 1468 computations (53.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
9.0b	(/.f64 (*.f64 t t) x)
26.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-+r+_binary64_10` `sum-log_binary64_169`
1×	`distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

4 calls:

15.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
5.0ms	(/.f64 (*.f64 t t) x)

series179.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
45.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
31.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
12.0ms	(/.f64 (*.f64 t t) x)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4971	2014
1	4971	2014

prune91.0ms (1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	76	15	91

Error

3.6b

Counts

91 → 15

Compiler

Compiled 2547 to 1066 computations (58.1% saved)

regimes1.7s (17.5%)

Accuracy

Total 6.6b remaining (62.9%)

Threshold costs 0b (0%)

Compiler

Compiled 18191 to 12681 computations (30.3% saved)

bsearch586.0ms (6.2%)

Steps

Iters	Range		Point
8	1.1098604389185157e+26	1.0524223840785883e+30	1.0360494278012444e+30
8	1.7577167728056605e-180	5.357364644093366e-178	1.7732721537111569e-180
11	3.720860227136851e-266	1.2681449723912961e-241	1.2532264623485196e-241
6	-3.878589224974133e-262	-8.672881625549915e-263	-3.8356938576006817e-262
5	-1.5822654374270273e-208	-7.079502792542368e-209	-7.168543711359687e-209
10	-2.6744939216037626e+17	-14619895.564651888	-2.650489049077127e+17

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	278	290
1	278	290

end0.0ms (0%)

sample3.5s (36.7%)

Algorithm

1×

intervals

Results

370.0ms	5247×	body	128	valid
326.0ms	1198×	body	1024	valid
213.0ms	796×	body	1024	nan
187.0ms	916×	body	512	valid
106.0ms	1560×	body	128	nan
102.0ms	527×	body	512	nan
76.0ms	568×	body	256	valid
38.0ms	280×	body	256	nan
24.0ms	71×	body	2048	valid

Compiler

Compiled 2712 to 1881 computations (30.6% saved)

Details

analyze772.0ms (8.1%)

sample56.0ms (0.6%)

simplify158.0ms (1.7%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite70.0ms (0.7%)

series1.1s (11.6%)

simplify60.0ms (0.6%)

prune261.0ms (2.7%)

localize17.0ms (0.2%)

rewrite33.0ms (0.3%)

series168.0ms (1.8%)

simplify67.0ms (0.7%)

prune138.0ms (1.5%)

localize19.0ms (0.2%)

rewrite33.0ms (0.3%)

series188.0ms (2%)

simplify83.0ms (0.9%)

prune115.0ms (1.2%)

localize16.0ms (0.2%)

rewrite43.0ms (0.5%)

series179.0ms (1.9%)

simplify67.0ms (0.7%)

prune91.0ms (1%)

regimes1.7s (17.5%)

bsearch586.0ms (6.2%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.5s (36.7%)

Profiling