Details

analyze791.0ms

Algorithm

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

sample64.0ms

Algorithm

intervals

Results

11.0ms	166×	body	80	valid
10.0ms	31×	body	1280	valid
8.0ms	33×	body	640	valid
8.0ms	26×	body	1280	nan
4.0ms	15×	body	640	nan
4.0ms	57×	body	80	nan
2.0ms	12×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	3×	body	160	nan

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5004	27

prune3.0ms

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: 43.6b

Counts

2 → 1

localize19.0ms

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)
12.5b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
22.0b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

20.0ms	(/.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))))
5.0ms	(*.f64 (sqrt.f64 2) t)
16.0ms	(-.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)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.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))))
4.0ms	(*.f64 (sqrt.f64 2) t)
62.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
216.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify60.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4974	2007
1	4974	2007

prune114.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 5.9b

Counts

92 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

4.2b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
6.4b	(/.f64 (*.f64 l l) x)
7.9b	(/.f64 (*.f64 t t) x)
28.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
4.0ms	(/.f64 (*.f64 l l) x)
4.0ms	(/.f64 (*.f64 t t) x)
30.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify29.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5022	1324

prune84.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 3.7b

Counts

91 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
4.2b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
7.9b	(/.f64 (*.f64 t t) x)
28.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 64

Calls

4 calls:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
16.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
4.0ms	(/.f64 (*.f64 t t) x)
31.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify27.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5126	1346

prune76.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Merged error: 3.7b

Counts

86 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))) (cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))) (cbrt.f64 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))))
28.9b	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
28.9b	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
28.9b	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div_binary64` `associate-*r/_binary64`
31×	`flip3-+_binary64` `flip-+_binary64`
28×	`frac-times_binary64` `sqrt-div_binary64`
26×	`frac-add_binary64`
14×	`associate-*l/_binary64`
9×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `sqrt-prod_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 80

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))) (cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))) (cbrt.f64 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))))
4.0ms	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
4.0ms	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
4.0ms	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))) (cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))) (cbrt.f64 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))))
26.0ms	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
26.0ms	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
31.0ms	(cbrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5065	3877

prune69.0ms

Filtered

70 candidates to 92 candidates (-31.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	92	12	104

Merged error: 3.7b

Counts

104 → 12

regimes509.0ms

Accuracy

78.7% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 28.2b

bsearch127.0ms

Steps

Iters	Range		Point
8	1.1368285470804771e+73	7.059261040782493e+77	2.777661710195414e+75
10	-4.476035420463226e+95	-3.02417232647103e+84	-1.9518411464144533e+95

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	99
1	140	99

end0.0ms

sample1.9s

Algorithm

intervals

Results

365.0ms	5212×	body	80	valid
273.0ms	828×	body	1280	valid
249.0ms	968×	body	640	valid
193.0ms	588×	body	1280	nan
165.0ms	625×	body	640	nan
126.0ms	636×	body	320	valid
95.0ms	1456×	body	80	nan
68.0ms	362×	body	320	nan
48.0ms	356×	body	160	valid
22.0ms	178×	body	160	nan

Details

analyze791.0ms

sample64.0ms

simplify61.0ms

prune3.0ms

localize19.0ms

rewrite58.0ms

series385.0ms

simplify60.0ms

prune114.0ms

localize15.0ms

rewrite30.0ms

series55.0ms

simplify29.0ms

prune84.0ms

localize15.0ms

rewrite29.0ms

series60.0ms

simplify27.0ms

prune76.0ms

localize20.0ms

rewrite34.0ms

series112.0ms

simplify52.0ms

prune69.0ms

regimes509.0ms

bsearch127.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling