Details

sample234.0ms

Algorithm

intervals

Results

110.0ms	97×	body	1280	valid
45.0ms	59×	body	640	valid
45.0ms	21×	body	2560	valid
13.0ms	24×	body	320	valid
7.0ms	42×	body	80	valid
4.0ms	13×	body	160	valid

simplify37.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize15.0ms

Local error

Found 2 expressions with local error:

2.7b	(sin (+ x eps))
1.6b	(- (sin (+ x eps)) (sin x))

rewrite80.0ms

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` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

65.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series79.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

43.0ms	(- (sin (+ x eps)) (sin x))
36.0ms	(sin (+ x eps))

simplify462.0ms

Counts: 61 → 48

prune465.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
0.2b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`sum-log` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `fma-def` `flip3-+` `flip3--` `associate--l+` `flip-+` `sin-cos-mult` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 89

Calls

4 calls:

Slowest

66.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
21.0ms	(* (sin x) (cos eps))
19.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
10.0ms	(* (cos x) (sin eps))

series467.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))
137.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
77.0ms	(* (cos x) (sin eps))
77.0ms	(* (sin x) (cos eps))

simplify521.0ms

Counts: 113 → 101

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.7b

localize38.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x)))
0.2b	(expm1 (fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x))))
0.2b	(* (sin eps) (cos x))
0.2b	(log1p (expm1 (fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

Slowest

10.0ms	(* (sin eps) (cos x))
1.0ms	(expm1 (fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x))))
0.0ms	(fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x)))
0.0ms	(log1p (expm1 (fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x)))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

247.0ms	(log1p (expm1 (fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x)))))
190.0ms	(expm1 (fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x))))
159.0ms	(fma (cos eps) (sin x) (- (* (sin eps) (cos x)) (sin x)))
74.0ms	(* (sin eps) (cos x))

simplify414.0ms

Counts: 67 → 69

prune789.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

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`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

Slowest

29.0ms	(- (* (sin x) (cos eps)) (sin x))
20.0ms	(* (sin x) (cos eps))
0.0ms	(fma (sin eps) (cos x) (- (* (sin x) (cos eps)) (sin x)))

series298.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

143.0ms	(fma (sin eps) (cos x) (- (* (sin x) (cos eps)) (sin x)))
92.0ms	(- (* (sin x) (cos eps)) (sin x))
63.0ms	(* (sin x) (cos eps))

simplify680.0ms

Counts: 66 → 61

prune580.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

regimes269.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.3s	3329×	body	1280	valid
2.0s	1859×	body	640	valid
1.4s	622×	body	2560	valid
413.0ms	785×	body	320	valid
193.0ms	1073×	body	80	valid
90.0ms	332×	body	160	valid