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

sample93.0ms

Algorithm

intervals

Results

54.0ms	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

simplify6.0ms

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

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)))
2.2b	(cos.f64 (+.f64 a b))

rewrite19.0ms

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:

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

series49.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
14.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
8.0ms	(cos.f64 (+.f64 a b))

simplify67.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5018	783

prune61.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.2b

Counts

77 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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)))
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)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.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 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
33.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5901	1692

prune100.0ms

Filtered

90 candidates to 111 candidates (-23.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	97	14	111
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	105	14	119

Merged error: 0.0b

Counts

119 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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)))
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))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 b) r)
17.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
60.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4996	1008
1	4996	1008

prune70.0ms

Filtered

66 candidates to 87 candidates (-31.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	88	13	101

Merged error: 0.0b

Counts

101 → 13

localize16.0ms

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

rewrite36.0ms

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))
8.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
14.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

series135.0ms

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))
47.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
62.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5575	1726

prune41.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	112	12	124

Merged error: 0b

Counts

124 → 12

regimes169.0ms

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	41	16
1	41	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	2889×	body	1280	valid
541.0ms	1858×	body	640	valid
162.0ms	792×	body	320	valid
148.0ms	2098×	body	80	valid
56.0ms	363×	body	160	valid

Details

analyze1.1s

sample93.0ms

simplify6.0ms

prune5.0ms

localize10.0ms

rewrite19.0ms

series49.0ms

simplify67.0ms

prune61.0ms

localize15.0ms

rewrite36.0ms

series113.0ms

simplify57.0ms

prune100.0ms

localize14.0ms

rewrite27.0ms

series93.0ms

simplify43.0ms

prune70.0ms

localize16.0ms

rewrite36.0ms

series135.0ms

simplify55.0ms

prune41.0ms

regimes169.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling