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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample70.0ms

Algorithm

intervals

Results

17.0ms	189×	body	80	valid
13.0ms	27×	body	1280	valid
7.0ms	21×	body	640	valid
6.0ms	67×	body	80	invalid
5.0ms	14×	body	640	invalid
4.0ms	4×	body	1280	invalid
2.0ms	10×	body	320	valid
2.0ms	7×	body	320	invalid
2.0ms	9×	body	160	valid
1.0ms	4×	body	160	invalid

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (211.0ms)

Iter	Nodes	Cost
0	7279	24

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: 30.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.8b	(.f64 (.f64 x (pow.f64 s 2)) x)
9.8b	(*.f64 x (pow.f64 s 2))
18.8b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log_binary64`
82×	`prod-exp_binary64`
34×	`add-cbrt-cube_binary64`
18×	`pow-to-exp_binary64` `add-sqr-sqrt_binary64` `pow-exp_binary64`
16×	`cbrt-unprod_binary64` `div-exp_binary64`
12×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
7×	`unpow-prod-down_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64`
3×	`unpow2_binary64` `sqr-pow_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `cos-2_binary64`

Counts

4 → 119

Calls

4 calls:

12.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
9.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))
10.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
27.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
27.0ms	(*.f64 x (pow.f64 s 2))
60.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

simplify75.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4975	2228
1	4975	2228

prune98.0ms

Filtered

68 candidates to 131 candidates (-92.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 1.2b

Counts

132 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
1.0b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
3.8b	(.f64 s (.f64 c x))
3.8b	(.f64 s (.f64 c x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`pow-prod-down_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-sqr_binary64` `cos-2_binary64` `pow2_binary64`

Counts

4 → 83

Calls

4 calls:

3.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))

series178.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
103.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
24.0ms	(.f64 s (.f64 c x))
27.0ms	(.f64 s (.f64 c x))

simplify95.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4951	1303
1	4951	1303

prune93.0ms

Filtered

57 candidates to 95 candidates (-66.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Merged error: 0.5b

Counts

105 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
1.1b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
3.8b	(.f64 s (.f64 c x))
3.8b	(.f64 s (.f64 c x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64` `times-frac_binary64`
15×	`pow1_binary64`
6×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64`
3×	`div-exp_binary64`
2×	`associate-r_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `pow-flip_binary64`

Counts

4 → 94

Calls

4 calls:

3.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
6.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))

series128.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
55.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
25.0ms	(.f64 s (.f64 c x))
25.0ms	(.f64 s (.f64 c x))

simplify95.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5056	1714

prune99.0ms

Filtered

65 candidates to 106 candidates (-63.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	104	16	120

Merged error: 0.5b

Counts

120 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
1.1b	(/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (fabs.f64 (.f64 s (*.f64 c x))))
3.8b	(.f64 s (.f64 c x))
3.8b	(.f64 s (.f64 c x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
27×	`times-frac_binary64`
20×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
15×	`pow1_binary64`
12×	`cbrt-prod_binary64`
9×	`associate-/l*_binary64`
6×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`div-exp_binary64`
2×	`associate-r_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `pow-flip_binary64`

Counts

4 → 106

Calls

4 calls:

3.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
4.0ms	(/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
7.0ms	(.f64 s (.f64 c x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
100.0ms	(/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (fabs.f64 (.f64 s (*.f64 c x))))
24.0ms	(.f64 s (.f64 c x))
25.0ms	(.f64 s (.f64 c x))

simplify119.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4926	2239
1	4926	2239

prune137.0ms

Filtered

77 candidates to 118 candidates (-53.2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	117	17	134

Merged error: 0.5b

Counts

134 → 17

regimes162.0ms

Accuracy

0% (1.2b remaining)

Error of 2.8b against oracle of 1.6b and baseline of 2.8b

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	31
1	20	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

554.0ms	5984×	body	80	valid
344.0ms	677×	body	1280	valid
266.0ms	755×	body	640	valid
161.0ms	1852×	body	80	invalid
101.0ms	388×	body	320	valid
95.0ms	265×	body	640	invalid
60.0ms	130×	body	1280	invalid
45.0ms	186×	body	320	invalid
39.0ms	196×	body	160	valid
18.0ms	106×	body	160	invalid

Details

analyze1.1s

sample70.0ms

simplify221.0ms

prune3.0ms

localize14.0ms

rewrite41.0ms

series190.0ms

simplify75.0ms

prune98.0ms

localize11.0ms

rewrite21.0ms

series178.0ms

simplify95.0ms

prune93.0ms

localize12.0ms

rewrite22.0ms

series128.0ms

simplify95.0ms

prune99.0ms

localize16.0ms

rewrite23.0ms

series180.0ms

simplify119.0ms

prune137.0ms

regimes162.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample2.0s

Profiling