Details

sample100.0ms

Algorithm

intervals

Results

57.0ms	146×	body	1280	valid
17.0ms	69×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	18×	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: 42.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.3b	(cos (+ x eps))

rewrite13.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series69.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune117.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
24.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series298.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune300.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.1b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series189.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(fma (sin x) (sin eps) (cos x))
138.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify117.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	87	209
1	240	182
2	795	182
3	3587	180
4	5001	180

prune139.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.2b	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
0.6b	(expm1 (fma (sin x) (sin eps) (cos x)))
5.1b	(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`fma-udef`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 42

Calls

4 calls:

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

series395.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma (sin x) (sin eps) (cos x))
86.0ms	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
81.0ms	(expm1 (fma (sin x) (sin eps) (cos x)))
178.0ms	(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	143	404
1	377	348
2	1274	346
3	5001	343

prune166.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.7b

regimes179.0ms

Accuracy

86.6% (1.3b remaining)

Error of 15.7b against oracle of 14.4b and baseline of 24.3b

bsearch163.0ms

Steps

Iters	Range		Point
11	1.951179291618044e-19	5702493.407928515	3.291024564528541e-08
9	-2.526286952290626e-15	-1.2437801318881542e-20	-2.4957789297588313e-15

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	52
1	59	52
2	59	52

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4529×	body	1280	valid
571.0ms	631×	body	2560	valid
448.0ms	1815×	body	640	valid
115.0ms	656×	body	320	valid
36.0ms	298×	body	160	valid
4.0ms	71×	body	80	valid