Details

sample234.0ms

Algorithm

intervals

Results

124.0ms	107×	body	1280	valid
46.0ms	63×	body	640	valid
34.0ms	18×	body	2560	valid
11.0ms	23×	body	320	valid
5.0ms	33×	body	80	valid
4.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

8.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize46.0ms

Local error

Found 2 expressions with local error:

3.4b	(sin (+ x eps))
1.2b	(- (sin (+ x eps)) (sin x))

rewrite69.0ms

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

53.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series81.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

50.0ms	(- (sin (+ x eps)) (sin x))
31.0ms	(sin (+ x eps))

simplify2.0s

Counts

33 → 48

Calls

33 calls:

Slowest

258.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
238.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
181.0ms	(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
156.0ms	(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
145.0ms	(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune459.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 3 expressions with local error:

3.3b	(cos (/ (+ x (+ eps x)) 2))
0.3b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite66.0ms

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

43.0ms	(cos (/ (+ x (+ eps x)) 2))
11.0ms	(+ x (+ eps x))
11.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

98.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
39.0ms	(cos (/ (+ x (+ eps x)) 2))
24.0ms	(+ x (+ eps x))

simplify1.9s

Counts

25 → 61

Calls

25 calls:

Slowest

675.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
450.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
277.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
75.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
53.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune691.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 2 expressions with local error:

3.3b	(cos (fma 1/2 eps x))
0.3b	(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))

rewrite26.0ms

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` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

Slowest

21.0ms	(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
5.0ms	(cos (fma 1/2 eps x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

73.0ms	(* (cos (fma 1/2 eps x)) (sin (/ eps 2)))
21.0ms	(cos (fma 1/2 eps x))

simplify1.1s

Counts

17 → 38

Calls

17 calls:

Slowest

358.0ms	(* (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
338.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/8 (pow eps 2))))
218.0ms	(- (* 1/2 eps) (+ (* 1/12 (pow eps 3)) (* 1/4 (* x (pow eps 2)))))
42.0ms	(+ (log (cos (fma 1/2 eps x))) (log (sin (/ eps 2))))
33.0ms	(* (sqrt (cos (fma 1/2 eps x))) (sqrt (sin (/ eps 2))))

prune379.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
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))

rewrite279.0ms

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-*l/` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 88

Calls

4 calls:

Slowest

152.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
66.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
36.0ms	(* (sin (* 1/2 eps)) (sin x))
23.0ms	(* (cos (* 1/2 eps)) (cos x))

series394.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
120.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
71.0ms	(* (sin (* 1/2 eps)) (sin x))
55.0ms	(* (cos (* 1/2 eps)) (cos x))

simplify5.4s

Counts

55 → 100

Calls

55 calls:

Slowest

713.0ms	(* (* (* (- (* (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)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
631.0ms	(* (- (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))) (sin (/ eps 2)))
406.0ms	(- (* (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) 2) (* 2 (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x)))))
339.0ms	(* (* (* (sin (* 1/2 eps)) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (sin x) (sin x)) (sin x)))
321.0ms	(- (+ (cos (+ (* 1/2 eps) x)) (cos (- (* 1/2 eps) x))) (- (cos (- (* 1/2 eps) x)) (cos (+ (* 1/2 eps) x))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch7.0ms

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.7s	3263×	body	1280	valid
1.6s	1872×	body	640	valid
1.4s	644×	body	2560	valid
518.0ms	757×	body	320	valid
174.0ms	1114×	body	80	valid
145.0ms	350×	body	160	valid