Details

sample99.0ms

Algorithm

intervals

Results

44.0ms	106×	body	1280	valid
24.0ms	26×	body	2560	valid
13.0ms	50×	body	640	valid
5.0ms	27×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	13×	body	160	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: 36.9b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
4.7b	(sin (+ x eps))

rewrite13.0ms

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))
5.0ms	(sin (+ x eps))

series58.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune109.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	37	9	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	9	47

Merged error: 14.7b

Counts

47 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
3.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite27.0ms

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

series499.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
49.0ms	(* (cos x) (sin eps))
43.0ms	(* (sin x) (cos eps))
117.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (43.0ms)

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

prune257.0ms

Filtered

97 candidates to 68 candidates (70.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	85	12	97
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	93	13	106

Merged error: 0.2b

Counts

106 → 13

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
1.7b	(- (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:

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

series171.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (cos x) (sin eps))
106.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
19.0ms	(- (cos eps) 1)

simplify102.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

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

prune201.0ms

Filtered

70 candidates to 45 candidates (64.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 0.1b

Counts

83 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (cbrt (pow (- (cos eps) 1) 3)) (* (cos x) (sin eps)))
0.3b	(cbrt (pow (- (cos eps) 1) 3))
0.4b	(pow (- (cos eps) 1) 3)
1.7b	(- (cos eps) 1)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
20×	`cbrt-prod`
17×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
10×	`difference-of-squares`
9×	`prod-diff`
6×	`add-exp-log` `add-log-exp`
5×	`pow1` `difference-of-sqr-1` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `expm1-def` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

1.0ms	(fma (sin x) (cbrt (pow (- (cos eps) 1) 3)) (* (cos x) (sin eps)))
9.0ms	(cbrt (pow (- (cos eps) 1) 3))
5.0ms	(pow (- (cos eps) 1) 3)
5.0ms	(- (cos eps) 1)

series199.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(fma (sin x) (cbrt (pow (- (cos eps) 1) 3)) (* (cos x) (sin eps)))
24.0ms	(cbrt (pow (- (cos eps) 1) 3))
45.0ms	(pow (- (cos eps) 1) 3)
19.0ms	(- (cos eps) 1)

simplify52.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	364	687
1	1398	624
2	5001	615

prune241.0ms

Filtered

121 candidates to 65 candidates (53.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Merged error: 0.1b

Counts

133 → 12

regimes107.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	9
1	16	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3317×	body	1280	valid
568.0ms	603×	body	2560	valid
483.0ms	1839×	body	640	valid
142.0ms	768×	body	320	valid
59.0ms	1107×	body	80	valid
44.0ms	366×	body	160	valid