Details

sample89.0ms

Algorithm

intervals

Results

44.0ms	107×	body	1280	valid
16.0ms	18×	body	2560	valid
12.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	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: 36.3b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
3.6b	(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))

series56.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune118.0ms

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: 14.6b

Counts

47 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
3.7b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite30.0ms

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:

4.0ms	(* (cos x) (sin eps))
10.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (sin x) (cos eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series288.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (sin eps))
88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms	(* (sin x) (cos eps))
111.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5001	741

prune284.0ms

Filtered

97 candidates to 68 candidates (70.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 0.3b

Counts

106 → 9

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
1.7b	(- (cos eps) 1)

rewrite11.0ms

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)

series176.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (cos x) (sin eps))
108.0ms	(fma (sin x) (- (cos eps) 1) (* (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	276	442
1	932	347
2	3460	325
3	5001	303

prune256.0ms

Filtered

70 candidates to 46 candidates (65.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	66	13	79

Merged error: 0.1b

Counts

79 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (cos eps) 1))
0.1b	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
1.7b	(- (cos eps) 1)
1.7b	(log (exp (- (cos eps) 1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
22×	`exp-sum`
14×	`log-prod` `exp-prod`
9×	`add-log-exp`
8×	`log-pow`
6×	`difference-of-squares`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `difference-of-sqr-1` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `expm1-def` `flip3--` `rem-log-exp` `flip--` `fma-udef`

Counts

4 → 104

Calls

4 calls:

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

series190.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(exp (- (cos eps) 1))
108.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
18.0ms	(- (cos eps) 1)
19.0ms	(log (exp (- (cos eps) 1)))

simplify93.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	289	790
1	850	565
2	2761	475
3	5002	431

prune347.0ms

Filtered

116 candidates to 67 candidates (57.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 0.1b

Counts

129 → 12

regimes130.0ms

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	17	12
1	17	12

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	3322×	body	1280	valid
640.0ms	1830×	body	640	valid
583.0ms	635×	body	2560	valid
126.0ms	767×	body	320	valid
56.0ms	1102×	body	80	valid
37.0ms	344×	body	160	valid