Details

sample224.0ms

Algorithm

intervals

Results

113.0ms	109×	body	1280	valid
55.0ms	56×	body	640	valid
27.0ms	16×	body	2560	valid
9.0ms	21×	body	320	valid
6.0ms	43×	body	80	valid
3.0ms	11×	body	160	valid

simplify8.0ms

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: 37.3b

localize12.0ms

Local error

Found 2 expressions with local error:

2.1b	(sin (+ x eps))
1.8b	(- (sin (+ x eps)) (sin x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`sin-sum` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `+-commutative` `add-cbrt-cube` `associate--l+` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

2 calls:

Slowest

59.0ms	(- (sin (+ x eps)) (sin x))
37.0ms	(sin (+ x eps))

series92.0ms

Calls

2 calls:

Slowest

59.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify2.1s

Calls

35 calls:

Slowest

252.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
216.0ms	(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
201.0ms	(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
182.0ms	(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
154.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))

prune536.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* (cos eps) (sin x)) (sin x))
0.1b	(* (cos eps) (sin x))
0.1b	(* (sin eps) (cos x))
0.1b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
72×	`prod-diff`
58×	`add-cube-cbrt`
38×	`associate-+r+`
36×	`associate-l`
33×	`associate-r`
12×	`fma-def` `fma-neg`
11×	`add-log-exp` `unswap-sqr`
10×	`*-commutative`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`distribute-lft-out` `distribute-lft-out--`
4×	`expm1-log1p-u` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sum-log` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `cbrt-unprod` `flip--` `difference-of-squares`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Calls

4 calls:

Slowest

139.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
46.0ms	(- (* (cos eps) (sin x)) (sin x))
12.0ms	(* (sin eps) (cos x))
12.0ms	(* (cos eps) (sin x))

series445.0ms

Calls

4 calls:

Slowest

204.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
102.0ms	(- (* (cos eps) (sin x)) (sin x))
77.0ms	(* (cos eps) (sin x))
61.0ms	(* (sin eps) (cos x))

simplify15.3s

Calls

191 calls:

Slowest

520.0ms	(fma (sqrt (cos eps)) (* (sqrt (cos eps)) (sin x)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
442.0ms	(fma 1 (* (cos eps) (sin x)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
442.0ms	(* (exp (* (sin eps) (cos x))) (/ (exp (* (cos eps) (sin x))) (exp (sin x))))
436.0ms	(fma (* (cos eps) 1) (sin x) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
432.0ms	(+ (* (+ (sin (- eps x)) (sin (+ eps x))) (+ (* (* (cos eps) (sin x)) (* (cos eps) (sin x))) (+ (* (sin x) (sin x)) (* (* (cos eps) (sin x)) (sin x))))) (* 2 (- (pow (* (cos eps) (sin x)) 3) (pow (sin x) 3))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

2.8b	(- (* (cos eps) (sin x)) (sin x))
0.1b	(* (cos eps) (sin x))
0.1b	(fma (cos x) (sin eps) (- (* (cos eps) (sin x)) (sin x)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `prod-diff`
31×	`add-cube-cbrt`
18×	`associate-r`
16×	`associate-l`
12×	`fma-neg`
6×	`unswap-sqr`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `*-commutative` `add-log-exp`
4×	`distribute-rgt-out--`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `flip--`

Calls

3 calls:

Slowest

58.0ms	(- (* (cos eps) (sin x)) (sin x))
22.0ms	(* (cos eps) (sin x))
0.0ms	(fma (cos x) (sin eps) (- (* (cos eps) (sin x)) (sin x)))

series362.0ms

Calls

3 calls:

Slowest

183.0ms	(fma (cos x) (sin eps) (- (* (cos eps) (sin x)) (sin x)))
113.0ms	(- (* (cos eps) (sin x)) (sin x))
66.0ms	(* (cos eps) (sin x))

simplify9.7s

Calls

116 calls:

Slowest

531.0ms	(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))
441.0ms	(fma (sqrt (cos eps)) (* (sqrt (cos eps)) (sin x)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
435.0ms	(fma (* (cos eps) 1) (sin x) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
424.0ms	(fma 1 (* (cos eps) (sin x)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
415.0ms	(fma 1 (* (cos eps) (sin x)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

2.9b	(- (cos eps) 1)
0.1b	(fma (cos x) (sin eps) (* (sin x) (- (cos eps) 1)))
0.1b	(* (sin x) (- (cos eps) 1))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `difference-of-sqr-1` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`expm1-def` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Calls

3 calls:

Slowest

33.0ms	(* (sin x) (- (cos eps) 1))
6.0ms	(- (cos eps) 1)
0.0ms	(fma (cos x) (sin eps) (* (sin x) (- (cos eps) 1)))

series285.0ms

Calls

3 calls:

Slowest

166.0ms	(fma (cos x) (sin eps) (* (sin x) (- (cos eps) 1)))
83.0ms	(* (sin x) (- (cos eps) 1))
35.0ms	(- (cos eps) 1)

simplify2.8s

Calls

75 calls:

Slowest

463.0ms	(* (* (* (sin x) (sin x)) (sin x)) (* (* (- (cos eps) 1) (- (cos eps) 1)) (- (cos eps) 1)))
192.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
149.0ms	(- (* 1/24 (pow eps 4)) (+ (* 1/2 (pow eps 2)) (* 1/720 (pow eps 6))))
75.0ms	(+ (* (cos eps) (cos eps)) (+ (* 1 1) (* (cos eps) 1)))
69.0ms	(fma (* (cbrt (cos eps)) (cbrt (cos eps))) (cbrt (cos eps)) (- (* (sqrt 1) (sqrt 1))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.8s	3388×	body	1280	valid
2.2s	1801×	body	640	valid
1.2s	606×	body	2560	valid
381.0ms	743×	body	320	valid
153.0ms	1114×	body	80	valid
148.0ms	348×	body	160	valid