Details

sample84.0ms

Algorithm

intervals

Results

47.0ms	142×	body	1280	valid
13.0ms	64×	body	640	valid
11.0ms	13×	body	2560	valid
3.0ms	18×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	3×	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: 38.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (cos (+ x eps)) (cos x))
4.5b	(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))
5.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune125.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
3.5b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite13.0ms

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:

4.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin x) (sin eps) (cos x))
8.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (cos x) (cos eps))
55.0ms	(fma (sin x) (sin eps) (cos x))
131.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify113.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (108.0ms)

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

prune218.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.5b	(- (- (* (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:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series302.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (cos x) (cos eps))
44.0ms	(* (sin x) (sin eps))
131.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5001	822

prune321.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.2b	(log1p (expm1 (* (cos x) (cos eps))))
0.4b	(expm1 (* (cos x) (cos eps)))
5.7b	(- (log1p (expm1 (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-log-exp`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
3×	`fma-neg`
2×	`log1p-udef` `diff-log` `fma-udef`
1×	`sub-neg` `expm1-log1p` `flip3--` `log1p-expm1` `flip--` `associate--r+` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(log1p (expm1 (* (cos x) (cos eps))))
0.0ms	(expm1 (* (cos x) (cos eps)))
3.0ms	(- (log1p (expm1 (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma (sin x) (sin eps) (cos x))
74.0ms	(log1p (expm1 (* (cos x) (cos eps))))
72.0ms	(expm1 (* (cos x) (cos eps)))
173.0ms	(- (log1p (expm1 (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	238	897
1	777	663
2	4362	615
3	5001	614

prune215.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 12.0b

regimes213.0ms

Accuracy

82.6% (1.7b remaining)

Error of 16.5b against oracle of 14.8b and baseline of 24.6b

bsearch103.0ms

Steps

Iters	Range		Point
7	0.00013951198456185504	0.004380743253548005	0.00014188596036111877
8	-8.894349585236044e-09	-1.0921156594031797e-11	-8.189106507089701e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4453×	body	1280	valid
543.0ms	632×	body	2560	valid
402.0ms	1853×	body	640	valid
98.0ms	690×	body	320	valid
27.0ms	283×	body	160	valid
5.0ms	89×	body	80	valid