Details

sample145.0ms

Algorithm

intervals

Results

70.0ms	57×	body	2560	valid
44.0ms	93×	body	1280	valid
14.0ms	58×	body	640	valid
5.0ms	28×	body	320	valid
3.0ms	1×	body	5120	valid
1.0ms	10×	body	160	valid
1.0ms	9×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
26.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune192.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	58	16	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	16	75

Merged error: 0.1b

Counts

75 → 16

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series183.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
125.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify35.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	61	148
1	188	130
2	1009	130
3	5002	130

prune95.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	26	16	42

Merged error: 0.1b

Counts

42 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.4b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
4.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
23.0ms	(exp (log (- 1.0 (cos x))))
69.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	354	1019
1	1045	861
2	5001	817

prune260.0ms

Filtered

130 candidates to 81 candidates (62.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	131	15	146

Merged error: 0.1b

Counts

146 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.4b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
9×	`prod-diff`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `log1p-expm1-u` `pow-sub`
3×	`fma-neg` `associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 144

Calls

4 calls:

8.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
5.0ms	(pow E (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series517.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
205.0ms	(pow E (log (- 1.0 (cos x))))
73.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify56.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	477	1423
1	1740	1205
2	5003	1166

prune316.0ms

Filtered

156 candidates to 109 candidates (69.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	155	16	171

Merged error: 0.1b

Counts

171 → 16

regimes177.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.0b

bsearch97.0ms

Steps

Iters	Range		Point
10	0.0002141056345597589	3206628.0142593775	0.02033085351791419
11	-4.816760182774211e+16	-0.0014803844373699059	-0.0247351870379494

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	43	27
2	43	27

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1562×	body	2560	valid
1.3s	2834×	body	1280	valid
463.0ms	1861×	body	640	valid
171.0ms	961×	body	320	valid
53.0ms	452×	body	160	valid
22.0ms	326×	body	80	valid
11.0ms	4×	body	5120	valid