Details

sample90.0ms

Algorithm

intervals

Results

49.0ms	142×	body	1280	valid
13.0ms	16×	body	2560	valid
13.0ms	64×	body	640	valid
3.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	80	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: 39.1b

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.4b	(cos (+ x eps))

rewrite25.0ms

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` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

14.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220

prune113.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(fma (sin x) (sin eps) (cos x))
2.7b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

13.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin x) (sin eps) (cos x))
12.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (cos x) (cos eps))
44.0ms	(fma (sin x) (sin eps) (cos x))
114.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify117.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4494	406
3	5001	404

prune207.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(fma (sin x) (sin eps) (cos x))
0.6b	(log (exp (* (cos x) (cos eps))))
7.3b	(- (log (exp (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
16×	`log-pow`
12×	`pow1`
10×	`add-log-exp`
6×	`add-exp-log` `log-prod` `fma-neg` `add-cbrt-cube`
5×	`exp-prod` `exp-to-pow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `associate--l+`
2×	`fma-udef` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `difference-of-squares` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

10.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin x) (sin eps) (cos x))
4.0ms	(log (exp (* (cos x) (cos eps))))
18.0ms	(- (log (exp (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
45.0ms	(fma (sin x) (sin eps) (cos x))
40.0ms	(log (exp (* (cos x) (cos eps))))
115.0ms	(- (log (exp (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

simplify132.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	280	1292
1	898	861
2	4742	832
3	5001	832

prune324.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 13.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
0.2b	(fma (sin x) (sin eps) (cos x))
0.2b	(log1p (expm1 (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))
2.7b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
3×	`prod-diff`
2×	`fma-udef`
1×	`sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `fma-neg` `diff-log` `log1p-expm1` `flip--` `associate--r+` `expm1-udef`

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(log1p (expm1 (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))
12.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(expm1 (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x))))
46.0ms	(fma (sin x) (sin eps) (cos x))
177.0ms	(log1p (expm1 (- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))))
120.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify101.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	205	670
1	681	565
2	3845	560
3	5001	557

prune179.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.5b

regimes212.0ms

Accuracy

79.3% (2.1b remaining)

Error of 16.3b against oracle of 14.1b and baseline of 24.5b

bsearch94.0ms

Steps

Iters	Range		Point
7	1.6623184518082866e-06	8.950540206577903e-05	2.824493182358224e-06
7	-6.488020188375565e-32	-1.2799005155204566e-33	-6.379118075739501e-32

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4420×	body	1280	valid
542.0ms	635×	body	2560	valid
387.0ms	1848×	body	640	valid
101.0ms	730×	body	320	valid
29.0ms	288×	body	160	valid
4.0ms	79×	body	80	valid