Details

Time bar (total: 18.5s)

sample196.0ms

Algorithm
intervals
Results
99.0ms144×body1280valid
57.0ms25×body2560valid
25.0ms58×body640valid
6.0ms19×body320valid
2.0ms8×body160valid
0.0ms2×body80valid

simplify10.0ms

Calls
1 calls:
Slowest
10.0ms
(- (cos (+ x eps)) (cos x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize24.0ms

Local error

Found 2 expressions with local error:

3.3b
(cos (+ x eps))
1.3b
(- (cos (+ x eps)) (cos x))

rewrite13.0ms

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
9.0ms
(- (cos (+ x eps)) (cos x))
3.0ms
(cos (+ x eps))

series105.0ms

Calls
2 calls:
Slowest
87.0ms
(- (cos (+ x eps)) (cos x))
18.0ms
(cos (+ x eps))

simplify728.0ms

Calls
13 calls:
Slowest
383.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
139.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
69.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
45.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
22.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune333.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

3.7b
(sin (/ (+ x (+ eps x)) 2))
0.2b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite25.0ms

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
9.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
8.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series339.0ms

Calls
4 calls:
Slowest
131.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
123.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
48.0ms
(+ x (+ eps x))
37.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.6s

Calls
22 calls:
Slowest
424.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
389.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
158.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
115.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
83.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune709.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 2 expressions with local error:

3.6b
(sin (+ x (* eps 1/2)))
0.2b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt *-un-lft-identity sin-sum associate-*r* add-cube-cbrt
2×insert-posit16 add-log-exp
1×distribute-rgt-in distribute-lft-in associate-*l* pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
2 calls:
Slowest
22.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
3.0ms
(sin (+ x (* eps 1/2)))

series108.0ms

Calls
2 calls:
Slowest
76.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
31.0ms
(sin (+ x (* eps 1/2)))

simplify972.0ms

Calls
15 calls:
Slowest
356.0ms
(* (* (* (* -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)))))
166.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
138.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
57.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
55.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))

prune365.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×add-log-exp
4×insert-posit16
3×pow-prod-down prod-exp *-commutative cbrt-unprod
2×flip3-+ associate-*r/ flip-+
1×distribute-rgt-in +-commutative sum-log distribute-lft-in sin-cos-mult
Calls
4 calls:
Slowest
50.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
17.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
6.0ms
(* (cos x) (sin (* eps 1/2)))
6.0ms
(* (sin x) (cos (* eps 1/2)))

series508.0ms

Calls
4 calls:
Slowest
199.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
159.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
83.0ms
(* (sin x) (cos (* eps 1/2)))
66.0ms
(* (cos x) (sin (* eps 1/2)))

simplify2.9s

Calls
40 calls:
Slowest
490.0ms
(* (* (* (* -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))))))
302.0ms
(- x (+ (* 1/8 (* x (pow eps 2))) (* 1/6 (pow x 3))))
267.0ms
(- (* 1/2 eps) (+ (* 1/4 (* (pow x 2) eps)) (* 1/48 (pow eps 3))))
234.0ms
(* -2 (* (sin (* 1/2 eps)) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps))))))
203.0ms
(* -2 (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 eps))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes164.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.0s4536×body1280valid
1.4s618×body2560valid
1.2s1816×body640valid
259.0ms677×body320valid
103.0ms263×body160valid
44.0ms90×body80valid