Details

Time bar (total: 16.4s)

sample243.0ms

Algorithm
intervals
Results
114.0ms124×body1280valid
52.0ms63×body640valid
51.0ms28×body2560valid
11.0ms27×body320valid
4.0ms12×body160valid
0.0ms2×body80valid

simplify7.0ms

Calls
1 calls:
Slowest
7.0ms
(- (cos (+ x eps)) (cos x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize60.0ms

Local error

Found 2 expressions with local error:

2.5b
(cos (+ x eps))
1.4b
(- (cos (+ x eps)) (cos x))

rewrite20.0ms

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
15.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series88.0ms

Calls
2 calls:
Slowest
68.0ms
(- (cos (+ x eps)) (cos x))
20.0ms
(cos (+ x eps))

simplify639.0ms

Calls
13 calls:
Slowest
329.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
147.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
44.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
28.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
16.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 3 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×associate-*r* associate-*l* insert-posit16 add-log-exp
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult
Calls
3 calls:
Slowest
17.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series136.0ms

Calls
3 calls:
Slowest
88.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
36.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

simplify936.0ms

Calls
18 calls:
Slowest
356.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
144.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
103.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
52.0ms
(sin (* 1/2 (+ (* 2 x) eps)))
35.0ms
(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune550.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.7b
(cbrt (sin (/ eps 2)))
0.7b
(cbrt (sin (/ eps 2)))
0.7b
(cbrt (sin (/ eps 2)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
Calls
4 calls:
Slowest
11.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))

series547.0ms

Calls
4 calls:
Slowest
177.0ms
(cbrt (sin (/ eps 2)))
173.0ms
(cbrt (sin (/ eps 2)))
162.0ms
(cbrt (sin (/ eps 2)))
35.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify913.0ms

Calls
21 calls:
Slowest
208.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
198.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
183.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
96.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
57.0ms
(sin (* 1/2 (+ (* 2 x) eps)))

prune831.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.7b
(cbrt (sin (/ eps 2)))
0.7b
(cbrt (sin (/ eps 2)))
0.7b
(cbrt (sin (/ eps 2)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
Calls
4 calls:
Slowest
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))

series447.0ms

Calls
4 calls:
Slowest
139.0ms
(cbrt (sin (/ eps 2)))
138.0ms
(cbrt (sin (/ eps 2)))
138.0ms
(cbrt (sin (/ eps 2)))
32.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify970.0ms

Calls
21 calls:
Slowest
250.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
246.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
180.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
120.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
40.0ms
(sin (* 1/2 (+ (* 2 x) eps)))

prune901.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.3b

regimes274.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.9b

bsearch187.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.1s4432×body1280valid
1.3s1855×body640valid
1.2s658×body2560valid
365.0ms712×body320valid
72.0ms275×body160valid
9.0ms68×body80valid