Details

sample108.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

62.0ms	149×	body	1280	valid
17.0ms	19×	body	2560	valid
12.0ms	53×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	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: 41.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
3.9b	(cos (+ x eps))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify108.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune73.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	19	11	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	11	31

Merged error: 16.7b

Counts

31 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
3.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify108.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	304	633
1	1061	601
2	4487	582
3	5002	582

prune136.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	67	15	82
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	75	18	93

Merged error: 16.5b

Counts

93 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
3.2b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
25.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	574
2	5002	565

prune149.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	72	23	95

Merged error: 16.4b

Counts

95 → 23

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.3b	(pow (cos x) 3)
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
3.1b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
11×	`add-log-exp`
10×	`add-cube-cbrt` `sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`cube-div`
2×	`cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-exp` `sum-log` `cos-mult` `flip--` `sin-mult` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `associate-+l-` `flip3-+` `frac-sub` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 100

Calls

4 calls:

8.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.0ms	(pow (cos x) 3)
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
15.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series196.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
5.0ms	(pow (cos x) 3)
27.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
144.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify95.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	599	1433
1	2889	1321
2	5002	1280

prune139.0ms

Filtered

63 candidates to 112 candidates (-77.8%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	12	10	22
Picked	1	0	1
Done	0	0	0
Total	112	23	135

Merged error: 16.4b

Counts

135 → 23

regimes348.0ms

Accuracy

82.8% (1.7b remaining)

Error of 16.2b against oracle of 14.5b and baseline of 24.3b

bsearch109.0ms

Steps

Iters	Range		Point
9	1.357635195057358e-14	2.2976179399794863e-05	2.497296142483899e-08
8	-7.15299763307286e-11	-9.013216439811169e-14	-5.3357552770968655e-11

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	97
1	76	97
2	76	97

end0.0ms

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

1.7s	4441×	body	1280	valid
595.0ms	640×	body	2560	valid
462.0ms	1894×	body	640	valid
108.0ms	670×	body	320	valid
31.0ms	267×	body	160	valid
5.0ms	88×	body	80	valid

Details

sample108.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series14.0ms

simplify108.0ms

prune73.0ms

localize15.0ms

rewrite23.0ms

series58.0ms

simplify108.0ms

prune136.0ms

localize15.0ms

rewrite23.0ms

series52.0ms

simplify39.0ms

prune149.0ms

localize27.0ms

rewrite35.0ms

series196.0ms

simplify95.0ms

prune139.0ms

regimes348.0ms

bsearch109.0ms

simplify4.0ms

end0.0ms

sample3.2s

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