Details

sample125.0ms

Algorithm

intervals

Results

55.0ms	41×	body	2560	valid
40.0ms	90×	body	1280	valid
12.0ms	53×	body	640	valid
5.0ms	31×	body	320	valid
3.0ms	24×	body	160	valid
1.0ms	17×	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: 26.3b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.8b	(- 1.0 (cos x))

rewrite12.0ms

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))
5.0ms	(- 1.0 (cos x))

series53.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 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

prune168.0ms

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: 0.1b

Counts

59 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.8b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.8b	(- 1.0 (cos x))

rewrite28.0ms

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))

series139.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- 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 (21.0ms)

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

prune309.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.1b

Counts

137 → 13

localize16.0ms

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)))
0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
2.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite50.0ms

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:

26.0ms	(/ (- (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))

series270.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (- (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)
35.0ms	(pow (cos x) 3)
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (66.0ms)

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

prune351.0ms

Filtered

151 candidates to 85 candidates (56.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	150	14	164

Merged error: 0.1b

Counts

164 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) 1.0))
0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
2.6b	(- 1.0 (pow (cos x) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-cube-cbrt` `difference-of-squares`
8×	`unpow-prod-down` `cube-prod` `associate-/l*` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`sqr-pow`
5×	`pow1` `distribute-lft-out--`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

14.0ms	(/ (- 1.0 (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) 1.0))
4.0ms	(+ (cos x) 1.0)
2.0ms	(pow (cos x) 3)
6.0ms	(- 1.0 (pow (cos x) 3))

series219.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- 1.0 (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) 1.0))
10.0ms	(+ (cos x) 1.0)
34.0ms	(pow (cos x) 3)
47.0ms	(- 1.0 (pow (cos x) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	455	1148
1	2054	1097
2	5003	1075

prune243.0ms

Filtered

116 candidates to 74 candidates (63.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	116	14	130

Merged error: 0.1b

Counts

130 → 14

regimes169.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.3b

bsearch97.0ms

Steps

Iters	Range		Point
10	0.00022027325057658872	62623256.830634765	0.021907997979399244
9	-17.831791951177678	-3.7534567552478157e-06	-0.02260905259882163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	35
1	44	35

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	1621×	body	2560	valid
1.2s	2741×	body	1280	valid
452.0ms	1865×	body	640	valid
360.0ms	982×	body	320	valid
54.0ms	473×	body	160	valid
21.0ms	315×	body	80	valid
13.0ms	3×	body	5120	valid

Details

sample125.0ms

simplify6.0ms

prune2.0ms

localize14.0ms

rewrite12.0ms

series53.0ms

simplify81.0ms

prune168.0ms

localize11.0ms

rewrite28.0ms

series139.0ms

simplify90.0ms

prune309.0ms

localize16.0ms

rewrite50.0ms

series270.0ms

simplify83.0ms

prune351.0ms

localize18.0ms

rewrite30.0ms

series219.0ms

simplify74.0ms

prune243.0ms

regimes169.0ms

bsearch97.0ms

simplify2.0ms

end0.0ms

sample4.4s

Profiling