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

sample86.0ms

Algorithm

intervals

Results

44.0ms	98×	body	1280	valid
14.0ms	51×	body	640	valid
6.0ms	33×	body	320	valid
4.0ms	67×	body	80	valid
1.0ms	7×	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: 17.9b

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)))
3.2b	(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))
6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))

series46.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(*.f64 r (sin.f64 b))
30.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
6.0ms	(cos.f64 (+.f64 a b))

simplify66.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4845	433
1	4845	433

prune70.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
7.0ms	(*.f64 r (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))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series94.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
11.0ms	(*.f64 r (sin.f64 b))
61.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
12.0ms	(*.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	5040	873

prune126.0ms

Filtered

67 candidates to 93 candidates (-38.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	12	93
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 0.0b

Counts

100 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.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 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))))

rewrite37.0ms

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))
13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
7.0ms	(*.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))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
64.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
12.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
34.0ms	(/.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

117 → 117

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5853	1589

prune121.0ms

Filtered

90 candidates to 117 candidates (-30.0%)

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: 0.0b

Counts

129 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
24.2b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64`
8×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64` `sin-mult_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-/r/_binary64` `associate-l*_binary64` `cube-div_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `cos-mult_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

12.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
6.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

series107.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
11.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
21.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
12.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5235	978

prune66.0ms

Filtered

62 candidates to 96 candidates (-54.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	96	12	108

Merged error: 0.0b

Counts

108 → 12

regimes225.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b 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

sample2.4s

Algorithm

intervals

Results

1.3s	2883×	body	1280	valid
520.0ms	1859×	body	640	valid
161.0ms	792×	body	320	valid
139.0ms	2096×	body	80	valid
58.0ms	370×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze1.2s

sample86.0ms

simplify5.0ms

prune6.0ms

localize10.0ms

rewrite16.0ms

series46.0ms

simplify66.0ms

prune70.0ms

localize15.0ms

rewrite29.0ms

series94.0ms

simplify42.0ms

prune126.0ms

localize15.0ms

rewrite37.0ms

series120.0ms

simplify57.0ms

prune121.0ms

localize18.0ms

rewrite28.0ms

series107.0ms

simplify42.0ms

prune66.0ms

regimes225.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling