Details

analyze779.0ms

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

sample65.0ms

Algorithm

intervals

Results

11.0ms	162×	body	80	valid
9.0ms	35×	body	640	valid
8.0ms	15×	body	1280	nan
8.0ms	23×	body	1280	valid
5.0ms	24×	body	320	valid
5.0ms	19×	body	640	nan
3.0ms	47×	body	80	nan
2.0ms	11×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5189	41

prune2.0ms

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: 42.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.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))))
0.5b	(*.f64 (sqrt.f64 2) t)
11.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
19.5b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite59.0ms

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:

22.0ms	(/.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)
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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

365.0ms	(/.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))))
27.0ms	(*.f64 (sqrt.f64 2) t)
180.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
766.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify58.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5217	3050

prune158.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 7.4b

Counts

92 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.0b	(/.f64 (*.f64 l l) x)
9.3b	(/.f64 (*.f64 t t) x)
27.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite29.0ms

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)))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
13.0ms	(/.f64 (*.f64 l l) x)
13.0ms	(/.f64 (*.f64 t t) x)
94.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5181	1977

prune106.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	82	12	94

Merged error: 5.3b

Counts

94 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) t)
4.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
9.3b	(/.f64 (*.f64 t t) x)
27.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r_binary64` `associate-r*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `pow1/2_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` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

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

series179.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (sqrt.f64 2) t)
49.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
15.0ms	(/.f64 (*.f64 t t) x)
92.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4970	1974
1	4970	1974

prune103.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	85	14	99

Merged error: 5.3b

Counts

99 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
4.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
9.3b	(/.f64 (*.f64 t t) x)
27.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite37.0ms

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:

11.0ms	(+.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)))))
5.0ms	(/.f64 (*.f64 t t) x)
10.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
50.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
15.0ms	(/.f64 (*.f64 t t) x)
92.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5557	2011

prune89.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	74	16	90

Merged error: 5.3b

Counts

90 → 16

regimes409.0ms

Accuracy

76.7% (5.5b remaining)

Error of 9.5b against oracle of 4.0b and baseline of 27.8b

bsearch270.0ms

Steps

Iters	Range		Point
0	9.877557925289223e+70	1.0044914929117374e+71	9.961236427203297e+70
9	-1.7080949674371795e-285	-6.464578662837893e-291	-1.6798737234628474e-285
5	-1.4443056956312788e-201	-7.152015967953739e-202	-7.2168921486126805e-202
8	-5.661574592413005e+134	-1.7888698217899963e+130	-1.1260799277907824e+131

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	153	262
1	153	262

end0.0ms

sample1.9s

Algorithm

intervals

Results

374.0ms	5159×	body	80	valid
290.0ms	857×	body	1280	valid
279.0ms	1043×	body	640	valid
196.0ms	580×	body	1280	nan
155.0ms	595×	body	640	nan
124.0ms	617×	body	320	valid
94.0ms	1374×	body	80	nan
66.0ms	322×	body	320	nan
46.0ms	324×	body	160	valid
24.0ms	187×	body	160	nan

Details

analyze779.0ms

sample65.0ms

simplify102.0ms

prune2.0ms

localize16.0ms

rewrite59.0ms

series1.3s

simplify58.0ms

prune158.0ms

localize15.0ms

rewrite29.0ms

series166.0ms

simplify53.0ms

prune106.0ms

localize15.0ms

rewrite29.0ms

series179.0ms

simplify97.0ms

prune103.0ms

localize17.0ms

rewrite37.0ms

series189.0ms

simplify50.0ms

prune89.0ms

regimes409.0ms

bsearch270.0ms

simplify6.0ms

end0.0ms

sample1.9s

Profiling