Details

sample99.0ms

Algorithm

intervals

Results

43.0ms	94×	body	1280	valid
22.0ms	25×	body	2560	valid
17.0ms	67×	body	640	valid
5.0ms	30×	body	320	valid
2.0ms	30×	body	80	valid
1.0ms	10×	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: 36.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
1.9b	(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))

series66.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune105.0ms

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: 15.9b

Counts

47 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.8b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite28.0ms

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))
10.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series306.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
45.0ms	(* (cos x) (sin eps))
50.0ms	(* (sin x) (cos eps))
118.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (43.0ms)

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

prune260.0ms

Filtered

97 candidates to 68 candidates (70.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 0.3b

Counts

107 → 8

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
1.9b	(- (cos eps) 1)

rewrite12.0ms

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)

series186.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
51.0ms	(* (cos x) (sin eps))
20.0ms	(- (cos eps) 1)

simplify99.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (93.0ms)

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

prune203.0ms

Filtered

70 candidates to 44 candidates (62.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	65	13	78

Merged error: 0.1b

Counts

78 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.9b	(- (cos eps) 1)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity` `prod-diff`
39×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`associate-r`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `expm1-def` `fma-def` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 135

Calls

4 calls:

11.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
13.0ms	(* (sin x) (- (cos eps) 1))
5.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)

series432.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
54.0ms	(* (sin x) (- (cos eps) 1))
47.0ms	(* (cos x) (sin eps))
20.0ms	(- (cos eps) 1)

simplify55.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	442	1224
1	1718	915
2	5001	884

prune310.0ms

Filtered

147 candidates to 91 candidates (61.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	147	13	160

Merged error: 0.0b

Counts

160 → 13

regimes113.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	15
1	23	15

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3279×	body	1280	valid
587.0ms	623×	body	2560	valid
489.0ms	1876×	body	640	valid
133.0ms	778×	body	320	valid
59.0ms	1091×	body	80	valid
40.0ms	353×	body	160	valid