Details

sample235.0ms

Algorithm

intervals

Results

148.0ms	148×	body	1280	valid
42.0ms	25×	body	2560	valid
27.0ms	49×	body	640	valid
8.0ms	21×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	5×	body	80	valid

simplify12.0ms

Calls

1 calls:

Slowest

12.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize26.0ms

Local error

Found 2 expressions with local error:

1.8b	(cos (+ x eps))
1.2b	(- (cos (+ x eps)) (cos x))

rewrite19.0ms

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`

Calls

2 calls:

Slowest

14.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series81.0ms

Calls

2 calls:

Slowest

66.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify1.4s

Calls

33 calls:

Slowest

321.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
257.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
66.0ms	(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cos x) 1)))
59.0ms	(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
56.0ms	(/ (exp (cos (+ x eps))) (exp (cos x)))

prune505.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.6b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))
0.0b	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

18.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
17.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms	(sin (/ (+ x (+ eps x)) 2))
2.0ms	(+ x (+ eps x))

series200.0ms

Calls

4 calls:

Slowest

93.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
65.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
28.0ms	(sin (/ (+ x (+ eps x)) 2))
13.0ms	(+ x (+ eps x))

simplify1.4s

Calls

22 calls:

Slowest

319.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
217.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
149.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
120.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
91.0ms	(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune768.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(sin (/ (+ x (+ eps x)) 2))
1.6b	(sin (/ (+ x (+ eps x)) 2))
1.6b	(sin (/ (+ x (+ eps x)) 2))
0.7b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Calls

4 calls:

Slowest

5.0ms	(sin (/ (+ x (+ eps x)) 2))
3.0ms	(sin (/ (+ x (+ eps x)) 2))
3.0ms	(sin (/ (+ x (+ eps x)) 2))
3.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series168.0ms

Calls

4 calls:

Slowest

100.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
25.0ms	(sin (/ (+ x (+ eps x)) 2))
24.0ms	(sin (/ (+ x (+ eps x)) 2))
20.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.2s

Calls

15 calls:

Slowest

275.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
209.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
157.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
131.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
63.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

prune790.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b	(sin (/ (+ x (+ eps x)) 2))
1.6b	(sin (/ (+ x (+ eps x)) 2))
1.6b	(sin (/ (+ x (+ eps x)) 2))
0.7b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Calls

4 calls:

Slowest

5.0ms	(sin (/ (+ x (+ eps x)) 2))
5.0ms	(sin (/ (+ x (+ eps x)) 2))
3.0ms	(sin (/ (+ x (+ eps x)) 2))
1.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series152.0ms

Calls

4 calls:

Slowest

86.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
24.0ms	(sin (/ (+ x (+ eps x)) 2))
21.0ms	(sin (/ (+ x (+ eps x)) 2))
20.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.3s

Calls

15 calls:

Slowest

291.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
183.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
155.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
148.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
72.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)

prune962.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.4b

regimes351.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.8b

bsearch253.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.8s	4405×	body	1280	valid
1.2s	715×	body	2560	valid
1.2s	1850×	body	640	valid
272.0ms	662×	body	320	valid
107.0ms	284×	body	160	valid
11.0ms	84×	body	80	valid