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

sample95.0ms

Algorithm

intervals

Results

50.0ms	97×	body	1280	valid
15.0ms	52×	body	640	valid
5.0ms	25×	body	320	valid
5.0ms	63×	body	80	valid
3.0ms	19×	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

prune15.0ms

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: 15.7b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.9b	(cos.f64 (+.f64 a b))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

7.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
10.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))

series169.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
47.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
16.0ms	(cos.f64 (+.f64 a b))

simplify88.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5042	1258

prune545.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.2b	(*.f64 (sin.f64 a) (sin.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))))

rewrite42.0ms

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:

4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
5.0ms	(*.f64 (sin.f64 a) (sin.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)))))
17.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
41.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
250.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
142.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

simplify94.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5176	2595

prune547.0ms

Filtered

91 candidates to 117 candidates (-28.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 0.0b

Counts

126 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(*.f64 (sin.f64 b) r)
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.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 (sin.f64 b) r)
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
10.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
29.0ms	(*.f64 (sin.f64 b) r)
41.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
278.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify69.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5168	1471

prune404.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
8.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
13.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
39.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
214.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
277.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5037	2693

prune405.0ms

Filtered

86 candidates to 117 candidates (-36.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	117	9	126

Merged error: 0.0b

Counts

126 → 9

regimes508.0ms

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

sample2.6s

Algorithm

intervals

Results

1.4s	2926×	body	1280	valid
550.0ms	1877×	body	640	valid
157.0ms	783×	body	320	valid
140.0ms	2081×	body	80	valid
51.0ms	333×	body	160	valid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.0s

sample95.0ms

simplify12.0ms

prune15.0ms

localize14.0ms

rewrite24.0ms

series169.0ms

simplify88.0ms

prune545.0ms

localize23.0ms

rewrite42.0ms

series473.0ms

simplify94.0ms

prune547.0ms

localize22.0ms

rewrite26.0ms

series389.0ms

simplify69.0ms

prune404.0ms

localize23.0ms

rewrite34.0ms

series567.0ms

simplify93.0ms

prune405.0ms

regimes508.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling