Details

Time bar (total: 19.0s)

sample229.0ms

Algorithm
intervals
Results
119.0ms111×body1280valid
48.0ms29×body2560valid
36.0ms55×body640valid
8.0ms20×body320valid
5.0ms32×body80valid
2.0ms9×body160valid

simplify16.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize68.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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
Calls
2 calls:
Slowest
8.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series436.0ms

Calls
2 calls:
Slowest
416.0ms
(- (sin (+ x eps)) (sin x))
20.0ms
(sin (+ x eps))

simplify1.2s

Calls
33 calls:
Slowest
174.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
104.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
86.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
64.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
57.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune410.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Calls
3 calls:
Slowest
15.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series149.0ms

Calls
3 calls:
Slowest
85.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
35.0ms
(+ x (+ eps x))
29.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify872.0ms

Calls
17 calls:
Slowest
229.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
212.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
113.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
53.0ms
(cos (* 1/2 (+ (* 2 x) eps)))
49.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune576.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

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)))

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×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Calls
4 calls:
Slowest
15.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
11.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
6.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))

series222.0ms

Calls
4 calls:
Slowest
90.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
70.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
32.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify1.9s

Calls
34 calls:
Slowest
257.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
238.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
217.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
189.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
142.0ms
(* (* (* (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))))

prune1.0s

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)))

rewrite25.0ms

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×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u 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
9.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
3.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))

series351.0ms

Calls
4 calls:
Slowest
152.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
90.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
77.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
31.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.1s

Calls
30 calls:
Slowest
273.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
242.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
224.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
221.0ms
(* (* (* (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))))
209.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune866.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes288.0ms

Accuracy

98.3% (0.3b remaining)

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

bsearch182.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.5s3252×body1280valid
1.4s653×body2560valid
1.3s1804×body640valid
327.0ms767×body320valid
188.0ms1142×body80valid
163.0ms382×body160valid