Details

sample258.0ms

Algorithm

intervals

Results

120.0ms	106×	body	1280	valid
56.0ms	21×	body	2560	valid
55.0ms	71×	body	640	valid
8.0ms	15×	body	320	valid
5.0ms	32×	body	80	valid
3.0ms	11×	body	160	valid

simplify13.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

12.0ms

(- (sin (+ x eps)) (sin x))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize63.0ms

Local error

Found 2 expressions with local error:

2.6b	(sin (+ x eps))
1.1b	(- (sin (+ x eps)) (sin x))

rewrite92.0ms

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

71.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

series91.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify2.2s

Counts

33 → 48

Calls

33 calls:

Slowest

252.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
211.0ms	(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
206.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
183.0ms	(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
170.0ms	(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune410.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize25.0ms

Local error

Found 3 expressions with local error:

2.7b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `sum-log` `fma-def` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

Slowest

45.0ms	(cos (/ (+ x (+ eps x)) 2))
24.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
20.0ms	(+ x (+ eps x))

series191.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

119.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms	(+ x (+ eps x))
29.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.7s

Counts

25 → 61

Calls

25 calls:

Slowest

462.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
423.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
239.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
67.0ms	(cos (* 1/2 (+ (* 2 x) eps)))
65.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune822.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 2 expressions with local error:

2.7b	(cos (fma 1/2 eps x))
0.2b	(* (sin (* eps 1/2)) (cos (fma 1/2 eps x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

Slowest

27.0ms	(* (sin (* eps 1/2)) (cos (fma 1/2 eps x)))
3.0ms	(cos (fma 1/2 eps x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

78.0ms	(* (sin (* eps 1/2)) (cos (fma 1/2 eps x)))
22.0ms	(cos (fma 1/2 eps x))

simplify1.3s

Counts

18 → 39

Calls

18 calls:

Slowest

405.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
336.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
249.0ms	(- (* 1/2 eps) (+ (* 1/12 (pow eps 3)) (* 1/4 (* x (pow eps 2)))))
75.0ms	(+ (sin (- (* eps 1/2) (fma 1/2 eps x))) (sin (+ (* eps 1/2) (fma 1/2 eps x))))
27.0ms	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))

prune556.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* eps 1/2)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
0.2b	(* (sin (* 1/2 eps)) (sin x))
0.1b	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
0.1b	(* (cos (* 1/2 eps)) (cos x))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`fma-neg` `diff-log`

Counts

4 → 94

Calls

4 calls:

Slowest

181.0ms	(* (sin (* eps 1/2)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
50.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
20.0ms	(* (sin (* 1/2 eps)) (sin x))
20.0ms	(* (cos (* 1/2 eps)) (cos x))

series437.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(* (sin (* eps 1/2)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
140.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
73.0ms	(* (cos (* 1/2 eps)) (cos x))
70.0ms	(* (sin (* 1/2 eps)) (sin x))

simplify5.9s

Counts

60 → 106

Calls

60 calls:

Slowest

1.4s	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
519.0ms	(- (* (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) 2) (* 2 (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))))
391.0ms	(* (* (* (cos (* 1/2 eps)) (cos (* 1/2 eps))) (cos (* 1/2 eps))) (* (* (cos x) (cos x)) (cos x)))
375.0ms	(+ (* (* (cos (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (cos x))) (+ (* (* (sin (* 1/2 eps)) (sin x)) (* (sin (* 1/2 eps)) (sin x))) (* (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
346.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch17.0ms

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.7s	3227×	body	1280	valid
1.6s	1967×	body	640	valid
1.2s	616×	body	2560	valid
388.0ms	764×	body	320	valid
223.0ms	351×	body	160	valid
152.0ms	1075×	body	80	valid