Details

sample88.0ms

Algorithm

intervals

Results

41.0ms	100×	body	1280	valid
19.0ms	22×	body	2560	valid
13.0ms	57×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	45×	body	80	valid
2.0ms	15×	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: 34.2b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
3.5b	(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:

11.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series55.0ms

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

prune104.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.5b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite25.0ms

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:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series279.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
41.0ms	(* (sin x) (cos eps))
109.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (42.0ms)

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

prune269.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

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))
1.1b	(- (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:

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:

109.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
41.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify99.0ms

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

prune226.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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))
1.1b	(- (cos eps) 1)
1.1b	(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)))
4.0ms	(* (cos x) (sin eps))
5.0ms	(- (cos eps) 1)
6.0ms	(log (exp (- (cos eps) 1)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma (sin x) (log (exp (- (cos eps) 1))) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)
20.0ms	(log (exp (- (cos eps) 1)))

simplify109.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (102.0ms)

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

prune296.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes123.0ms

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	18	8
1	20	8
2	20	8

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3279×	body	1280	valid
597.0ms	663×	body	2560	valid
442.0ms	1809×	body	640	valid
118.0ms	761×	body	320	valid
60.0ms	1110×	body	80	valid
39.0ms	378×	body	160	valid