Details

sample88.0ms

Algorithm

intervals

Results

44.0ms	108×	body	1280	valid
16.0ms	18×	body	2560	valid
11.0ms	51×	body	640	valid
4.0ms	27×	body	320	valid
3.0ms	43×	body	80	valid
1.0ms	9×	body	160	valid

simplify6.0ms

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: 35.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
24.0ms	(sin (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	193	397
1	530	295
2	2598	285
3	5002	230

prune85.0ms

Filtered

48 candidates to 33 candidates (68.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	3	49

Merged error: 0.3b

Counts

49 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
3.0b	(- (cos eps) 1)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

5.0ms	(* (sin eps) (cos x))
9.0ms	(* (sin x) (- (cos eps) 1))
24.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
5.0ms	(- (cos eps) 1)

series238.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin eps) (cos x))
50.0ms	(* (sin x) (- (cos eps) 1))
119.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
24.0ms	(- (cos eps) 1)

simplify65.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	522	1296
1	2055	1023
2	5001	1014

prune366.0ms

Filtered

165 candidates to 101 candidates (61.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	151	14	165
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	154	14	168

Merged error: 0.1b

Counts

168 → 14

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(fma (sin eps) (cos x) (* (sin x) (- (cos eps) 1)))
3.0b	(- (cos eps) 1)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `difference-of-sqr-1` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`expm1-def` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 89

Calls

3 calls:

12.0ms	(* (sin x) (- (cos eps) 1))
1.0ms	(fma (sin eps) (cos x) (* (sin x) (- (cos eps) 1)))
5.0ms	(- (cos eps) 1)

series174.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (sin x) (- (cos eps) 1))
104.0ms	(fma (sin eps) (cos x) (* (sin x) (- (cos eps) 1)))
20.0ms	(- (cos eps) 1)

simplify119.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	291	804
1	1094	593
2	4256	547
3	5001	543

prune230.0ms

Filtered

98 candidates to 54 candidates (55.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	98	14	112

Merged error: 0.1b

Counts

112 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (sin eps) (cos x) (cbrt (pow (* (sin x) (- (cos eps) 1)) 3)))
0.2b	(pow (* (sin x) (- (cos eps) 1)) 3)
3.0b	(- (cos eps) 1)
11.5b	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`unpow-prod-down`
29×	`*-un-lft-identity`
21×	`cbrt-prod`
19×	`add-cube-cbrt`
14×	`associate-r`
9×	`prod-diff`
8×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u`
3×	`fma-neg` `difference-of-sqr-1` `distribute-lft-out--`
2×	`pow-pow` `unpow3` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `expm1-def` `flip3--` `pow1/3` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `fma-udef`

Counts

4 → 111

Calls

4 calls:

1.0ms	(fma (sin eps) (cos x) (cbrt (pow (* (sin x) (- (cos eps) 1)) 3)))
8.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
5.0ms	(- (cos eps) 1)
9.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

series308.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(fma (sin eps) (cos x) (cbrt (pow (* (sin x) (- (cos eps) 1)) 3)))
133.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
20.0ms	(- (cos eps) 1)
52.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	452	838
1	1874	769
2	5001	760

prune291.0ms

Filtered

123 candidates to 76 candidates (61.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	123	14	137

Merged error: 0.1b

Counts

137 → 14

regimes123.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	20	9
2	20	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3298×	body	1280	valid
530.0ms	603×	body	2560	valid
446.0ms	1868×	body	640	valid
133.0ms	768×	body	320	valid
56.0ms	1119×	body	80	valid
37.0ms	344×	body	160	valid