Details

sample92.0ms

Algorithm

intervals

Results

41.0ms	100×	body	1280	valid
20.0ms	22×	body	2560	valid
14.0ms	58×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	38×	body	80	valid
1.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 36.2b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series57.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	386
1	538	285
2	2616	275
3	5002	220

prune111.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	36	10	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	10	47

Merged error: 14.4b

Counts

47 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
1.4b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series304.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
48.0ms	(* (sin x) (cos eps))
44.0ms	(* (cos x) (sin eps))
120.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5001	741

prune265.0ms

Filtered

97 candidates to 68 candidates (70.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.3b

Counts

107 → 10

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
1.8b	(- (cos eps) 1)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `flip3--` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)

series181.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify105.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	276	442
1	932	347
2	3460	325
3	5001	303

prune223.0ms

Filtered

70 candidates to 44 candidates (62.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	62	18	80

Merged error: 0.1b

Counts

80 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
0.4b	(+ (cos eps) 1)
0.4b	(pow (cos eps) 3)
1.5b	(- (pow (cos eps) 3) 1)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
53×	`add-cube-cbrt`
48×	`times-frac`
40×	`difference-of-squares`
36×	`prod-diff`
30×	`unpow-prod-down` `cube-prod`
20×	`difference-of-sqr-1` `sqr-pow`
16×	`associate-/l*`
12×	`fma-neg`
9×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube`
5×	`pow1` `cube-mult` `unpow3` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `expm1-def` `fma-def` `associate-/r*`
2×	`pow-to-exp` `flip3--` `pow-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 204

Calls

4 calls:

12.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
4.0ms	(+ (cos eps) 1)
3.0ms	(pow (cos eps) 3)
12.0ms	(- (pow (cos eps) 3) 1)

series204.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
10.0ms	(+ (cos eps) 1)
35.0ms	(pow (cos eps) 3)
51.0ms	(- (pow (cos eps) 3) 1)

simplify89.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	544	2069
1	2349	1758
2	5001	1700

prune626.0ms

Filtered

216 candidates to 97 candidates (44.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	216	18	234

Merged error: 0.1b

Counts

234 → 18

regimes159.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3276×	body	1280	valid
607.0ms	641×	body	2560	valid
473.0ms	1829×	body	640	valid
134.0ms	803×	body	320	valid
61.0ms	1114×	body	80	valid
39.0ms	337×	body	160	valid