Details

analyze1.0s

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
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample84.0ms

Algorithm

intervals

Results

51.0ms	108×	body	1280	valid
12.0ms	45×	body	640	valid
6.0ms	29×	body	320	valid
4.0ms	66×	body	80	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune8.0ms

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: 13.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.6b	(cos.f64 (+.f64 a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `cos-sum_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(*.f64 r (sin.f64 b))
5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(*.f64 r (sin.f64 b))
105.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
17.0ms	(cos.f64 (+.f64 a b))

simplify104.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5361	692

prune47.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.1b

Counts

57 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cos-mult_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
4.0ms	(*.f64 r (sin.f64 b))
10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series360.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
34.0ms	(*.f64 r (sin.f64 b))
249.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
41.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify68.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4978	1420
1	4978	1420

prune86.0ms

Filtered

67 candidates to 93 candidates (-38.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	90	11	101

Merged error: 0.0b

Counts

101 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
23×	`associate-r_binary64`
19×	`times-frac_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-l_binary64`
8×	`associate-/r/_binary64`
5×	`cos-mult_binary64` `sin-mult_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 105

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
12.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series475.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
252.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
143.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
40.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify100.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5722	2593

prune95.0ms

Filtered

85 candidates to 117 candidates (-37.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	118	10	128

Merged error: 0b

Counts

128 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.2b	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
0.2b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
4×	`associate-/l*_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cos-mult_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
6.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
38.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
79.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
224.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))

simplify117.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4936	2329
1	4936	2329

prune63.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	103	10	113

Merged error: 0b

Counts

113 → 10

regimes67.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2933×	body	1280	valid
528.0ms	1805×	body	640	valid
157.0ms	771×	body	320	valid
138.0ms	2138×	body	80	valid
51.0ms	353×	body	160	valid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.0s

sample84.0ms

simplify12.0ms

prune8.0ms

localize11.0ms

rewrite16.0ms

series156.0ms

simplify104.0ms

prune47.0ms

localize15.0ms

rewrite26.0ms

series360.0ms

simplify68.0ms

prune86.0ms

localize14.0ms

rewrite35.0ms

series475.0ms

simplify100.0ms

prune95.0ms

localize14.0ms

rewrite30.0ms

series439.0ms

simplify117.0ms

prune63.0ms

regimes67.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.5s

Profiling