Details

sample5.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.15564%

Results

82.0ms	56×	body	2560	valid
42.0ms	89×	body	1280	valid
14.0ms	58×	body	640	valid
6.0ms	33×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	9×	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: 32.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 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))

series11.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify84.0ms

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

prune116.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

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: 0.3b

Counts

59 → 12

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/240 (pow x 5))
0.1b	(* 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))

series8.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify183.0ms

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

prune107.0ms

Filtered

38 candidates to 62 candidates (-63.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	62	12	74

Merged error: 0.3b

Counts

74 → 12

localize10.0ms

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)))
1.0b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite25.0ms

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))))
3.0ms	(- 1.0 (cos x))

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
5.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

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

prune182.0ms

Filtered

90 candidates to 124 candidates (-37.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	124	12	136

Merged error: 0.3b

Counts

136 → 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)))
0.3b	(pow (cos x) 3)
0.3b	(+ (cos x) 1.0)
1.4b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite48.0ms

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)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series37.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (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))

simplify101.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (70.0ms)

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

prune284.0ms

Filtered

105 candidates to 201 candidates (-91.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	200	13	213

Merged error: 0.2b

Counts

213 → 13

regimes164.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.0b

bsearch54.0ms

Steps

Iters	Range		Point
8	7.702016267863962e-07	0.02530291237915767	0.017518773564637047
8	-0.041209885716879134	-1.742235367917608e-06	-0.022520001615656753

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	31
1	46	31

end0.0ms

sample9.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.15564%

Results

2.3s	1574×	body	2560	valid
1.4s	2761×	body	1280	valid
490.0ms	1913×	body	640	valid
159.0ms	897×	body	320	valid
61.0ms	501×	body	160	valid
26.0ms	350×	body	80	valid
14.0ms	4×	body	5120	valid

Details

sample5.0s

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series11.0ms

simplify84.0ms

prune116.0ms

localize10.0ms

rewrite13.0ms

series8.0ms

simplify183.0ms

prune107.0ms

localize10.0ms

rewrite25.0ms

series32.0ms

simplify89.0ms

prune182.0ms

localize15.0ms

rewrite48.0ms

series37.0ms

simplify101.0ms

prune284.0ms

regimes164.0ms

bsearch54.0ms

simplify2.0ms

end0.0ms

sample9.8s

Profiling