Details

Time bar (total: 23.9s)

sample206.0ms

Algorithm
intervals
Results
82.0ms89×body1280valid
55.0ms71×body640valid
44.0ms29×body2560valid
9.0ms23×body320valid
5.0ms37×body80valid
2.0ms7×body160valid

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: 37.0b

localize36.0ms

Local error

Found 2 expressions with local error:

3.4b
(sin (+ x eps))
1.1b
(- (sin (+ x eps)) (sin x))

rewrite58.0ms

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
48.0ms
(- (sin (+ x eps)) (sin x))
9.0ms
(sin (+ x eps))

series94.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
60.0ms
(- (sin (+ x eps)) (sin x))
34.0ms
(sin (+ x eps))

simplify2.2s

Counts
33 → 48
Calls
33 calls:
Slowest
332.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
203.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
187.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
171.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
158.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))

prune375.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

3.3b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sum-log fma-def distribute-lft-out
2×*-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
31.0ms
(cos (/ (+ x (+ eps x)) 2))
21.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
20.0ms
(+ x (+ eps x))
12.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
83.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
33.0ms
(cos (/ (+ x (+ eps x)) 2))
32.0ms
(+ x (+ eps x))

simplify3.0s

Counts
37 → 85
Calls
37 calls:
Slowest
600.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
500.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
356.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
348.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
211.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune823.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 3 expressions with local error:

3.3b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-log-exp
5×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u sum-log fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative associate-+r+ flip3-+ associate-*l* *-commutative flip-+
Counts
3 → 52
Calls
3 calls:
Slowest
28.0ms
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
27.0ms
(+ x (+ eps x))
20.0ms
(cos (/ (+ x (+ eps x)) 2))

series177.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
111.0ms
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
41.0ms
(+ x (+ eps x))
25.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.5s

Counts
24 → 61
Calls
24 calls:
Slowest
923.0ms
(* (* (* (* 2 2) 2) (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
435.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
421.0ms
(* (* (* (* 2 (cos (/ (+ x (+ eps x)) 2))) (* 2 (cos (/ (+ x (+ eps x)) 2)))) (* 2 (cos (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
193.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
88.0ms
(* 2 (* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune602.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

3.3b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(log1p (cos (/ (+ x (+ eps x)) 2)))
0.2b
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (* 2 (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
1×log1p-udef expm1-log1p associate-*l* log1p-expm1 *-commutative expm1-udef
Counts
4 → 55
Calls
4 calls:
Slowest
36.0ms
(* (* 2 (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
29.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(log1p (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* (* 2 (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
71.0ms
(log1p (cos (/ (+ x (+ eps x)) 2)))
49.0ms
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
43.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify3.1s

Counts
23 → 67
Calls
23 calls:
Slowest
510.0ms
(* (* (* (* 2 (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (* 2 (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))) (* 2 (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
508.0ms
(* (* (* (* 2 2) 2) (* (* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
424.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
398.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
252.0ms
(- (log 2) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))

prune791.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes229.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.5b

bsearch303.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.4s3275×body1280valid
1.5s1782×body640valid
1.3s658×body2560valid
828.0ms783×body320valid
176.0ms1131×body80valid
112.0ms371×body160valid