Details

sample99.0ms

Algorithm

intervals

Results

43.0ms	101×	body	1280	valid
26.0ms	29×	body	2560	valid
13.0ms	52×	body	640	valid
4.0ms	23×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	15×	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: 38.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (72.0ms)

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: 17.4b

Counts

47 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
3.5b	(- (+ (* (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:

5.0ms	(* (sin x) (cos eps))
6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin x) (cos eps))
88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
112.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5002	741

prune249.0ms

Filtered

97 candidates to 67 candidates (69.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Merged error: 0.4b

Counts

107 → 8

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
1.6b	(- (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)

series174.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify98.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (92.0ms)

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

prune190.0ms

Filtered

70 candidates to 45 candidates (64.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	67	11	78

Merged error: 0.0b

Counts

78 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(log1p (expm1 (* (cos x) (sin eps))))
0.1b	(expm1 (* (cos x) (sin eps)))
1.6b	(- (cos eps) 1)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
1.0ms	(log1p (expm1 (* (cos x) (sin eps))))
1.0ms	(expm1 (* (cos x) (sin eps)))
5.0ms	(- (cos eps) 1)

series222.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos x) (sin eps))
82.0ms	(log1p (expm1 (* (cos x) (sin eps))))
69.0ms	(expm1 (* (cos x) (sin eps)))
23.0ms	(- (cos eps) 1)

simplify92.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	267	471
1	892	366
2	3234	344
3	5001	321

prune192.0ms

Filtered

85 candidates to 52 candidates (61.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

regimes99.0ms

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	15	9
1	15	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3237×	body	1280	valid
601.0ms	654×	body	2560	valid
488.0ms	1857×	body	640	valid
133.0ms	786×	body	320	valid
61.0ms	1120×	body	80	valid
45.0ms	346×	body	160	valid