Details

sample85.0ms

Algorithm

intervals

Results

44.0ms	141×	body	1280	valid
15.0ms	19×	body	2560	valid
11.0ms	57×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	4×	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: 38.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite34.0ms

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:

22.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series67.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify71.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (67.0ms)

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

prune122.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.2b

localize17.0ms

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))
1.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite116.0ms

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:

11.0ms	(* (cos x) (cos eps))
19.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
13.0ms	(* (sin x) (sin eps))
71.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series310.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
86.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
133.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify46.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (38.0ms)

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

prune328.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.1b

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))
1.8b	(+ (* (cos x) (cos eps)) (- (fma (sin x) (sin eps) (cos x))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
2×	`sum-log` `fma-udef`
1×	`+-commutative` `neg-sub0` `associate-+r-` `associate-+r+` `distribute-neg-in` `fma-def` `flip3-+` `unsub-neg` `pow-prod-down` `neg-log` `prod-exp` `cos-mult` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

11.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin x) (sin eps) (cos x))
14.0ms	(+ (* (cos x) (cos eps)) (- (fma (sin x) (sin eps) (cos x))))

series238.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (cos x) (cos eps))
54.0ms	(fma (sin x) (sin eps) (cos x))
138.0ms	(+ (* (cos x) (cos eps)) (- (fma (sin x) (sin eps) (cos x))))

simplify132.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	246	418
1	954	377
2	4899	369
3	5001	369

prune247.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (sin x) (sin eps)))
0.1b	(- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps)))))
0.2b	(* (sin x) (sin eps))
1.8b	(- (- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps))))) (cos x))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

0.0ms	(log1p (* (sin x) (sin eps)))
14.0ms	(- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps)))))
13.0ms	(* (sin x) (sin eps))
65.0ms	(- (- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps))))) (cos x))

series436.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(log1p (* (sin x) (sin eps)))
130.0ms	(- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps)))))
46.0ms	(* (sin x) (sin eps))
181.0ms	(- (- (* (cos x) (cos eps)) (expm1 (log1p (* (sin x) (sin eps))))) (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	380	1217
1	1405	893
2	5002	877

prune287.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.0b

regimes221.0ms

Accuracy

83.7% (1.6b remaining)

Error of 15.7b against oracle of 14.1b and baseline of 24.0b

bsearch126.0ms

Steps

Iters	Range		Point
8	2.6312679778022526e-07	0.0004221944073348045	3.4724220740038346e-07
10	-4.57643111655563e-14	-8.576014553851025e-27	-4.51775150735862e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	49
1	48	49
2	48	49

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4441×	body	1280	valid
596.0ms	1907×	body	640	valid
518.0ms	615×	body	2560	valid
92.0ms	669×	body	320	valid
32.0ms	290×	body	160	valid
4.0ms	78×	body	80	valid