Details

sample89.0ms

Algorithm

intervals

Results

40.0ms	96×	body	1280	valid
20.0ms	22×	body	2560	valid
14.0ms	57×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	39×	body	80	valid
2.0ms	17×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize13.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ x eps))

rewrite30.0ms

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:

24.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series59.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (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

prune111.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.4b

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)))
0.1b	(* (cos x) (sin eps))
4.0b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite36.0ms

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	(* (sin x) (cos eps))
4.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
21.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series280.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin x) (cos eps))
86.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (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	5002	741

prune276.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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))
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)

series171.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify95.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (90.0ms)

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

prune217.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
0.3b	(log1p (expm1 (- (cos eps) 1)))
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 eps) 1))
4.0ms	(* (cos x) (sin eps))
0.0ms	(log1p (expm1 (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)

series275.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(expm1 (- (cos eps) 1))
42.0ms	(* (cos x) (sin eps))
145.0ms	(log1p (expm1 (- (cos eps) 1)))
21.0ms	(- (cos eps) 1)

simplify93.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	273	429
1	890	340
2	3171	320
3	5002	298

prune239.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes104.0ms

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	23	15
1	25	15
2	25	15

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3282×	body	1280	valid
628.0ms	686×	body	2560	valid
437.0ms	1818×	body	640	valid
129.0ms	736×	body	320	valid
62.0ms	1121×	body	80	valid
39.0ms	357×	body	160	valid