Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

sample94.0ms

Algorithm

intervals

Results

24.0ms	43×	body	1280	valid
15.0ms	20×	body	2560	valid
11.0ms	34×	body	640	valid
10.0ms	131×	body	80	valid
7.0ms	88×	body	80	nan
3.0ms	14×	body	320	valid
3.0ms	39×	body	80	invalid
2.0ms	14×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	756	19
1	756	19

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 24.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
0.5b	(/.f64 a (*.f64 b 3))
26.0b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`times-frac_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64` `cos-diff_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(/.f64 (*.f64 z t) 3)
7.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
5.0ms	(/.f64 a (*.f64 b 3))
6.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 (*.f64 z t) 3)
34.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
3.0ms	(/.f64 a (*.f64 b 3))
12.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

simplify58.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4946	780
1	4946	780

prune209.0ms

Filtered

59 candidates to 83 candidates (-40.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	65	18	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	18	84

Merged error: 19.1b

Counts

84 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 t (sqrt.f64 3))
0.4b	(/.f64 z (sqrt.f64 3))
0.5b	(/.f64 a (*.f64 b 3))
26.0b	(cos.f64 (-.f64 y (*.f64 (/.f64 z (sqrt.f64 3)) (/.f64 t (sqrt.f64 3)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
13×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `cbrt-unprod_binary64` `cos-diff_binary64` `prod-exp_binary64` `cos-sum_binary64`

Counts

4 → 108

Calls

4 calls:

5.0ms	(/.f64 t (sqrt.f64 3))
5.0ms	(/.f64 z (sqrt.f64 3))
5.0ms	(/.f64 a (*.f64 b 3))
4.0ms	(cos.f64 (-.f64 y (*.f64 (/.f64 z (sqrt.f64 3)) (/.f64 t (sqrt.f64 3)))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 t (sqrt.f64 3))
7.0ms	(/.f64 z (sqrt.f64 3))
4.0ms	(/.f64 a (*.f64 b 3))
25.0ms	(cos.f64 (-.f64 y (*.f64 (/.f64 z (sqrt.f64 3)) (/.f64 t (sqrt.f64 3)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5396	925

prune257.0ms

Filtered

79 candidates to 120 candidates (-51.9%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	109	11	120
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	112	26	138

Merged error: 18.9b

Counts

138 → 26

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (+.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 z (/.f64 t 3)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (/.f64 t 3))))))
0.5b	(/.f64 a (*.f64 b 3))
30.3b	(cos.f64 (*.f64 z (/.f64 t 3)))
30.5b	(sin.f64 (*.f64 z (/.f64 t 3)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-/l_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `associate-/r_binary64` `cos-mult_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

12.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (+.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 z (/.f64 t 3)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (/.f64 t 3))))))
6.0ms	(/.f64 a (*.f64 b 3))
2.0ms	(cos.f64 (*.f64 z (/.f64 t 3)))
2.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (+.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 z (/.f64 t 3)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (/.f64 t 3))))))
4.0ms	(/.f64 a (*.f64 b 3))
4.0ms	(cos.f64 (*.f64 z (/.f64 t 3)))
5.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))

simplify43.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4992	1024
1	4992	1024

prune251.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	1	23	24
Picked	1	0	1
Done	0	1	1
Total	64	32	96

Merged error: 18.8b

Counts

96 → 32

localize45.0ms

Local error

Found 4 expressions with local error:

30.5b	(sin.f64 (*.f64 z (/.f64 t 3)))
30.5b	(sin.f64 (*.f64 z (/.f64 t 3)))
30.5b	(sin.f64 (*.f64 z (/.f64 t 3)))
30.5b	(sin.f64 (*.f64 z (/.f64 t 3)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

4 calls:

2.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))
2.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))
2.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))
2.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))
5.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))
4.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))
5.0ms	(sin.f64 (*.f64 z (/.f64 t 3)))

simplify125.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4739	300
1	4739	300

prune120.0ms

Filtered

36 candidates to 40 candidates (-11.1%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	1	29	30
Picked	1	0	1
Done	0	1	1
Total	38	34	72

Merged error: 18.8b

Counts

72 → 34

regimes4.4s

Accuracy

53.4% (2.1b remaining)

Error of 17.8b against oracle of 15.7b and baseline of 20.2b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	133	54
1	133	54

end0.0ms

sample2.5s

Algorithm

intervals

Results

669.0ms	1417×	body	1280	valid
365.0ms	4618×	body	80	valid
312.0ms	944×	body	640	valid
279.0ms	366×	body	2560	valid
179.0ms	2247×	body	80	nan
105.0ms	425×	body	320	valid
82.0ms	1064×	body	80	invalid
42.0ms	230×	body	160	valid

Details

analyze1.1s

sample94.0ms

simplify39.0ms

prune10.0ms

localize20.0ms

rewrite25.0ms

series54.0ms

simplify58.0ms

prune209.0ms

localize24.0ms

rewrite22.0ms

series42.0ms

simplify68.0ms

prune257.0ms

localize25.0ms

rewrite25.0ms

series81.0ms

simplify43.0ms

prune251.0ms

localize45.0ms

rewrite9.0ms

series18.0ms

simplify125.0ms

prune120.0ms

regimes4.4s

bsearch2.0ms

simplify3.0ms

end0.0ms

sample2.5s

Profiling