Details

Time bar (total: 18.5s)

sample206.0ms

Algorithm
intervals
Results
137.0ms148×body1280valid
28.0ms19×body2560valid
21.0ms49×body640valid
8.0ms24×body320valid
3.0ms14×body160valid
0.0ms2×body80valid

simplify9.0ms

Calls
1 calls:
Slowest
9.0ms
(- (cos (+ x eps)) (cos x))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize19.0ms

Local error

Found 2 expressions with local error:

2.9b
(cos (+ x eps))
1.1b
(- (cos (+ x eps)) (cos x))

rewrite9.0ms

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
6.0ms
(- (cos (+ x eps)) (cos x))
2.0ms
(cos (+ x eps))

series75.0ms

Calls
2 calls:
Slowest
62.0ms
(- (cos (+ x eps)) (cos x))
13.0ms
(cos (+ x eps))

simplify838.0ms

Calls
13 calls:
Slowest
435.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
189.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
56.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
55.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
23.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune353.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize41.0ms

Local error

Found 4 expressions with local error:

2.9b
(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))))

rewrite27.0ms

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
12.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
10.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
4.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series236.0ms

Calls
4 calls:
Slowest
114.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
76.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
24.0ms
(sin (/ (+ x (+ eps x)) 2))
22.0ms
(+ x (+ eps x))

simplify1.6s

Calls
22 calls:
Slowest
417.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
363.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
140.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
136.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
73.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune689.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 3 expressions with local error:

2.9b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1 add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×associate-*r* insert-posit16 add-log-exp
1×+-commutative associate-+r+ flip3-+ associate-*l* pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Calls
3 calls:
Slowest
22.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series170.0ms

Calls
3 calls:
Slowest
114.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
37.0ms
(sin (/ (+ x (+ eps x)) 2))
19.0ms
(+ x (+ eps x))

simplify1.4s

Calls
15 calls:
Slowest
460.0ms
(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
373.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
164.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
79.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
68.0ms
(+ (log (* -2 (sin (/ (+ x (+ eps x)) 2)))) (log (sin (/ eps 2))))

prune562.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

6.8b
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
6.8b
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
6.8b
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
2.9b
(sin (/ (+ x (+ eps x)) 2))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod cbrt-div pow1/3 associate-*r/ sin-mult
Calls
4 calls:
Slowest
12.0ms
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
9.0ms
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
9.0ms
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
6.0ms
(sin (/ (+ x (+ eps x)) 2))

series582.0ms

Calls
4 calls:
Slowest
218.0ms
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
183.0ms
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
159.0ms
(cbrt (* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
23.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify2.1s

Calls
18 calls:
Slowest
373.0ms
(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
363.0ms
(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
334.0ms
(- (+ (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4))))) (* 1/3 (* x (* (cbrt -2) (exp (* 1/3 (- (log 2) (log eps)))))))) (+ (* 1/9 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (- (log 16) (* 4 (log eps)))))))) (* 1/6 (* (pow x 2) (* (cbrt -2) (exp (* 1/3 (+ (* 2 (log eps)) (log 1/4)))))))))
140.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
102.0ms
(cbrt (* -2 (- (cos (- (/ (+ x (+ eps x)) 2) (/ eps 2))) (cos (+ (/ (+ x (+ eps x)) 2) (/ eps 2))))))

prune879.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.5b

regimes489.0ms

Accuracy

97.9% (0.3b remaining)

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

bsearch269.0ms

end0.0ms

sample7.8s

Algorithm
intervals
Results
4.9s4469×body1280valid
1.2s1820×body640valid
1.2s636×body2560valid
329.0ms713×body320valid
119.0ms290×body160valid
10.0ms72×body80valid