Details

Time bar (total: 27.3s)

sample228.0ms

Algorithm
intervals
Results
142.0ms147×body1280valid
37.0ms63×body640valid
28.0ms16×body2560valid
8.0ms16×body320valid
3.0ms11×body160valid
0.0ms3×body80valid

simplify8.0ms

Calls
1 calls:
Slowest
8.0ms
(- (cos (+ x eps)) (cos x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize70.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (cos (+ x eps)) (cos x))
1.9b
(cos (+ x eps))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt cos-sum *-un-lft-identity add-log-exp
2×associate--l- pow1 +-commutative add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
26.0ms
(- (cos (+ x eps)) (cos x))
17.0ms
(cos (+ x eps))

series94.0ms

Calls
2 calls:
Slowest
77.0ms
(- (cos (+ x eps)) (cos x))
17.0ms
(cos (+ x eps))

simplify563.0ms

Calls
15 calls:
Slowest
207.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
144.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
62.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
34.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
21.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune441.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

2.0b
(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))))

rewrite644.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×associate-*r*
15×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×associate-*l* add-log-exp
5×unswap-sqr
4×pow-prod-down prod-exp cbrt-unprod insert-posit16
3×sum-log *-commutative distribute-lft-out
2×+-commutative associate-+r+ sin-mult
1×flip3-+ associate-*r/ flip-+
Calls
4 calls:
Slowest
408.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
147.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
64.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(+ x (+ eps x))

series305.0ms

Calls
4 calls:
Slowest
138.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
94.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms
(sin (/ (+ x (+ eps x)) 2))
30.0ms
(+ x (+ eps x))

simplify3.8s

Calls
51 calls:
Slowest
663.0ms
(* (* (* -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)))))
560.0ms
(* (* (* -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)))))
500.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
266.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
226.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 2 expressions with local error:

2.0b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*l*
13×add-sqr-sqrt
7×pow1 add-cbrt-cube add-exp-log
6×*-un-lft-identity sin-sum associate-*r* add-cube-cbrt
4×unswap-sqr
3×+-commutative pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in distribute-lft-in *-commutative insert-posit16 add-log-exp
Calls
2 calls:
Slowest
156.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
26.0ms
(sin (+ x (* eps 1/2)))

series115.0ms

Calls
2 calls:
Slowest
86.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
29.0ms
(sin (+ x (* eps 1/2)))

simplify2.5s

Calls
34 calls:
Slowest
678.0ms
(* (* (* (* -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)))))
547.0ms
(* (* (* (* -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)))))
258.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
240.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
91.0ms
(* (* (cos (* eps 1/2)) (sin x)) (* -2 (sin (* eps 1/2))))

prune630.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite540.0ms

Algorithm
rewrite-expression-head
Rules
29×associate-*l*
28×*-un-lft-identity
23×add-sqr-sqrt
16×associate-*r*
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
8×distribute-lft-out
6×add-log-exp unswap-sqr
5×pow-prod-down prod-exp cbrt-unprod
4×*-commutative insert-posit16
3×+-commutative
2×distribute-rgt-in distribute-lft-in flip3-+ associate-*r/ flip-+
1×sum-log sin-cos-mult
Calls
4 calls:
Slowest
402.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))
90.0ms
(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
27.0ms
(* (sin (* eps 1/2)) (cos x))
20.0ms
(* (cos (* eps 1/2)) (sin x))

series475.0ms

Calls
4 calls:
Slowest
201.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))
128.0ms
(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
86.0ms
(* (sin (* eps 1/2)) (cos x))
61.0ms
(* (cos (* eps 1/2)) (sin x))

simplify5.2s

Calls
70 calls:
Slowest
568.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))))
559.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))))
382.0ms
(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (cos x) (cos x)) (cos x)))
328.0ms
(* (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))) (* (* (sin x) (sin x)) (sin x)))
292.0ms
(+ (* (* (sin (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (cos x))) (- (* (* (cos (* eps 1/2)) (sin x)) (* (cos (* eps 1/2)) (sin x))) (* (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
5.7s4550×body1280valid
1.2s1792×body640valid
1.0s606×body2560valid
360.0ms671×body320valid
76.0ms295×body160valid
12.0ms86×body80valid