Details

analyze1.2s

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

46.0ms	97×	body	1280	valid
19.0ms	70×	body	640	valid
4.0ms	64×	body	80	valid
3.0ms	17×	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

prune5.0ms

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: 14.6b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.3b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.2b	(cos.f64 (+.f64 a b))

rewrite17.0ms

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:

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

series40.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(*.f64 r (sin.f64 b))
26.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
7.0ms	(cos.f64 (+.f64 a b))

simplify64.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5357	439

prune51.0ms

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: 0.2b

Counts

57 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 r (sin.f64 b))
18.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
54.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4979	974
1	4979	974

prune79.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	74	13	87
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 0.0b

Counts

95 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
15.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
56.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
31.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6025	1735

prune77.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	112	13	125

Merged error: 0.0b

Counts

125 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
0.2b	(/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.3b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`associate-r_binary64` `add-cbrt-cube_binary64`
18×	`times-frac_binary64`
13×	`prod-exp_binary64`
12×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`cbrt-unprod_binary64` `sin-mult_binary64`
6×	`add-log-exp_binary64` `cos-mult_binary64` `div-exp_binary64`
4×	`pow-prod-down_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `associate-/l_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 109

Calls

4 calls:

6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
9.0ms	(/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
15.0ms	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
26.0ms	(/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
57.0ms	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5089	1769

prune40.0ms

Filtered

75 candidates to 121 candidates (-61.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	121	13	134

Merged error: 0.0b

Counts

134 → 13

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	18
1	44	18

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2889×	body	1280	valid
530.0ms	1858×	body	640	valid
169.0ms	792×	body	320	valid
143.0ms	2098×	body	80	valid
54.0ms	363×	body	160	valid

Details

analyze1.2s

sample84.0ms

simplify5.0ms

prune5.0ms

localize17.0ms

rewrite17.0ms

series40.0ms

simplify64.0ms

prune51.0ms

localize15.0ms

rewrite30.0ms

series88.0ms

simplify44.0ms

prune79.0ms

localize15.0ms

rewrite39.0ms

series114.0ms

simplify60.0ms

prune77.0ms

localize19.0ms

rewrite39.0ms

series110.0ms

simplify59.0ms

prune40.0ms

regimes177.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling