Details

Time bar (total: 18.9s)

sample225.0ms

Algorithm
intervals
Results
129.0ms146×body1280valid
46.0ms29×body2560valid
30.0ms54×body640valid
7.0ms18×body320valid
1.0ms6×body160valid
0.0ms3×body80valid

simplify16.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize27.0ms

Local error

Found 2 expressions with local error:

3.4b
(cos (+ x eps))
0.9b
(- (cos (+ x eps)) (cos x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 cos-sum add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
11.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series119.0ms

Calls
2 calls:
Slowest
61.0ms
(cos (+ x eps))
58.0ms
(- (cos (+ x eps)) (cos x))

simplify689.0ms

Calls
13 calls:
Slowest
319.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
176.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
57.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
45.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
20.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune367.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

3.2b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×associate-*r* insert-posit16 add-log-exp
3×associate-*l*
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp associate-*r/ cbrt-unprod flip-+
Calls
4 calls:
Slowest
17.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
9.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series269.0ms

Calls
4 calls:
Slowest
122.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
86.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
37.0ms
(sin (/ (+ x (+ eps x)) 2))
24.0ms
(+ x (+ eps x))

simplify1.7s

Calls
22 calls:
Slowest
460.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
351.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
157.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
125.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
63.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune704.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 3 expressions with local error:

3.2b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
0.0b
(* -2 (sin (* eps 1/2)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*r*
5×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×sin-sum insert-posit16 add-log-exp
2×*-commutative
1×distribute-rgt-in distribute-lft-in associate-*l* pow-prod-down prod-exp cbrt-unprod
Calls
3 calls:
Slowest
10.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
3.0ms
(* -2 (sin (* eps 1/2)))
2.0ms
(sin (+ x (* eps 1/2)))

series186.0ms

Calls
3 calls:
Slowest
104.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
50.0ms
(sin (+ x (* eps 1/2)))
31.0ms
(* -2 (sin (* eps 1/2)))

simplify1.4s

Calls
21 calls:
Slowest
494.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (sin (+ x (* eps 1/2))) (sin (+ x (* eps 1/2)))) (sin (+ x (* eps 1/2)))))
234.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
140.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
83.0ms
(- (* 1/24 (pow eps 3)) (+ (* 1/1920 (pow eps 5)) eps))
76.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

prune550.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
0.2b
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
0.2b
(* (cos x) (sin (* eps 1/2)))
0.1b
(* (sin x) (cos (* eps 1/2)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
4×*-commutative insert-posit16 add-log-exp
2×sin-cos-mult
1×associate-*l/
Calls
4 calls:
Slowest
39.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
31.0ms
(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
7.0ms
(* (cos x) (sin (* eps 1/2)))
6.0ms
(* (sin x) (cos (* eps 1/2)))

series364.0ms

Calls
4 calls:
Slowest
147.0ms
(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
111.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
55.0ms
(* (sin x) (cos (* eps 1/2)))
51.0ms
(* (cos x) (sin (* eps 1/2)))

simplify3.0s

Calls
46 calls:
Slowest
372.0ms
(- x (+ (* 1/8 (* x (pow eps 2))) (* 1/6 (pow x 3))))
306.0ms
(- (* 1/2 eps) (+ (* 1/4 (* (pow x 2) eps)) (* 1/48 (pow eps 3))))
254.0ms
(- (+ (* 1/4 (* (pow x 2) (pow eps 2))) (* 1/24 (pow eps 4))) (* 1/2 (pow eps 2)))
203.0ms
(* (* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2)))) (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))))
156.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))

prune995.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes242.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.8s

Algorithm
intervals
Results
4.0s4384×body1280valid
1.6s653×body2560valid
1.2s1878×body640valid
433.0ms91×body80valid
364.0ms693×body320valid
118.0ms301×body160valid