Details

sample99.0ms

Algorithm

intervals

Results

47.0ms	109×	body	1280	valid
18.0ms	20×	body	2560	valid
17.0ms	68×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	21×	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: 38.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.5b	(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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(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

prune109.0ms

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: 15.2b

Counts

47 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.2b	(* (sin x) (cos eps))
3.4b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 82

Calls

4 calls:

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

series264.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin eps))
58.0ms	(- (* (cos x) (sin eps)) (sin x))
48.0ms	(* (sin x) (cos eps))
110.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	414	729
1	1617	662
2	5002	648

prune263.0ms

Filtered

94 candidates to 69 candidates (73.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.5b

Counts

104 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
1.8b	(- (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:

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

series172.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* (cos x) (sin eps))
112.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
19.0ms	(- (cos eps) 1)

simplify96.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	272	454
1	926	348
2	3454	326
3	5001	304

prune201.0ms

Filtered

70 candidates to 45 candidates (64.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	66	13	79

Merged error: 0.1b

Counts

79 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (sin x) (/ (fma (cos eps) (cos eps) (- 1)) (+ (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(/ (fma (cos eps) (cos eps) (- 1)) (+ (cos eps) 1))
0.5b	(+ (cos eps) 1)
2.2b	(fma (cos eps) (cos eps) (- 1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 72

Calls

4 calls:

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

series306.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(fma (sin x) (/ (fma (cos eps) (cos eps) (- 1)) (+ (cos eps) 1)) (* (cos x) (sin eps)))
64.0ms	(/ (fma (cos eps) (cos eps) (- 1)) (+ (cos eps) 1))
10.0ms	(+ (cos eps) 1)
36.0ms	(fma (cos eps) (cos eps) (- 1))

simplify40.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	283	770
1	1177	673
2	5001	621

prune242.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.1b

Counts

97 → 12

regimes107.0ms

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	20	12
1	21	12
2	21	12

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	3365×	body	1280	valid
692.0ms	1815×	body	640	valid
594.0ms	637×	body	2560	valid
142.0ms	770×	body	320	valid
60.0ms	1080×	body	80	valid
40.0ms	333×	body	160	valid