Details

Time bar (total: 16.8s)

sample221.0ms

Algorithm
intervals
Results
98.0ms109×body1280valid
64.0ms55×body640valid
36.0ms25×body2560valid
7.0ms20×body320valid
5.0ms39×body80valid
2.0ms8×body160valid

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: 35.9b

localize12.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (sin (+ x eps)) (sin x))
1.6b
(sin (+ x eps))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube sin-sum add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
7.0ms
(- (sin (+ x eps)) (sin x))
2.0ms
(sin (+ x eps))

series68.0ms

Calls
2 calls:
Slowest
54.0ms
(- (sin (+ x eps)) (sin x))
14.0ms
(sin (+ x eps))

simplify613.0ms

Calls
13 calls:
Slowest
391.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
74.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
47.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
47.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
10.0ms
(- (sin (+ x eps)) (sin x))

prune324.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 3 expressions with local error:

1.6b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×associate-*r* associate-*l* insert-posit16 add-log-exp
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Calls
3 calls:
Slowest
14.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
4.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series111.0ms

Calls
3 calls:
Slowest
82.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
17.0ms
(cos (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

simplify814.0ms

Calls
17 calls:
Slowest
221.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
164.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
128.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
48.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
41.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune621.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b
(cos (/ (+ x (+ eps x)) 2))
1.6b
(cos (/ (+ x (+ eps x)) 2))
1.6b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Calls
4 calls:
Slowest
20.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cos (/ (+ x (+ eps x)) 2))

series87.0ms

Calls
4 calls:
Slowest
26.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
26.0ms
(cos (/ (+ x (+ eps x)) 2))
18.0ms
(cos (/ (+ x (+ eps x)) 2))
17.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.5s

Calls
15 calls:
Slowest
300.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
285.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
285.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
250.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
72.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune628.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Calls
4 calls:
Slowest
18.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
10.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
4.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))

series165.0ms

Calls
4 calls:
Slowest
63.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
58.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
26.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
18.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.9s

Calls
34 calls:
Slowest
318.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
317.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
168.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
160.0ms
(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
151.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune790.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

regimes181.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch257.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.3s3268×body1280valid
1.9s715×body2560valid
1.3s1824×body640valid
336.0ms758×body320valid
197.0ms1090×body80valid
104.0ms345×body160valid