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

sample89.0ms

Algorithm

intervals

Results

49.0ms	91×	body	1280	valid
15.0ms	52×	body	640	valid
7.0ms	35×	body	320	valid
5.0ms	70×	body	80	valid
1.0ms	8×	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: 14.1b

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

series42.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(*.f64 r (sin.f64 b))
29.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
6.0ms	(cos.f64 (+.f64 a b))

simplify64.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5357	439

prune78.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 r (sin.f64 b))
17.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
52.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4979	974
1	4979	974

prune112.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

localize16.0ms

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)))
0.2b	(.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))))
0.2b	(*.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)))
13.0ms	(.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))))
6.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series113.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
53.0ms	(.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))))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify63.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5901	1692

prune119.0ms

Filtered

86 candidates to 111 candidates (-29.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Merged error: 0.0b

Counts

121 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.4b	(.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1_binary64`
39×	`associate-l_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`cos-mult_binary64`
22×	`sin-mult_binary64`
20×	`pow-prod-down_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-/r/_binary64`
14×	`associate-*r/_binary64`
13×	`times-frac_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
10×	`associate-r_binary64`
9×	`frac-sub_binary64`
5×	`sub-div_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `*-commutative_binary64`
3×	`difference-of-squares_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `pow-plus_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `swap-sqr_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 134

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
29.0ms	(.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
10.0ms	(.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
84.0ms	(.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
15.0ms	(.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))

simplify59.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5025	2146

prune127.0ms

Filtered

105 candidates to 146 candidates (-39.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	146	11	157

Merged error: 0.0b

Counts

157 → 11

regimes228.0ms

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

sample2.6s

Algorithm

intervals

Results

1.4s	2899×	body	1280	valid
572.0ms	1873×	body	640	valid
172.0ms	784×	body	320	valid
150.0ms	2108×	body	80	valid
64.0ms	336×	body	160	valid
0.0ms	1×	body	640	invalid
0.0ms	1×	body	80	invalid

Details

analyze1.2s

sample89.0ms

simplify5.0ms

prune6.0ms

localize10.0ms

rewrite16.0ms

series42.0ms

simplify64.0ms

prune78.0ms

localize15.0ms

rewrite29.0ms

series85.0ms

simplify45.0ms

prune112.0ms

localize16.0ms

rewrite36.0ms

series113.0ms

simplify63.0ms

prune119.0ms

localize21.0ms

rewrite55.0ms

series117.0ms

simplify59.0ms

prune127.0ms

regimes228.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling