Details

Time bar (total: 36.2s)

sample225.0ms

Algorithm
intervals
Results
109.0ms142×body1280valid
63.0ms58×body640valid
29.0ms18×body2560valid
9.0ms27×body320valid
3.0ms11×body160valid

simplify16.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize14.0ms

Local error

Found 2 expressions with local error:

2.9b
(cos (+ x eps))
0.8b
(- (cos (+ x eps)) (cos x))

rewrite24.0ms

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
17.0ms
(- (cos (+ x eps)) (cos x))
7.0ms
(cos (+ x eps))

series122.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(- (cos (+ x eps)) (cos x))
46.0ms
(cos (+ x eps))

simplify1.5s

Counts
36 → 32
Calls
36 calls:
Slowest
371.0ms
(* (* (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x))) (- (cos (+ x eps)) (cos x)))
182.0ms
(- (pow (cos (+ x eps)) 3) (pow (cos x) 3))
163.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
149.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
99.0ms
(- (* (cos (+ x eps)) (cos (+ x eps))) (* (cos x) (cos x)))

prune423.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(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))))

rewrite135.0ms

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
54.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
46.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
19.0ms
(sin (/ (+ x (+ eps x)) 2))
15.0ms
(+ x (+ eps x))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
115.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
44.0ms
(sin (/ (+ x (+ eps x)) 2))
36.0ms
(+ x (+ eps x))

simplify7.6s

Counts
76 → 76
Calls
76 calls:
Slowest
847.0ms
(* (* (+ x (+ eps x)) (+ x (+ eps x))) (+ x (+ eps x)))
667.0ms
(* (* (* -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)))))
629.0ms
(* (* (* -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)))))
585.0ms
(* (* (* -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)))))
571.0ms
(- (* x x) (* (+ eps x) (+ eps x)))

prune845.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 2 expressions with local error:

2.9b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite75.0ms

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)))

series152.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
109.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
43.0ms
(sin (+ x (* eps 1/2)))

simplify3.6s

Counts
38 → 36
Calls
38 calls:
Slowest
583.0ms
(* (* (* (* -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 -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)))))
450.0ms
(* (* (* (* -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)))))
279.0ms
(exp (* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2)))))
270.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune434.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

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)))))
0.2b
(* (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))))

rewrite226.0ms

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
157.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
26.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
25.0ms
(* (cos x) (sin (* eps 1/2)))
17.0ms
(* (sin x) (cos (* eps 1/2)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
115.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
72.0ms
(* (sin x) (cos (* eps 1/2)))
68.0ms
(* (cos x) (sin (* eps 1/2)))

simplify10.5s

Counts
88 → 86
Calls
88 calls:
Slowest
736.0ms
(* (* (* (* -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))))))
586.0ms
(exp (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
554.0ms
(* (* (* (* -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))))))
528.0ms
(* (* (* (* -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))))))
526.0ms
(* (* -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))))))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes233.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 1.0b

bsearch7.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
4.7s4387×body1280valid
1.3s689×body2560valid
1.1s1817×body640valid
762.0ms716×body320valid
120.0ms297×body160valid
11.0ms94×body80valid