Details

Time bar (total: 19.6s)

sample208.0ms

Algorithm
intervals
Results
116.0ms107×body1280valid
35.0ms60×body640valid
31.0ms19×body2560valid
7.0ms18×body320valid
6.0ms43×body80valid
3.0ms9×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (sin (+ x eps)) (sin x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize26.0ms

Local error

Found 2 expressions with local error:

3.4b
(sin (+ x eps))
1.1b
(- (sin (+ x eps)) (sin x))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube sin-sum add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
60.0ms
(- (sin (+ x eps)) (sin x))
14.0ms
(sin (+ x eps))

series83.0ms

Calls
2 calls:
Slowest
54.0ms
(- (sin (+ x eps)) (sin x))
29.0ms
(sin (+ x eps))

simplify773.0ms

Calls
13 calls:
Slowest
372.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
236.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
57.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
11.0ms
(- (sin (+ x eps)) (sin x))

prune324.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite92.0ms

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
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Calls
4 calls:
Slowest
41.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
18.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
13.0ms
(+ x (+ eps x))

series293.0ms

Calls
4 calls:
Slowest
112.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
101.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms
(+ x (+ eps x))
37.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify3.1s

Calls
35 calls:
Slowest
665.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
567.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
355.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
351.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
283.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune695.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ x (+ eps x)) 2))
3.4b
(cos (/ (+ x (+ eps x)) 2))
3.4b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite75.0ms

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
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Calls
4 calls:
Slowest
25.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(cos (/ (+ x (+ eps x)) 2))
12.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series130.0ms

Calls
4 calls:
Slowest
41.0ms
(cos (/ (+ x (+ eps x)) 2))
31.0ms
(cos (/ (+ x (+ eps x)) 2))
31.0ms
(cos (/ (+ x (+ eps x)) 2))
27.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

simplify1.7s

Calls
15 calls:
Slowest
300.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
268.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
264.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
259.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
62.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune716.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ x (+ eps x)) 2))
3.4b
(cos (/ (+ x (+ eps x)) 2))
3.4b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

rewrite97.0ms

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
1×cbrt-prod cbrt-div pow1/3 cos-mult
Calls
4 calls:
Slowest
40.0ms
(cos (/ (+ x (+ eps x)) 2))
32.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))

series266.0ms

Calls
4 calls:
Slowest
140.0ms
(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))))
45.0ms
(cos (/ (+ x (+ eps x)) 2))
42.0ms
(cos (/ (+ x (+ eps x)) 2))
38.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.1s

Calls
14 calls:
Slowest
374.0ms
(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
348.0ms
(pow (pow (cos (* 1/2 (+ (* 2 x) eps))) 2) 1/3)
282.0ms
(- 1 (+ (* 1/3 (* x eps)) (* 1/3 (pow x 2))))
275.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
259.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune681.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes154.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch227.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.1s3277×body1280valid
1.4s1880×body640valid
1.2s660×body2560valid
366.0ms722×body320valid
191.0ms1097×body80valid
98.0ms364×body160valid