Details

sample86.0ms

Algorithm

intervals

Results

41.0ms	102×	body	1280	valid
15.0ms	17×	body	2560	valid
13.0ms	58×	body	640	valid
5.0ms	36×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	11×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize14.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite32.0ms

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:

26.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series59.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

simplify73.0ms

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

prune103.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.5b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite38.0ms

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)) (* (cos x) (sin eps)))
5.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
23.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series279.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms	(* (sin x) (cos eps))
45.0ms	(* (cos x) (sin eps))
108.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

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

prune278.0ms

Filtered

97 candidates to 67 candidates (69.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

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))
1.7b	(- (cos eps) 1)

rewrite10.0ms

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:

0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series166.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
19.0ms	(- (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

prune222.0ms

Filtered

70 candidates to 45 candidates (64.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (* (cos x) (sin eps)))
0.2b	(log1p (expm1 (* (cos x) (sin eps))))
0.2b	(* (cos x) (sin eps))
1.7b	(- (cos eps) 1)

rewrite10.0ms

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:

0.0ms	(expm1 (* (cos x) (sin eps)))
0.0ms	(log1p (expm1 (* (cos x) (sin eps))))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series214.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(expm1 (* (cos x) (sin eps)))
79.0ms	(log1p (expm1 (* (cos x) (sin eps))))
45.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify91.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	271	459
1	898	365
2	3241	343
3	5001	320

prune231.0ms

Filtered

85 candidates to 52 candidates (61.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes118.0ms

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	17	11
1	17	11

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3309×	body	1280	valid
556.0ms	623×	body	2560	valid
461.0ms	1864×	body	640	valid
136.0ms	772×	body	320	valid
64.0ms	1077×	body	80	valid
38.0ms	355×	body	160	valid