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

55.0ms	135×	body	1280	valid
21.0ms	22×	body	2560	valid
15.0ms	62×	body	640	valid
5.0ms	26×	body	320	valid
1.0ms	5×	body	160	valid
0.0ms	6×	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: 40.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
3.5b	(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

prune68.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	20	10	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	10	31

Merged error: 15.1b

Counts

31 → 10

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))
2.5b	(- (- (* (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)))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series57.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (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))

simplify110.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune121.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 15.0b

Counts

92 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
2.5b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite24.0ms

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:

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

series52.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* (sin x) (sin eps)) (cos x))
8.0ms	(* (cos x) (cos eps))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

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

prune116.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	76	14	90

Merged error: 15.0b

Counts

90 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(pow (cos x) 3)
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
2.3b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite34.0ms

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))

series201.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (- (* (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)
150.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify98.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (84.0ms)

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

prune133.0ms

Filtered

63 candidates to 112 candidates (-77.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	108	18	126

Merged error: 14.9b

Counts

126 → 18

regimes291.0ms

Accuracy

81% (1.9b remaining)

Error of 16.5b against oracle of 14.7b and baseline of 24.5b

bsearch97.0ms

Steps

Iters	Range		Point
8	1.3874688846413837e-27	1.3414564253747318e-23	1.3152880610052117e-23
9	-3.870097754638671e-05	-6.920880231058545e-12	-7.436214131801607e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	52
1	50	52
2	50	52

end0.0ms

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

1.7s	4444×	body	1280	valid
834.0ms	671×	body	2560	valid
472.0ms	1809×	body	640	valid
144.0ms	721×	body	320	valid
33.0ms	278×	body	160	valid
5.0ms	77×	body	80	valid

Details

sample108.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify108.0ms

prune68.0ms

localize15.0ms

rewrite23.0ms

series57.0ms

simplify110.0ms

prune121.0ms

localize13.0ms

rewrite24.0ms

series52.0ms

simplify46.0ms

prune116.0ms

localize27.0ms

rewrite34.0ms

series201.0ms

simplify98.0ms

prune133.0ms

regimes291.0ms

bsearch97.0ms

simplify2.0ms

end0.0ms

sample3.5s

Profiling