Details

sample100.0ms

Algorithm

intervals

Results

44.0ms	108×	body	1280	valid
27.0ms	26×	body	2560	valid
12.0ms	52×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	8×	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: 35.9b

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sin (+ x eps)) (sin x))
3.0b	(sin (+ x eps))

rewrite60.0ms

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:

50.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series52.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

simplify78.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	192	386
1	538	285
2	2616	275
3	5002	220

prune101.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.2b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite71.0ms

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:

15.0ms	(- (* (cos x) (sin eps)) (sin x))
11.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (cos eps))
32.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* (cos x) (sin eps)) (sin x))
42.0ms	(* (cos x) (sin eps))
39.0ms	(* (sin x) (cos eps))
101.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (45.0ms)

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

prune271.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))
1.5b	(- (cos eps) 1)

rewrite24.0ms

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)))
13.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series156.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
39.0ms	(* (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

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
0.3b	(pow (cos eps) 3)
0.4b	(+ (cos eps) 1)
1.3b	(- (pow (cos eps) 3) 1)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
53×	`add-cube-cbrt`
48×	`times-frac`
40×	`difference-of-squares`
36×	`prod-diff`
30×	`unpow-prod-down` `cube-prod`
20×	`difference-of-sqr-1` `sqr-pow`
16×	`associate-/l*`
12×	`fma-neg`
9×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube`
5×	`pow1` `cube-mult` `unpow3` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `expm1-def` `fma-def` `associate-/r*`
2×	`pow-to-exp` `flip3--` `pow-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 204

Calls

4 calls:

47.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
3.0ms	(pow (cos eps) 3)
7.0ms	(+ (cos eps) 1)
21.0ms	(- (pow (cos eps) 3) 1)

series178.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
26.0ms	(pow (cos eps) 3)
9.0ms	(+ (cos eps) 1)
47.0ms	(- (pow (cos eps) 3) 1)

simplify87.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	544	2069
1	2349	1758
2	5001	1700

prune539.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

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	27	21
1	35	21
2	37	21
3	37	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3274×	body	1280	valid
558.0ms	627×	body	2560	valid
462.0ms	1856×	body	640	valid
117.0ms	748×	body	320	valid
63.0ms	1143×	body	80	valid
43.0ms	352×	body	160	valid