Details

sample123.0ms

Algorithm

intervals

Results

53.0ms	44×	body	2560	valid
42.0ms	90×	body	1280	valid
12.0ms	58×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	15×	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: 30.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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))

series59.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

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

prune147.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	46	12	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	12	59

Merged error: 0.1b

Counts

59 → 12

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))

rewrite31.0ms

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

series93.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
35.0ms	(/ (sin x) (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (45.0ms)

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

prune437.0ms

Filtered

168 candidates to 85 candidates (50.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	168	12	180

Merged error: 0.1b

Counts

180 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.3b	(+ (cos x) 1.0)
0.3b	(pow (cos x) 3)
1.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

25.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
4.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series259.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
10.0ms	(+ (cos x) 1.0)
32.0ms	(pow (cos x) 3)
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	566	1663
1	2538	1547
2	5001	1503

prune353.0ms

Filtered

151 candidates to 85 candidates (56.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	142	9	151
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	147	16	163

Merged error: 0.1b

Counts

163 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(/ (- (pow 1.0 3) (* (cos x) (pow (cos x) 2))) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
0.3b	(+ (cos x) 1.0)
1.7b	(- (pow 1.0 3) (* (cos x) (pow (cos x) 2)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `*-un-lft-identity`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`times-frac` `associate-/l*` `unpow2`
3×	`difference-cubes` `unpow-prod-down` `pow-unpow` `cube-unmult`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

2.0ms	(pow (cos x) 2)
15.0ms	(/ (- (pow 1.0 3) (* (cos x) (pow (cos x) 2))) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
4.0ms	(+ (cos x) 1.0)
7.0ms	(- (pow 1.0 3) (* (cos x) (pow (cos x) 2)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
165.0ms	(/ (- (pow 1.0 3) (* (cos x) (pow (cos x) 2))) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
10.0ms	(+ (cos x) 1.0)
50.0ms	(- (pow 1.0 3) (* (cos x) (pow (cos x) 2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	486	877
1	2323	722
2	5003	720

prune215.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	84	15	99

Merged error: 0.1b

Counts

99 → 15

regimes71.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.7b

bsearch88.0ms

Steps

Iters	Range		Point
8	2.0262054515877825e-05	0.3235305135594418	0.022624277856211048
10	-85019.06990604498	-4.503960361653909e-11	-0.02058278953964613

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	25
1	46	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	1640×	body	2560	valid
1.2s	2700×	body	1280	valid
435.0ms	1880×	body	640	valid
133.0ms	908×	body	320	valid
52.0ms	501×	body	160	valid
23.0ms	6×	body	5120	valid
23.0ms	365×	body	80	valid