Details

analyze1.0s

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

45.0ms	87×	body	1280	valid
22.0ms	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:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.6b	(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)))
4.0ms	(cos.f64 (+.f64 a b))

series54.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
14.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
7.0ms	(cos.f64 (+.f64 a b))

simplify64.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5018	783

prune94.0ms

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:

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

rewrite34.0ms

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 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))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
60.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
37.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

simplify58.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5806	1575

prune141.0ms

Filtered

91 candidates to 117 candidates (-28.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	114	11	125

Merged error: 0.0b

Counts

125 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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

series95.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 b) r)
9.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
11.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
67.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify41.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5067	909

prune101.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 0.0b

Counts

104 → 10

localize13.0ms

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))

rewrite30.0ms

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))

series109.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
9.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
54.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
21.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

simplify68.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4923	1426
1	4923	1426

prune78.0ms

Filtered

73 candidates to 103 candidates (-41.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	103	10	113

Merged error: 0b

Counts

113 → 10

regimes201.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	2954×	body	1280	valid
509.0ms	1828×	body	640	valid
151.0ms	755×	body	320	valid
142.0ms	2121×	body	80	valid
54.0ms	342×	body	160	valid
0.0ms	1×	body	160	invalid

Details

analyze1.0s

sample87.0ms

simplify5.0ms

prune6.0ms

localize10.0ms

rewrite19.0ms

series54.0ms

simplify64.0ms

prune94.0ms

localize15.0ms

rewrite34.0ms

series117.0ms

simplify58.0ms

prune141.0ms

localize17.0ms

rewrite26.0ms

series95.0ms

simplify41.0ms

prune101.0ms

localize13.0ms

rewrite30.0ms

series109.0ms

simplify68.0ms

prune78.0ms

regimes201.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling