Details

sample95.0ms

Algorithm

intervals

Results

42.0ms	100×	body	1280	valid
21.0ms	23×	body	2560	valid
14.0ms	57×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	21×	body	160	valid
2.0ms	30×	body	80	valid

simplify6.0ms

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: 40.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ x eps))

rewrite13.0ms

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))

series64.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune107.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	37	9	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	9	47

Merged error: 16.7b

Counts

47 → 9

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)))
0.2b	(* (cos x) (sin eps))
4.2b	(- (+ (* (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:

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))

series292.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin x) (cos eps))
90.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
112.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (43.0ms)

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

prune266.0ms

Filtered

97 candidates to 68 candidates (70.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	93	13	106

Merged error: 0.3b

Counts

106 → 13

localize14.0ms

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))
2.1b	(- (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)

series178.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
42.0ms	(* (cos x) (sin eps))
24.0ms	(- (cos eps) 1)

simplify100.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (94.0ms)

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

prune203.0ms

Filtered

70 candidates to 43 candidates (61.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	68	15	83

Merged error: 0.1b

Counts

83 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
2.1b	(- (cos eps) 1)
2.2b	(log (exp (- (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)))
5.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)
6.0ms	(log (exp (- (cos eps) 1)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)
19.0ms	(log (exp (- (cos eps) 1)))

simplify112.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	339	680
1	1045	506
2	3697	442
3	5002	434

prune247.0ms

Filtered

106 candidates to 67 candidates (63.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	106	15	121

Merged error: 0.0b

Counts

121 → 15

regimes135.0ms

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	19	13
1	19	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	3326×	body	1280	valid
562.0ms	608×	body	2560	valid
488.0ms	1878×	body	640	valid
124.0ms	739×	body	320	valid
59.0ms	1106×	body	80	valid
45.0ms	343×	body	160	valid