Details

Time bar (total: 25.5s)

sample231.0ms

Algorithm
intervals
Results
131.0ms146×body1280valid
49.0ms29×body2560valid
31.0ms54×body640valid
8.0ms18×body320valid
2.0ms6×body160valid
0.0ms3×body80valid

simplify8.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize63.0ms

Local error

Found 2 expressions with local error:

3.4b
(cos (+ x eps))
0.9b
(- (cos (+ x eps)) (cos x))

rewrite25.0ms

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
13.0ms
(cos (+ x eps))
11.0ms
(- (cos (+ x eps)) (cos x))

series96.0ms

Calls
2 calls:
Slowest
76.0ms
(- (cos (+ x eps)) (cos x))
19.0ms
(cos (+ x eps))

simplify524.0ms

Calls
13 calls:
Slowest
181.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
165.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
60.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
53.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
10.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune282.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

3.2b
(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))))

rewrite160.0ms

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
Calls
4 calls:
Slowest
54.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
44.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
41.0ms
(sin (/ (+ x (+ eps x)) 2))
20.0ms
(+ x (+ eps x))

series298.0ms

Calls
4 calls:
Slowest
125.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
101.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
48.0ms
(sin (/ (+ x (+ eps x)) 2))
25.0ms
(+ x (+ eps x))

simplify3.2s

Calls
36 calls:
Slowest
668.0ms
(* (* (* -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)))))
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)))))
371.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
258.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
229.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune870.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 3 expressions with local error:

3.2b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
0.0b
(* -2 (sin (* eps 1/2)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×*-un-lft-identity associate-*r* add-cube-cbrt
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sin-sum insert-posit16 add-log-exp
2×*-commutative
1×distribute-rgt-in distribute-lft-in unswap-sqr
Calls
3 calls:
Slowest
51.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
33.0ms
(* -2 (sin (* eps 1/2)))
15.0ms
(sin (+ x (* eps 1/2)))

series161.0ms

Calls
3 calls:
Slowest
101.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
33.0ms
(sin (+ x (* eps 1/2)))
28.0ms
(* -2 (sin (* eps 1/2)))

simplify2.5s

Calls
31 calls:
Slowest
557.0ms
(* (* (* (* -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)))))
491.0ms
(* (* (* (* -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)))))
377.0ms
(- (* 1/24 (pow eps 3)) (+ (* 1/1920 (pow eps 5)) eps))
222.0ms
(* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
220.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune576.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

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-*r/
Calls
4 calls:
Slowest
97.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
66.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
22.0ms
(* (sin x) (cos (* eps 1/2)))
17.0ms
(* (cos x) (sin (* eps 1/2)))

series336.0ms

Calls
4 calls:
Slowest
116.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
87.0ms
(* (sin x) (cos (* eps 1/2)))
73.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
59.0ms
(* (cos x) (sin (* eps 1/2)))

simplify6.1s

Calls
59 calls:
Slowest
495.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
472.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
426.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
410.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))
344.0ms
(- (+ (* 1/4 (* (pow x 2) (pow eps 2))) (* 1/24 (pow eps 4))) (* 1/2 (pow eps 2)))

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.0s4384×body1280valid
1.3s1878×body640valid
1.2s653×body2560valid
324.0ms693×body320valid
131.0ms301×body160valid
11.0ms91×body80valid