Details

Time bar (total: 36.6s)

sample237.0ms

Algorithm
intervals
Results
122.0ms140×body1280valid
53.0ms61×body640valid
37.0ms21×body2560valid
10.0ms22×body320valid
3.0ms10×body160valid
0.0ms2×body80valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(- (cos (+ x eps)) (cos x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize21.0ms

Local error

Found 2 expressions with local error:

2.6b
(cos (+ x eps))
1.2b
(- (cos (+ x eps)) (cos x))

rewrite45.0ms

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
Counts
2 → 26
Calls
2 calls:
Slowest
26.0ms
(cos (+ x eps))
18.0ms
(- (cos (+ x eps)) (cos x))

series408.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
390.0ms
(- (cos (+ x eps)) (cos x))
18.0ms
(cos (+ x eps))

simplify1.6s

Counts
36 → 32
Calls
36 calls:
Slowest
336.0ms
(* (* (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)))
236.0ms
(- (pow (cos (+ x eps)) 3) (pow (cos x) 3))
192.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
173.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
143.0ms
(- (* (cos (+ x eps)) (cos (+ x eps))) (* (cos x) (cos x)))

prune333.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b
(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))))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16
3×sum-log distribute-lft-out
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 64
Calls
4 calls:
Slowest
86.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
71.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
38.0ms
(sin (/ (+ x (+ eps x)) 2))
21.0ms
(+ x (+ eps x))

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
136.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
54.0ms
(sin (/ (+ x (+ eps x)) 2))
42.0ms
(+ x (+ eps x))

simplify7.4s

Counts
76 → 76
Calls
76 calls:
Slowest
651.0ms
(* (* (+ x (+ eps x)) (+ x (+ eps x))) (+ x (+ eps x)))
595.0ms
(* (* (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))) (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
587.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
530.0ms
(- (* x x) (* (+ eps x) (+ eps x)))
521.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))

prune896.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 2 expressions with local error:

2.7b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt *-un-lft-identity sin-sum associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×insert-posit16 add-log-exp
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
2 → 30
Calls
2 calls:
Slowest
60.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
15.0ms
(sin (+ x (* eps 1/2)))

series139.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
104.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
35.0ms
(sin (+ x (* eps 1/2)))

simplify3.7s

Counts
38 → 36
Calls
38 calls:
Slowest
641.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (sin (+ x (* eps 1/2))) (sin (+ x (* eps 1/2)))) (sin (+ x (* eps 1/2)))))
607.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2)))) (* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))) (* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2)))))
548.0ms
(* (* (* (* -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)))))
297.0ms
(exp (* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2)))))
256.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))

prune430.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
0.1b
(* (sin x) (cos (* eps 1/2)))
0.1b
(* (cos x) (sin (* eps 1/2)))
0.1b
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16
3×*-commutative
2×flip3-+ associate-*r/ flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in sin-cos-mult
Counts
4 → 74
Calls
4 calls:
Slowest
136.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
35.0ms
(* (sin x) (cos (* eps 1/2)))
32.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
25.0ms
(* (cos x) (sin (* eps 1/2)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
214.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
158.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
90.0ms
(* (cos x) (sin (* eps 1/2)))
85.0ms
(* (sin x) (cos (* eps 1/2)))

simplify9.6s

Counts
88 → 86
Calls
88 calls:
Slowest
625.0ms
(exp (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
538.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))
523.0ms
(* (* -2 (sin (* eps 1/2))) (- (* (* (sin x) (cos (* eps 1/2))) (* (sin x) (cos (* eps 1/2)))) (* (* (cos x) (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))
487.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))) (* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))) (* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))
473.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes240.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.3s4514×body1280valid
1.6s622×body2560valid
1.3s1867×body640valid
336.0ms659×body320valid
106.0ms257×body160valid
11.0ms81×body80valid