Details

sample95.0ms

Algorithm

intervals

Results

47.0ms	103×	body	1280	valid
19.0ms	22×	body	2560	valid
12.0ms	51×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	39×	body	80	valid
2.0ms	15×	body	160	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

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))
19.0ms	(sin (+ x eps))

simplify143.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune80.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
1.9b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

5.0ms	(- (* (cos x) (sin eps)) (sin x))
5.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
9.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* (cos x) (sin eps)) (sin x))
42.0ms	(* (sin x) (cos eps))
47.0ms	(* (cos x) (sin eps))
107.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune226.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
0.7b	(- (cos eps) 1)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

9.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
8.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series221.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
49.0ms	(* (sin x) (- (cos eps) 1))
42.0ms	(* (cos x) (sin eps))
23.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune242.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (+ (cos eps) 1))
0.3b	(+ (cos eps) 1)
0.3b	(pow (cos eps) 3)
0.6b	(- (pow (cos eps) 3) 1)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`difference-of-sqr-1` `associate-r` `sqr-pow`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

7.0ms	(* (cos eps) (+ (cos eps) 1))
4.0ms	(+ (cos eps) 1)
3.0ms	(pow (cos eps) 3)
7.0ms	(- (pow (cos eps) 3) 1)

series117.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cos eps) (+ (cos eps) 1))
10.0ms	(+ (cos eps) 1)
27.0ms	(pow (cos eps) 3)
50.0ms	(- (pow (cos eps) 3) 1)

simplify62.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	307	461
1	1609	414
2	5001	398

prune259.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

0% (0.4b 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	27	17
1	27	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3226×	body	1280	valid
566.0ms	632×	body	2560	valid
441.0ms	1862×	body	640	valid
128.0ms	800×	body	320	valid
61.0ms	1106×	body	80	valid
39.0ms	374×	body	160	valid