Details

sample94.0ms

Algorithm

intervals

Results

40.0ms	94×	body	1280	valid
22.0ms	25×	body	2560	valid
17.0ms	65×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	44×	body	80	valid
1.0ms	8×	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: 35.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
4.5b	(sin (+ x eps))

rewrite16.0ms

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))
9.0ms	(sin (+ x eps))

series57.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify72.0ms

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

prune98.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	38	8	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	8	47

Merged error: 14.0b

Counts

47 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

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

series255.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* (cos x) (sin eps)) (sin x))
41.0ms	(* (cos x) (sin eps))
47.0ms	(* (sin x) (cos eps))
106.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

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

prune254.0ms

Filtered

94 candidates to 69 candidates (73.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 0.6b

Counts

102 → 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))
2.3b	(- (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)

series169.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
41.0ms	(* (cos x) (sin eps))
23.0ms	(- (cos eps) 1)

simplify96.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	276	442
1	932	347
2	3460	334
3	5001	312

prune191.0ms

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	2	5	7
Picked	1	0	1
Done	0	0	0
Total	65	13	78

Merged error: 0.1b

Counts

78 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
2.3b	(log (exp (- (cos eps) 1)))
2.3b	(- (cos eps) 1)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
14×	`log-prod`
11×	`exp-sum`
8×	`log-pow`
7×	`pow1` `add-exp-log` `exp-prod`
6×	`add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg` `associate-r` `associate-l`
2×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--`
1×	`log-div` `expm1-def` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

1.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
6.0ms	(log (exp (- (cos eps) 1)))
5.0ms	(- (cos eps) 1)

series190.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
18.0ms	(log (exp (- (cos eps) 1)))
19.0ms	(- (cos eps) 1)

simplify111.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	339	680
1	1052	506
2	3734	442
3	5001	434

prune244.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Merged error: 0.0b

Counts

119 → 13

regimes114.0ms

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	15	9
1	15	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3303×	body	1280	valid
561.0ms	614×	body	2560	valid
463.0ms	1831×	body	640	valid
127.0ms	780×	body	320	valid
63.0ms	1147×	body	80	valid
35.0ms	325×	body	160	valid