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

sample78.0ms

Algorithm

intervals

Results

38.0ms	79×	body	1280	valid
17.0ms	61×	body	640	valid
6.0ms	30×	body	320	valid
5.0ms	74×	body	80	valid
2.0ms	12×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune3.0ms

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: 10.5b

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)))
2.8b	(cos.f64 (+.f64 a b))

rewrite15.0ms

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

series160.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(*.f64 r (sin.f64 b))
112.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
17.0ms	(cos.f64 (+.f64 a b))

simplify102.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5361	692

prune52.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	11	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 0.1b

Counts

57 → 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)))
0.1b	(*.f64 r (sin.f64 b))
0.1b	(*.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))))

rewrite25.0ms

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:

5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
4.0ms	(*.f64 r (sin.f64 b))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
30.0ms	(*.f64 r (sin.f64 b))
39.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
250.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify111.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4968	1582
1	4968	1582

prune85.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	84	14	98

Merged error: 0.0b

Counts

98 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

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

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:

4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
10.0ms	(-.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))
9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
91.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
73.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
220.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))

simplify117.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4936	2329
1	4936	2329

prune88.0ms

Filtered

71 candidates to 103 candidates (-45.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 0.0b

Counts

117 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.1b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
3.7b	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `log-prod_binary64` `log-pow_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 74

Calls

4 calls:

4.0ms	(*.f64 r (sin.f64 b))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(*.f64 r (sin.f64 b))
42.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
244.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
42.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

simplify90.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4997	1318
1	4997	1318

prune50.0ms

Filtered

58 candidates to 86 candidates (-48.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	86	13	99

Merged error: 0.0b

Counts

99 → 13

regimes86.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	30
1	28	30

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2960×	body	1280	valid
537.0ms	1845×	body	640	valid
158.0ms	759×	body	320	valid
145.0ms	2122×	body	80	valid
52.0ms	314×	body	160	valid

Details

analyze1.1s

sample78.0ms

simplify18.0ms

prune3.0ms

localize10.0ms

rewrite15.0ms

series160.0ms

simplify102.0ms

prune52.0ms

localize15.0ms

rewrite25.0ms

series396.0ms

simplify111.0ms

prune85.0ms

localize14.0ms

rewrite31.0ms

series422.0ms

simplify117.0ms

prune88.0ms

localize18.0ms

rewrite22.0ms

series362.0ms

simplify90.0ms

prune50.0ms

regimes86.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample2.5s

Profiling