Details

sample96.0ms

Algorithm

intervals

Results

51.0ms	134×	body	1280	valid
16.0ms	67×	body	640	valid
12.0ms	13×	body	2560	valid
7.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	6×	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: 37.4b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
2.9b	(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))

series66.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(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

prune121.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.3b

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))
3.0b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite41.0ms

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)))
7.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
38.0ms	(* (cos x) (cos eps))
47.0ms	(* (sin x) (sin eps))
124.0ms	(- (- (* (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

prune314.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.0b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
3.1b	(log (exp (* (sin x) (sin eps))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

3.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
35.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.0ms	(log (exp (* (sin x) (sin eps))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
43.0ms	(* (sin x) (sin eps))
124.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
49.0ms	(log (exp (* (sin x) (sin eps))))

simplify47.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	358	1094
1	1206	803
2	5001	791

prune356.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))))
0.5b	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
0.5b	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
3.0b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
12×	`prod-diff`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate--r+`
9×	`add-exp-log` `add-cbrt-cube`
8×	`flip3--` `cos-mult` `frac-sub` `flip--`
6×	`diff-log`
4×	`pow1` `expm1-log1p-u` `sub-neg` `associate-*r/` `associate-/r/` `log1p-expm1-u` `associate-/l/`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `fma-neg` `div-exp` `associate--r-`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 95

Calls

4 calls:

43.0ms	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))))
13.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
13.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (* (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))))
106.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
99.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
135.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify85.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	469	1910
1	2400	1481
2	5002	1477

prune412.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.1b

regimes241.0ms

Accuracy

87.3% (1.3b remaining)

Error of 16.0b against oracle of 14.8b and baseline of 24.7b

bsearch125.0ms

Steps

Iters	Range		Point
8	1.7085304078792323e-11	2.2698285208946172e-07	1.6624442377015138e-07
7	-0.00034188071245303247	-1.912514877855927e-06	-7.616433541907881e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4474×	body	1280	valid
613.0ms	663×	body	2560	valid
452.0ms	1831×	body	640	valid
115.0ms	667×	body	320	valid
34.0ms	277×	body	160	valid
9.0ms	88×	body	80	valid