Details

sample91.0ms

Algorithm

intervals

Results

39.0ms	87×	body	1280	valid
20.0ms	22×	body	2560	valid
14.0ms	56×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	48×	body	80	valid
2.0ms	12×	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: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.6b	(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))

series60.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (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

prune110.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

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))
2.9b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
11.0ms	(+ (* (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))
45.0ms	(* (cos x) (sin eps))
109.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	414	729
1	1617	662
2	5002	648

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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))
1.8b	(- (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)

series173.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify95.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	272	454
1	926	348
2	3454	326
3	5001	304

prune255.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
1.8b	(log (exp (- (cos eps) 1)))
1.8b	(- (cos eps) 1)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
28×	`add-cube-cbrt`
27×	`prod-diff`
22×	`exp-sum`
14×	`log-prod` `exp-prod`
9×	`add-log-exp`
8×	`log-pow`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `difference-of-sqr-1` `associate-r` `associate-l` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `expm1-def` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

9.0ms	(exp (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
9.0ms	(log (exp (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)

series125.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp (- (cos eps) 1))
41.0ms	(* (cos x) (sin eps))
22.0ms	(log (exp (- (cos eps) 1)))
18.0ms	(- (cos eps) 1)

simplify102.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	312	784
1	989	541
2	3382	449
3	5002	441

prune373.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes145.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	27	13
2	29	13
3	29	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3335×	body	1280	valid
596.0ms	650×	body	2560	valid
430.0ms	1731×	body	640	valid
133.0ms	802×	body	320	valid
56.0ms	1129×	body	80	valid
37.0ms	353×	body	160	valid