Details

Time bar (total: 21.0s)

sample263.0ms

Algorithm
intervals
Results
112.0ms100×body1280valid
66.0ms52×body640valid
48.0ms23×body2560valid
15.0ms31×body320valid
6.0ms40×body80valid
3.0ms10×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: 36.3b

localize16.0ms

Local error

Found 2 expressions with local error:

2.8b
(sin (+ x eps))
2.1b
(- (sin (+ x eps)) (sin x))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube sin-sum add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 42
Calls
2 calls:
Slowest
51.0ms
(- (sin (+ x eps)) (sin x))
7.0ms
(sin (+ x eps))

series78.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(- (sin (+ x eps)) (sin x))
21.0ms
(sin (+ x eps))

simplify2.0s

Counts
33 → 48
Calls
33 calls:
Slowest
237.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
202.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
182.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
159.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
147.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))

prune381.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 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))
0.0b
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sum-log fma-def distribute-lft-out
2×*-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
27.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
15.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
11.0ms
(+ x (+ eps x))

series277.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
94.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
36.0ms
(cos (/ (+ x (+ eps x)) 2))
32.0ms
(+ x (+ eps x))

simplify3.2s

Counts
37 → 85
Calls
37 calls:
Slowest
627.0ms
(* (* (* 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)))))
532.0ms
(* (* (* 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)))))
418.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
413.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
225.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune714.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-log-exp
5×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u sum-log fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative associate-+r+ flip3-+ associate-*l* *-commutative flip-+
Counts
3 → 52
Calls
3 calls:
Slowest
22.0ms
(cos (/ (+ x (+ eps x)) 2))
19.0ms
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
11.0ms
(+ x (+ eps x))

series179.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
104.0ms
(* (* 2 (cos (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
38.0ms
(cos (/ (+ x (+ eps x)) 2))
37.0ms
(+ x (+ eps x))

simplify2.2s

Counts
24 → 61
Calls
24 calls:
Slowest
533.0ms
(* (* (* (* 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))))
491.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
352.0ms
(* (* (* (* 2 (cos (/ (+ x (+ eps x)) 2))) (* 2 (cos (/ (+ x (+ eps x)) 2)))) (* 2 (cos (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
208.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
72.0ms
(* 2 (* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune575.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

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))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Counts
4 → 44
Calls
4 calls:
Slowest
32.0ms
(cos (/ (+ x (+ eps x)) 2))
30.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cos (/ (+ x (+ eps x)) 2))
20.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
38.0ms
(cos (/ (+ x (+ eps x)) 2))
37.0ms
(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
33.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.2s

Counts
15 → 56
Calls
15 calls:
Slowest
462.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
453.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
424.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
336.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
76.0ms
(cbrt (* (+ (cos (+ (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2))) (cos (- (/ (+ x (+ eps x)) 2) (/ (+ x (+ eps x)) 2)))) (cos (/ (+ x (+ eps x)) 2))))

prune645.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes172.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.1b

bsearch207.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.6s3297×body1280valid
1.5s1848×body640valid
1.1s658×body2560valid
742.0ms774×body320valid
198.0ms1093×body80valid
81.0ms330×body160valid