Details

sample89.0ms

Algorithm

intervals

Results

46.0ms	136×	body	1280	valid
15.0ms	18×	body	2560	valid
14.0ms	64×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	4×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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: 38.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
2.6b	(cos (+ x eps))

rewrite15.0ms

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))
8.0ms	(cos (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify115.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune93.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	18	12	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	12	31

Merged error: 15.7b

Counts

31 → 12

localize14.0ms

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))
2.3b	(- (* (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))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (sin x) (sin eps)) (cos x))
41.0ms	(* (cos x) (cos eps))
44.0ms	(* (sin x) (sin eps))
127.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

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

prune235.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	61	16	77
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	68	21	89

Merged error: 15.6b

Counts

89 → 21

localize14.0ms

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))
2.3b	(- (- (* (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))

series298.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

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

prune232.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	4	16	20
Picked	1	0	1
Done	0	0	0
Total	82	21	103

Merged error: 15.6b

Counts

103 → 21

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (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)
2.1b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
12×	`add-cube-cbrt`
10×	`sqr-pow`
8×	`pow1` `add-exp-log` `frac-times` `cos-mult` `add-cbrt-cube` `sin-mult`
6×	`pow-unpow` `add-log-exp`
5×	`flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out--`
4×	`cube-div` `associate-r` `associate-*l/` `frac-sub` `sub-div`
3×	`associate-l`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `associate-*r/` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

14.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (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)
19.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series930.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
27.0ms	(pow (cos x) 3)
114.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
593.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify180.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	809	2240
1	4804	2061
2	5001	2061

prune469.0ms

Filtered

131 candidates to 87 candidates (66.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	116	15	131
Fresh	11	9	20
Picked	1	0	1
Done	0	0	0
Total	128	24	152

Merged error: 15.5b

Counts

152 → 24

regimes329.0ms

Accuracy

83.2% (1.7b remaining)

Error of 16.1b against oracle of 14.5b and baseline of 24.3b

bsearch147.0ms

Steps

Iters	Range		Point
9	1.513845840511263e-15	3.965834506966397e-09	3.732711387604417e-09
10	-14871018171.432148	-0.0001070084605982428	-0.00010840851373423032

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	72
1	58	72
2	58	72

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	4520×	body	1280	valid
524.0ms	603×	body	2560	valid
400.0ms	1824×	body	640	valid
115.0ms	701×	body	320	valid
28.0ms	269×	body	160	valid
4.0ms	83×	body	80	valid

Details

sample89.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite15.0ms

series65.0ms

simplify115.0ms

prune93.0ms

localize14.0ms

rewrite24.0ms

series261.0ms

simplify43.0ms

prune235.0ms

localize14.0ms

rewrite23.0ms

series298.0ms

simplify113.0ms

prune232.0ms

localize24.0ms

rewrite46.0ms

series930.0ms

simplify180.0ms

prune469.0ms

regimes329.0ms

bsearch147.0ms

simplify2.0ms

end0.0ms

sample2.8s

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