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

sample87.0ms

Algorithm

intervals

Results

39.0ms	87×	body	1280	valid
27.0ms	76×	body	640	valid
4.0ms	68×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	5×	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: 16.5b

Counts

2 → 1

localize10.0ms

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))

series49.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(*.f64 r (sin.f64 b))
34.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
6.0ms	(cos.f64 (+.f64 a b))

simplify65.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5357	439

prune81.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.1b

Counts

57 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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:

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

series94.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 r (sin.f64 b))
12.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
63.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4976	875
1	4976	875

prune119.0ms

Filtered

67 candidates to 93 candidates (-38.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	91	12	103

Merged error: 0.0b

Counts

103 → 12

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

rewrite31.0ms

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

series113.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
10.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
56.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
22.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

simplify70.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4923	1426
1	4923	1426

prune115.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 0b

Counts

115 → 12

localize15.0ms

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

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))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
12.0ms	(.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))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
11.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
64.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
37.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

simplify63.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6041	1616

prune84.0ms

Filtered

89 candidates to 117 candidates (-31.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	117	12	129

Merged error: 0b

Counts

129 → 12

regimes228.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b 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

sample2.5s

Algorithm

intervals

Results

1.4s	2954×	body	1280	valid
526.0ms	1828×	body	640	valid
149.0ms	755×	body	320	valid
138.0ms	2121×	body	80	valid
50.0ms	342×	body	160	valid
0.0ms	1×	body	160	invalid

Details

analyze1.2s

sample87.0ms

simplify5.0ms

prune6.0ms

localize10.0ms

rewrite16.0ms

series49.0ms

simplify65.0ms

prune81.0ms

localize15.0ms

rewrite29.0ms

series94.0ms

simplify42.0ms

prune119.0ms

localize14.0ms

rewrite31.0ms

series113.0ms

simplify70.0ms

prune115.0ms

localize15.0ms

rewrite35.0ms

series122.0ms

simplify63.0ms

prune84.0ms

regimes228.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling