Details

Time bar (total: 25.9s)

sample272.0ms

Algorithm
intervals
Results
152.0ms134×body1280valid
49.0ms69×body640valid
44.0ms23×body2560valid
10.0ms21×body320valid
1.0ms4×body160valid
1.0ms5×body80valid

simplify16.0ms

Counts
1 → 1
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: 39.3b

localize26.0ms

Local error

Found 2 expressions with local error:

4.2b
(cos (+ x eps))
1.0b
(- (cos (+ x eps)) (cos x))

rewrite59.0ms

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
41.0ms
(cos (+ x eps))
17.0ms
(- (cos (+ x eps)) (cos x))

series110.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
90.0ms
(- (cos (+ x eps)) (cos x))
20.0ms
(cos (+ x eps))

simplify531.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
218.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
156.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
46.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
40.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
13.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune291.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

4.0b
(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))))

rewrite198.0ms

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
79.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
68.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
28.0ms
(sin (/ (+ x (+ eps x)) 2))
22.0ms
(+ x (+ eps x))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
111.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
44.0ms
(sin (/ (+ x (+ eps x)) 2))
29.0ms
(+ x (+ eps x))

simplify3.1s

Counts
36 → 76
Calls
36 calls:
Slowest
631.0ms
(* (* (* -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)))))
467.0ms
(* (* (* -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)))))
419.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
240.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
228.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune899.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 2 expressions with local error:

4.0b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite64.0ms

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
56.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
8.0ms
(sin (+ x (* eps 1/2)))

series133.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
92.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
41.0ms
(sin (+ x (* eps 1/2)))

simplify1.8s

Counts
18 → 36
Calls
18 calls:
Slowest
496.0ms
(* (* (* (* -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)))))
489.0ms
(* (* (* (* -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)))))
226.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
191.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
56.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

prune403.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-cbrt-cube add-exp-log
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×*-commutative insert-posit16 add-log-exp
2×sin-cos-mult unswap-sqr
1×associate-*l/
Counts
4 → 86
Calls
4 calls:
Slowest
118.0ms
(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
89.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
34.0ms
(* (sin x) (cos (* eps 1/2)))
23.0ms
(* (cos x) (sin (* eps 1/2)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
94.0ms
(* (cos x) (sin (* eps 1/2)))
80.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
79.0ms
(* (sin x) (cos (* eps 1/2)))

simplify6.8s

Counts
62 → 98
Calls
62 calls:
Slowest
750.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))
596.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
507.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
418.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
368.0ms
(- (+ (* 1/4 (* (pow x 2) (pow eps 2))) (* 1/24 (pow eps 4))) (* 1/2 (pow eps 2)))

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes245.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.5s4484×body1280valid
1.6s646×body2560valid
1.3s1826×body640valid
795.0ms676×body320valid
80.0ms293×body160valid
11.0ms75×body80valid