Details

analyze1.1s

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

sample87.0ms

Algorithm

intervals

Results

43.0ms	91×	body	1280	valid
16.0ms	52×	body	640	valid
9.0ms	70×	body	80	valid
7.0ms	35×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune6.0ms

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: 14.1b

Counts

2 → 1

localize10.0ms

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)))
3.2b	(cos.f64 (+.f64 a b))

rewrite18.0ms

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

series44.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
12.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
7.0ms	(cos.f64 (+.f64 a b))

simplify68.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5018	783

prune103.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.2b

Counts

77 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`associate-r_binary64`
19×	`times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-/r/_binary64`
7×	`sin-mult_binary64`
6×	`add-log-exp_binary64` `cos-mult_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 99

Calls

4 calls:

6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.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)))))
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))

series105.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
52.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
29.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5901	1692

prune136.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0.0b

Counts

121 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

4.0ms	(*.f64 (sin.f64 b) r)
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.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))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series88.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 b) r)
16.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
56.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4996	1008
1	4996	1008

prune93.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	87	11	98

Merged error: 0.0b

Counts

98 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r)
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(/.f64 (sin.f64 b) (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

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

series116.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
30.0ms	(/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r)
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
62.0ms	(/.f64 (sin.f64 b) (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r))

simplify53.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5347	3000

prune109.0ms

Filtered

120 candidates to 146 candidates (-21.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	146	11	157

Merged error: 0.0b

Counts

157 → 11

regimes284.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	16
1	41	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	2899×	body	1280	valid
560.0ms	1873×	body	640	valid
328.0ms	784×	body	320	valid
148.0ms	2108×	body	80	valid
52.0ms	336×	body	160	valid
0.0ms	1×	body	640	invalid
0.0ms	1×	body	80	invalid

Details

analyze1.1s

sample87.0ms

simplify5.0ms

prune6.0ms

localize10.0ms

rewrite18.0ms

series44.0ms

simplify68.0ms

prune103.0ms

localize15.0ms

rewrite35.0ms

series105.0ms

simplify57.0ms

prune136.0ms

localize15.0ms

rewrite28.0ms

series88.0ms

simplify42.0ms

prune93.0ms

localize15.0ms

rewrite32.0ms

series116.0ms

simplify53.0ms

prune109.0ms

regimes284.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling