Details

Time bar (total: 16.9s)

sample276.0ms

Algorithm
intervals
Results
119.0ms105×body1280valid
71.0ms63×body640valid
53.0ms25×body2560valid
14.0ms25×body320valid
5.0ms30×body80valid
3.0ms8×body160valid

simplify15.0ms

Calls
1 calls:
Slowest
15.0ms
(- (sin (+ x eps)) (sin x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize26.0ms

Local error

Found 2 expressions with local error:

3.5b
(sin (+ x eps))
1.1b
(- (sin (+ x eps)) (sin x))

rewrite18.0ms

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
14.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series113.0ms

Calls
2 calls:
Slowest
59.0ms
(- (sin (+ x eps)) (sin x))
54.0ms
(sin (+ x eps))

simplify581.0ms

Calls
13 calls:
Slowest
345.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
63.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
56.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
35.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
17.0ms
(- (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

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-+
Calls
3 calls:
Slowest
19.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series151.0ms

Calls
3 calls:
Slowest
84.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
42.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(+ x (+ eps x))

simplify969.0ms

Calls
17 calls:
Slowest
232.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
187.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
139.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
58.0ms
(cos (* 1/2 (+ (* 2 x) eps)))
56.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune521.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

3.7b
(cos (/ (+ x (+ eps x)) 2))
3.7b
(cos (/ (+ x (+ eps x)) 2))
3.7b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite38.0ms

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
21.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
4.0ms
(cos (/ (+ x (+ eps x)) 2))

series156.0ms

Calls
4 calls:
Slowest
47.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.6s

Calls
15 calls:
Slowest
324.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
309.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
275.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
257.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
69.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune652.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

3.7b
(cos (/ (+ x (+ eps x)) 2))
3.7b
(cos (/ (+ x (+ eps x)) 2))
3.7b
(cos (/ (+ x (+ eps x)) 2))
3.7b
(cos (/ (+ x (+ eps x)) 2))

rewrite24.0ms

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
Calls
4 calls:
Slowest
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cos (/ (+ x (+ eps x)) 2))
6.0ms
(cos (/ (+ x (+ eps x)) 2))

series151.0ms

Calls
4 calls:
Slowest
42.0ms
(cos (/ (+ x (+ eps x)) 2))
41.0ms
(cos (/ (+ x (+ eps x)) 2))
37.0ms
(cos (/ (+ x (+ eps x)) 2))
31.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.5s

Calls
12 calls:
Slowest
320.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
290.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
278.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
268.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
63.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune631.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.2b

regimes209.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.8b

bsearch303.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.6s3357×body1280valid
1.7s618×body2560valid
1.3s1809×body640valid
372.0ms801×body320valid
177.0ms1073×body80valid
99.0ms342×body160valid