Details

analyze788.0ms

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

13.0ms	161×	body	80	valid
11.0ms	34×	body	1280	valid
8.0ms	32×	body	640	valid
7.0ms	26×	body	640	nan
5.0ms	15×	body	1280	nan
3.0ms	44×	body	80	nan
3.0ms	14×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	8×	body	320	nan
1.0ms	7×	body	160	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

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: 44.0b

Counts

2 → 1

localize16.0ms

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)
14.5b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.0b	(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:

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)
17.0ms	(-.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:

360.0ms	(/.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))))
24.0ms	(*.f64 (sqrt.f64 2) t)
179.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
764.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify57.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5217	3050

prune154.0ms

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: 6.0b

Counts

92 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

4.8b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
8.3b	(/.f64 (*.f64 l l) x)
9.0b	(/.f64 (*.f64 t t) x)
24.6b	(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)))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+.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)
91.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5181	1977

prune103.0ms

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: 2.9b

Counts

91 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
4.8b	(+.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)
24.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite28.0ms

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

series186.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
48.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
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 l x))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4965	2011
1	4965	2011

prune91.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	75	11	86

Merged error: 2.9b

Counts

86 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

2.4b	(/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x))
4.8b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x)))))
9.0b	(/.f64 (*.f64 t t) x)
24.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

11.0ms	(/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 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 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x))))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x))
58.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x)))))
15.0ms	(/.f64 (*.f64 t t) x)
107.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) l) (cbrt.f64 x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5412	2267

prune98.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	95	13	108

Merged error: 2.9b

Counts

108 → 13

regimes245.0ms

Accuracy

75.4% (5.8b remaining)

Error of 9.5b against oracle of 3.6b and baseline of 27.3b

bsearch176.0ms

Steps

Iters	Range		Point
9	2.42721730114719e+45	5.473726802386931e+51	5.411969238321326e+51
8	-8.802466151713679e-13	-5.182961738255739e-17	-8.677514333815515e-13

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	142	152
1	142	152

end0.0ms

sample1.9s

Algorithm

intervals

Results

366.0ms	5096×	body	80	valid
297.0ms	884×	body	1280	valid
267.0ms	998×	body	640	valid
187.0ms	556×	body	1280	nan
164.0ms	609×	body	640	nan
135.0ms	666×	body	320	valid
91.0ms	1362×	body	80	nan
63.0ms	326×	body	320	nan
48.0ms	356×	body	160	valid
22.0ms	166×	body	160	nan

Details

analyze788.0ms

sample65.0ms

simplify105.0ms

prune2.0ms

localize16.0ms

rewrite59.0ms

series1.3s

simplify57.0ms

prune154.0ms

localize16.0ms

rewrite29.0ms

series163.0ms

simplify52.0ms

prune103.0ms

localize15.0ms

rewrite28.0ms

series186.0ms

simplify78.0ms

prune91.0ms

localize20.0ms

rewrite35.0ms

series206.0ms

simplify58.0ms

prune98.0ms

regimes245.0ms

bsearch176.0ms

simplify5.0ms

end0.0ms

sample1.9s

Profiling