Details

sample149.0ms

Algorithm

intervals

Results

79.0ms	61×	body	2560	valid
41.0ms	83×	body	1280	valid
16.0ms	66×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	12×	body	160	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: 32.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 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))
3.0ms	(- 1.0 (cos x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 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

prune155.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Merged error: 0.2b

Counts

59 → 13

localize10.0ms

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

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

series145.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
41.0ms	(* 1/24 (pow x 3))
50.0ms	(* 1/240 (pow x 5))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5001	346

prune167.0ms

Filtered

78 candidates to 49 candidates (62.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	78	13	91

Merged error: 0.2b

Counts

91 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
39.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune285.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	121	16	137

Merged error: 0.2b

Counts

137 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

10.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
3.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series172.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
28.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	434	688
1	1925	638
2	5001	618

prune217.0ms

Filtered

101 candidates to 61 candidates (60.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	5	9	14
Picked	1	0	1
Done	0	1	1
Total	103	14	117

Merged error: 0.1b

Counts

117 → 14

regimes159.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.4b

bsearch75.0ms

Steps

Iters	Range		Point
8	6.042829624826513e-05	0.09081442282169057	0.022951625532469207
8	-6.238959787773506	-0.00010711273713490883	-0.02251962811893695

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	28
1	46	28

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.1s	1551×	body	2560	valid
1.5s	2788×	body	1280	valid
463.0ms	1876×	body	640	valid
166.0ms	941×	body	320	valid
63.0ms	480×	body	160	valid
25.0ms	360×	body	80	valid
18.0ms	4×	body	5120	valid

Details

sample149.0ms

simplify6.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series58.0ms

simplify81.0ms

prune155.0ms

localize10.0ms

rewrite21.0ms

series145.0ms

simplify45.0ms

prune167.0ms

localize11.0ms

rewrite27.0ms

series138.0ms

simplify90.0ms

prune285.0ms

localize15.0ms

rewrite30.0ms

series172.0ms

simplify66.0ms

prune217.0ms

regimes159.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

sample4.5s

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