Details

Time bar (total: 26.8s)

sample190.0ms

Algorithm
intervals
Results
98.0ms97×body1280valid
32.0ms21×body2560valid
32.0ms59×body640valid
9.0ms24×body320valid
4.0ms42×body80valid
3.0ms13×body160valid

simplify16.0ms

Counts
1 → 1
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: 36.2b

localize26.0ms

Local error

Found 2 expressions with local error:

2.7b
(sin (+ x eps))
1.6b
(- (sin (+ x eps)) (sin x))

rewrite100.0ms

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
Counts
2 → 26
Calls
2 calls:
Slowest
86.0ms
(- (sin (+ x eps)) (sin x))
14.0ms
(sin (+ x eps))

series90.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
56.0ms
(- (sin (+ x eps)) (sin x))
34.0ms
(sin (+ x eps))

simplify1.8s

Counts
36 → 32
Calls
36 calls:
Slowest
376.0ms
(* (* (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x))) (- (sin (+ x eps)) (sin x)))
343.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
241.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
238.0ms
(- (pow (sin (+ x eps)) 3) (pow (sin x) 3))
97.0ms
(- (* (sin (+ x eps)) (sin (+ x eps))) (* (sin x) (sin x)))

prune280.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 3 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
5×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r* associate-*l* insert-posit16 distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
38.0ms
(cos (/ (+ x (+ eps x)) 2))
22.0ms
(+ x (+ eps x))
21.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series201.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
115.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
44.0ms
(+ x (+ eps x))
42.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify4.1s

Counts
53 → 52
Calls
53 calls:
Slowest
702.0ms
(* (* (+ x (+ eps x)) (+ x (+ eps x))) (+ x (+ eps x)))
614.0ms
(- (* x x) (* (+ eps x) (+ eps x)))
374.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
247.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
242.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune569.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize70.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
2.7b
(cos (/ (+ x (+ eps x)) 2))
2.7b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite105.0ms

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
Counts
4 → 36
Calls
4 calls:
Slowest
39.0ms
(cos (/ (+ x (+ eps x)) 2))
35.0ms
(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))))

series139.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
41.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
37.0ms
(cos (/ (+ x (+ eps x)) 2))
31.0ms
(cos (/ (+ x (+ eps x)) 2))
29.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify3.2s

Counts
48 → 48
Calls
48 calls:
Slowest
335.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
301.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
262.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
238.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
110.0ms
(sqrt (cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2)))))

prune650.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize57.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 59
Calls
4 calls:
Slowest
76.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
50.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
37.0ms
(cos (/ (+ x (+ eps x)) 2))
26.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
72.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify4.6s

Counts
72 → 71
Calls
72 calls:
Slowest
407.0ms
(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
316.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
287.0ms
(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2))) (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))) (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2))))
255.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
232.0ms
(log (exp (* (cbrt (cos (/ (+ x (+ eps x)) 2))) (cbrt (cos (/ (+ x (+ eps x)) 2))))))

prune782.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

regimes325.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.3b

bsearch276.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
4.4s3329×body1280valid
2.1s1859×body640valid
1.4s622×body2560valid
406.0ms785×body320valid
151.0ms1073×body80valid
100.0ms332×body160valid