Details

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

83.0ms	60×	body	2560	valid
33.0ms	68×	body	1280	valid
20.0ms	79×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	11×	body	80	valid

simplify5.0ms

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

prune3.0ms

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: 32.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.9b	(- 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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify78.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2640	373
3	5002	373

prune119.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 0.2b

Counts

59 → 14

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	(* 1/240 (pow x 5))
0.3b	(* 1/24 (pow x 3))

rewrite20.0ms

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:

7.0ms	(+ (* 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))

series14.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

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

prune140.0ms

Filtered

49 candidates to 78 candidates (-59.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	78	14	92

Merged error: 0.2b

Counts

92 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
0.9b	(- 1.0 (cos x))

rewrite26.0ms

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))

series31.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 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

prune193.0ms

Filtered

89 candidates to 124 candidates (-39.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	5	7	12
Picked	1	0	1
Done	0	1	1
Total	123	15	138

Merged error: 0.2b

Counts

138 → 15

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)))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
0.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
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 → 189

Calls

4 calls:

22.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
10.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series38.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
5.0ms	(pow (cos x) 3)
2.0ms	(+ (cos x) 1.0)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5002	2810

prune283.0ms

Filtered

105 candidates to 201 candidates (-91.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	196	5	201
Fresh	6	7	13
Picked	1	0	1
Done	0	1	1
Total	203	13	216

Merged error: 0.1b

Counts

216 → 13

regimes198.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	48
1	55	48

end0.0ms

sample6.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

2.6s	1569×	body	2560	valid
1.4s	2796×	body	1280	valid
517.0ms	1927×	body	640	valid
163.0ms	866×	body	320	valid
56.0ms	447×	body	160	valid
43.0ms	393×	body	80	valid
8.0ms	2×	body	5120	valid

Details

sample1.9s

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series14.0ms

simplify78.0ms

prune119.0ms

localize10.0ms

rewrite20.0ms

series14.0ms

simplify44.0ms

prune140.0ms

localize10.0ms

rewrite26.0ms

series31.0ms

simplify90.0ms

prune193.0ms

localize15.0ms

rewrite47.0ms

series38.0ms

simplify102.0ms

prune283.0ms

regimes198.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling