Details

analyze761.0ms (8.6%)

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)

sample54.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	186×	body	128	valid
9.0ms	35×	body	1024	valid
4.0ms	17×	body	1024	nan
4.0ms	20×	body	512	valid
3.0ms	52×	body	128	nan
2.0ms	11×	body	512	nan
2.0ms	12×	body	256	valid
1.0ms	11×	body	256	nan
1.0ms	3×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify156.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5192	41

prune5.0ms (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

Merged error: 42.1b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
9.9b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
23.3b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `associate--l+_binary64_15` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 80

Calls

4 calls:

19.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (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))
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)))
5.0ms	(*.f64 (sqrt.f64 2) t)

series1.4s (16.1%)

Counts

4 → 12

Calls

4 calls:

832.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
401.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
169.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
23.0ms	(*.f64 (sqrt.f64 2) t)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5269	3058

prune179.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 4.7b

Counts

93 → 5

Compiler

Compiled 3586 to 2100 computations (41.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.9b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.6b	(/.f64 (*.f64 l l) x)
10.4b	(/.f64 (*.f64 t t) x)
28.1b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite33.0ms (0.4%)

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:

9.0ms	(+.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)

series171.0ms (1.9%)

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)))))
49.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
15.0ms	(/.f64 (*.f64 l l) x)
15.0ms	(/.f64 (*.f64 t t) x)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4990	1973
1	4990	1973

prune123.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 2.7b

Counts

91 → 12

Compiler

Compiled 3246 to 1496 computations (53.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) t)
4.9b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
10.4b	(/.f64 (*.f64 t t) x)
28.1b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_100`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`associate-*r/_binary64_20`
7×	`sqrt-prod_binary64_94` `pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117`
4×	`frac-add_binary64_86` `flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`times-frac_binary64_84` `associate-r_binary64_18` `associate-/r*_binary64_22`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `associate-+r+_binary64_10` `unswap-sqr_binary64_46`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `pow-prod-down_binary64_149` `clear-num_binary64_77` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 75

Calls

4 calls:

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

series177.0ms (2%)

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 l (/.f64 x l))))))
47.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
24.0ms	(*.f64 (sqrt.f64 2) t)
13.0ms	(/.f64 (*.f64 t t) x)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4973	1974
1	4973	1974

prune125.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	87	12	99

Merged error: 2.7b

Counts

99 → 12

Compiler

Compiled 3293 to 1534 computations (53.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
4.9b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
10.4b	(/.f64 (*.f64 t t) x)
28.1b	(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:

12.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
10.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
8.0ms	(+.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)

series188.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
48.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
33.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
13.0ms	(/.f64 (*.f64 t t) x)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4971	2014
1	4971	2014

prune135.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	77	11	88

Merged error: 2.7b

Counts

88 → 11

Compiler

Compiled 3231 to 1750 computations (45.8% saved)

regimes1.4s (15.7%)

Compiler: Compiled 15279 to 10338 computations (32.3% saved)

bsearch362.0ms (4.1%)

Steps

Iters	Range		Point
9	4.8562945904563464e+64	3.2942657960820247e+73	3.213319977435534e+73
9	6.1612029101791026e-170	4.08020500711254e-165	6.213018724746611e-170
7	1.7808557980494506e-208	2.990734007936335e-206	2.918991300642878e-206
8	-1.2248956379418868e+82	-1.0055773212651376e+78	-1.2048443837139665e+82

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	162	229
1	162	229

end0.0ms (0%)

sample3.1s (35.4%)

Algorithm

1×

intervals

Results

371.0ms	5329×	body	128	valid
299.0ms	1130×	body	1024	valid
205.0ms	793×	body	1024	nan
172.0ms	896×	body	512	valid
102.0ms	1571×	body	128	nan
95.0ms	498×	body	512	nan
78.0ms	572×	body	256	valid
35.0ms	274×	body	256	nan
28.0ms	73×	body	2048	valid

Compiler

Compiled 2309 to 1549 computations (32.9% saved)

Details

analyze761.0ms (8.6%)

sample54.0ms (0.6%)

simplify156.0ms (1.8%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite63.0ms (0.7%)

series1.4s (16.1%)

simplify49.0ms (0.5%)

prune179.0ms (2%)

localize14.0ms (0.2%)

rewrite33.0ms (0.4%)

series171.0ms (1.9%)

simplify59.0ms (0.7%)

prune123.0ms (1.4%)

localize17.0ms (0.2%)

rewrite33.0ms (0.4%)

series177.0ms (2%)

simplify60.0ms (0.7%)

prune125.0ms (1.4%)

localize18.0ms (0.2%)

rewrite43.0ms (0.5%)

series188.0ms (2.1%)

simplify59.0ms (0.7%)

prune135.0ms (1.5%)

regimes1.4s (15.7%)

bsearch362.0ms (4.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.1s (35.4%)

Profiling