Details

sample97.0ms

Algorithm

intervals

Results

51.0ms	119×	body	1280	valid
15.0ms	59×	body	640	valid
13.0ms	15×	body	2560	valid
5.0ms	26×	body	320	valid
2.0ms	26×	body	80	valid
2.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite31.0ms

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:

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

series59.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify144.0ms

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

prune87.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.2b	(* (sin x) (cos eps))
1.0b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite23.0ms

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:

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

series258.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (sin eps))
61.0ms	(- (* (cos x) (sin eps)) (sin x))
46.0ms	(* (sin x) (cos eps))
108.0ms	(+ (* (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

prune240.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

4.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
3.0ms	(- (cos eps) 1)

series221.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (sin eps))
43.0ms	(* (sin x) (- (cos eps) 1))
109.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
22.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	333	552
1	1271	503
2	5002	501

prune245.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
0.2b	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
0.3b	(* (sin eps) (sin eps))
0.4b	(+ (cos eps) 1)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
49×	`times-frac`
39×	`add-sqr-sqrt`
33×	`associate-r`
32×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
6×	`associate-l` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `swap-sqr` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `distribute-frac-neg` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `sin-mult`
1×	`+-commutative` `pow2` `neg-sub0` `frac-2neg` `pow-plus` `div-sub` `associate-*r/` `clear-num` `sum-log` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out` `sqr-sin` `associate-/l/` `distribute-neg-frac`

Counts

4 → 140

Calls

4 calls:

19.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
7.0ms	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
4.0ms	(* (sin eps) (sin eps))
3.0ms	(+ (cos eps) 1)

series185.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin x) (/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1)))
56.0ms	(/ (- (* (sin eps) (sin eps))) (+ (cos eps) 1))
18.0ms	(* (sin eps) (sin eps))
10.0ms	(+ (cos eps) 1)

simplify106.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	512	1250
1	2976	1104
2	5001	1096

prune474.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes298.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	3322×	body	1280	valid
608.0ms	656×	body	2560	valid
477.0ms	1815×	body	640	valid
152.0ms	766×	body	320	valid
85.0ms	1110×	body	80	valid
42.0ms	331×	body	160	valid