Details

Time bar (total: 18.0s)

sample257.0ms

Algorithm
intervals
Results
122.0ms111×body1280valid
56.0ms29×body2560valid
48.0ms55×body640valid
10.0ms20×body320valid
5.0ms32×body80valid
3.0ms9×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (sin (+ x eps)) (sin x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize53.0ms

Local error

Found 2 expressions with local error:

3.4b
(sin (+ x eps))
1.4b
(- (sin (+ x eps)) (sin x))

rewrite18.0ms

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
13.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series84.0ms

Calls
2 calls:
Slowest
56.0ms
(- (sin (+ x eps)) (sin x))
29.0ms
(sin (+ x eps))

simplify671.0ms

Calls
13 calls:
Slowest
395.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
95.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
62.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
56.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
13.0ms
(- (sin (+ x eps)) (sin x))

prune295.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 3 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite22.0ms

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)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series161.0ms

Calls
3 calls:
Slowest
90.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(+ x (+ eps x))

simplify881.0ms

Calls
17 calls:
Slowest
270.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
145.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
143.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
64.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
46.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune523.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.6b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.3b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite46.0ms

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
21.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
11.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
7.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))

series233.0ms

Calls
4 calls:
Slowest
91.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
56.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
47.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
39.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.8s

Calls
34 calls:
Slowest
313.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
297.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
161.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
145.0ms
(* (* (* (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))))
144.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))

prune809.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.6b
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
0.3b
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(pow E (cos (/ (+ x (+ eps x)) 2)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×add-exp-log
6×pow1 add-cbrt-cube
4×associate-*l* insert-posit16 add-log-exp
3×pow-unpow log-prod associate-*r*
2×pow-to-exp rem-log-exp log-pow
1×pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
18.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
14.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
6.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))

series368.0ms

Calls
4 calls:
Slowest
142.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
97.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
93.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
36.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.0s

Calls
30 calls:
Slowest
301.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
291.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
229.0ms
(* (* (* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (log (pow E (cos (/ (+ x (+ eps x)) 2))))) (log (pow E (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
176.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
169.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune891.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes220.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.2b

bsearch169.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.7s3252×body1280valid
1.5s1804×body640valid
1.2s653×body2560valid
409.0ms767×body320valid
168.0ms1142×body80valid
155.0ms382×body160valid