Details

sample283.0ms

Algorithm

intervals

Results

147.0ms	145×	body	1280	valid
44.0ms	21×	body	2560	valid
43.0ms	64×	body	640	valid
31.0ms	12×	body	320	valid
3.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

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

24.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series107.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

67.0ms	(- (cos (+ x eps)) (cos x))
39.0ms	(cos (+ x eps))

simplify2.1s

Counts

33 → 48

Calls

33 calls:

Slowest

224.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
212.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
199.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
186.0ms	(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
162.0ms	(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune495.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize42.0ms

Local error

Found 3 expressions with local error:

2.7b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite113.0ms

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-+` `sin-mult` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

Slowest

72.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
21.0ms	(sin (/ (+ x (+ eps x)) 2))
18.0ms	(+ x (+ eps x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

105.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms	(+ x (+ eps x))
38.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.6s

Counts

26 → 62

Calls

26 calls:

Slowest

387.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
274.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
259.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
68.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
68.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune746.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 2 expressions with local error:

2.8b	(sin (fma 1/2 eps x))
0.3b	(* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

Slowest

45.0ms	(* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))
5.0ms	(sin (fma 1/2 eps x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

60.0ms	(* (sin (* eps 1/2)) (sin (fma 1/2 eps x)))
43.0ms	(sin (fma 1/2 eps x))

simplify1.2s

Counts

20 → 41

Calls

20 calls:

Slowest

356.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (sin (fma 1/2 eps x)) (sin (fma 1/2 eps x))) (sin (fma 1/2 eps x))))
254.0ms	(- (+ x (* 1/2 eps)) (* 1/48 (pow eps 3)))
184.0ms	(- (+ (* 1/2 (* x eps)) (* 1/4 (pow eps 2))) (* 1/48 (pow eps 4)))
71.0ms	(- (cos (- (* eps 1/2) (fma 1/2 eps x))) (cos (+ (* eps 1/2) (fma 1/2 eps x))))
41.0ms	(* (sin (* eps 1/2)) (* (cos (* 1/2 eps)) (sin x)))

prune520.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 86

Calls

4 calls:

Slowest

92.0ms	(* (sin (* eps 1/2)) (* (sin (* 1/2 eps)) (cos x)))
72.0ms	(* (sin (* eps 1/2)) (* (cos (* 1/2 eps)) (sin x)))
29.0ms	(* (sin (* 1/2 eps)) (cos x))
22.0ms	(* (cos (* 1/2 eps)) (sin x))

series328.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

115.0ms	(* (sin (* eps 1/2)) (* (cos (* 1/2 eps)) (sin x)))
86.0ms	(* (sin (* 1/2 eps)) (cos x))
66.0ms	(* (cos (* 1/2 eps)) (sin x))
61.0ms	(* (sin (* eps 1/2)) (* (sin (* 1/2 eps)) (cos x)))

simplify4.1s

Counts

51 → 98

Calls

51 calls:

Slowest

640.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (* (cos (* 1/2 eps)) (sin x)) (* (cos (* 1/2 eps)) (sin x))) (* (cos (* 1/2 eps)) (sin x))))
511.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (* (cos (* 1/2 eps)) (cos (* 1/2 eps))) (cos (* 1/2 eps))) (* (* (sin x) (sin x)) (sin x))))
441.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (* (sin (* 1/2 eps)) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos x) (cos x)) (cos x))))
395.0ms	(* (* (* (sin (* 1/2 eps)) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos x) (cos x)) (cos x)))
354.0ms	(* (* (* (cos (* 1/2 eps)) (cos (* 1/2 eps))) (cos (* 1/2 eps))) (* (* (sin x) (sin x)) (sin x)))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes222.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch5.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.1s	4392×	body	1280	valid
1.2s	1944×	body	640	valid
1.1s	616×	body	2560	valid
280.0ms	662×	body	320	valid
78.0ms	313×	body	160	valid
9.0ms	73×	body	80	valid