Details

sample231.0ms

Algorithm

intervals

Results

120.0ms	140×	body	1280	valid
47.0ms	61×	body	640	valid
40.0ms	21×	body	2560	valid
9.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize46.0ms

Local error

Found 2 expressions with local error:

2.6b	(cos (+ x eps))
1.2b	(- (cos (+ x eps)) (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

21.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series89.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

simplify412.0ms

Counts: 61 → 48

prune461.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

localize31.0ms

Local error

Found 3 expressions with local error:

2.4b	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))
0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin eps) (sin x) (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `insert-posit16` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

Slowest

16.0ms	(* (cos x) (cos eps))
11.0ms	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))
0.0ms	(fma (sin eps) (sin x) (cos x))

series349.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

214.0ms	(- (* (cos x) (cos eps)) (fma (sin eps) (sin x) (cos x)))
89.0ms	(fma (sin eps) (sin x) (cos x))
45.0ms	(* (cos x) (cos eps))

simplify968.0ms

Counts: 67 → 62

prune877.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

localize46.0ms

Local error

Found 2 expressions with local error:

2.4b	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))
0.1b	(fma (sin eps) (sin x) (cos x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 22

Calls

2 calls:

Slowest

1.0ms	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))
0.0ms	(fma (sin eps) (sin x) (cos x))

series279.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

190.0ms	(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))
90.0ms	(fma (sin eps) (sin x) (cos x))

simplify778.0ms

Counts: 28 → 28

prune461.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

localize29.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma (cos x) (cos eps) (- (log1p (expm1 (fma (sin eps) (sin x) (cos x))))))
0.7b	(expm1 (fma (sin eps) (sin x) (cos x)))
0.2b	(log1p (expm1 (fma (sin eps) (sin x) (cos x))))
0.1b	(fma (sin eps) (sin x) (cos x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`fma-udef`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 46

Calls

4 calls:

Slowest

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

series584.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

254.0ms	(fma (cos x) (cos eps) (- (log1p (expm1 (fma (sin eps) (sin x) (cos x))))))
138.0ms	(log1p (expm1 (fma (sin eps) (sin x) (cos x))))
98.0ms	(expm1 (fma (sin eps) (sin x) (cos x)))
93.0ms	(fma (sin eps) (sin x) (cos x))

simplify406.0ms

Counts: 56 → 58

prune901.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 13.7b

regimes295.0ms

Accuracy

86.3% (1.3b remaining)

Error of 16.0b against oracle of 14.6b and baseline of 24.4b

bsearch265.0ms

end0.0ms

sample8.5s

Algorithm

intervals

Results

5.2s	4514×	body	1280	valid
1.5s	1867×	body	640	valid
1.2s	622×	body	2560	valid
302.0ms	659×	body	320	valid
67.0ms	257×	body	160	valid
10.0ms	81×	body	80	valid