Details

sample130.0ms

Algorithm

intervals

Results

62.0ms	50×	body	2560	valid
37.0ms	86×	body	1280	valid
13.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	24×	body	160	valid
3.0ms	1×	body	5120	valid
1.0ms	12×	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: 30.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune165.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	43	15	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	15	59

Merged error: 0.2b

Counts

59 → 15

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/240 (pow x 5))
0.2b	(* 1/24 (pow x 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

8.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series148.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
52.0ms	(* 1/240 (pow x 5))
36.0ms	(* 1/24 (pow x 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5002	346

prune170.0ms

Filtered

78 candidates to 49 candidates (62.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	78	15	93

Merged error: 0.2b

Counts

93 → 15

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 1/240 (pow x 5))
0.2b	(* 1/24 (pow x 3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series88.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* 1/240 (pow x 5))
41.0ms	(* 1/24 (pow x 3))

simplify189.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	208	209
1	871	193
2	4634	193
3	5001	193

prune131.0ms

Filtered

62 candidates to 38 candidates (61.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	62	15	77

Merged error: 0.2b

Counts

77 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
10.0ms	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series95.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
35.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	510	1595
1	2396	1452
2	5002	1339

prune203.0ms

Filtered

168 candidates to 85 candidates (50.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	169	14	183

Merged error: 0.2b

Counts

183 → 14

regimes123.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.8b

bsearch83.0ms

Steps

Iters	Range		Point
9	2.1846438371975785e-05	719.5386143167987	0.024263645019990638
10	-43540924890.08803	-0.0051836583041924315	-0.023228222164187143

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	26
1	48	26

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1541×	body	2560	valid
1.3s	2872×	body	1280	valid
426.0ms	1851×	body	640	valid
165.0ms	918×	body	320	valid
51.0ms	474×	body	160	valid
24.0ms	6×	body	5120	valid
22.0ms	338×	body	80	valid