Details

sample98.0ms

Algorithm

intervals

Results

50.0ms	135×	body	1280	valid
21.0ms	25×	body	2560	valid
12.0ms	63×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	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: 39.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite11.0ms

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))

series70.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify111.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune91.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	17	13	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	13	31

Merged error: 16.3b

Counts

31 → 13

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))
2.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

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))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series308.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
85.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify112.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune238.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	80	15	95

Merged error: 16.2b

Counts

95 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.1b	(- (* (cos eps) (cos x)) (+ (* (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:

4.0ms	(* (cos eps) (cos x))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos eps) (cos x))
56.0ms	(+ (* (sin x) (sin eps)) (cos x))
45.0ms	(* (sin x) (sin eps))
140.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	329	606
1	1247	575
2	5002	567

prune257.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	72	20	92

Merged error: 16.1b

Counts

92 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x)))
0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.3b	(* (cos x) (cos x))
2.8b	(- (* (cos eps) (cos x)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
18×	`pow-prod-down`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`sin-mult`
9×	`prod-exp` `cbrt-unprod`
7×	`cos-mult` `associate-/l/`
6×	`add-log-exp`
5×	`pow-sqr` `pow-prod-up`
4×	`swap-sqr` `associate-r` `associate-l` `frac-sub` `associate-/l*` `difference-of-squares`
3×	`flip3--` `pow-plus` `associate-r/` `associate-l/` `associate-/r*` `flip--`
2×	`pow2` `frac-times` `div-sub` `associate-/r/` `*-commutative` `sub-div`
1×	`cbrt-undiv` `sub-neg` `sqr-cos` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv` `associate--r-` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

18.0ms	(/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x)))
9.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
5.0ms	(* (cos x) (cos x))
14.0ms	(- (* (cos eps) (cos x)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x)))
56.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
16.0ms	(* (cos x) (cos x))
328.0ms	(- (* (cos eps) (cos x)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

simplify88.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	553	1737
1	2796	1447
2	5002	1409

prune361.0ms

Filtered

131 candidates to 83 candidates (63.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	132	19	151

Merged error: 16.1b

Counts

151 → 19

regimes210.0ms

Accuracy

85.4% (1.5b remaining)

Error of 16.5b against oracle of 15.0b and baseline of 25.2b

bsearch145.0ms

Steps

Iters	Range		Point
10	1.5855828678791284e-19	2.4853599159652707e-08	1.080875223529136e-08
10	-1.2252616440760547e-11	-5.2655362403227905e-23	-1.7648464678937232e-14

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	29
1	41	29

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4435×	body	1280	valid
587.0ms	685×	body	2560	valid
391.0ms	1834×	body	640	valid
110.0ms	704×	body	320	valid
33.0ms	268×	body	160	valid
4.0ms	74×	body	80	valid