Details

Time bar (total: 18.2s)

sample217.0ms

Algorithm
intervals
Results
126.0ms144×body1280valid
38.0ms25×body2560valid
31.0ms58×body640valid
7.0ms19×body320valid
2.0ms8×body160valid
0.0ms2×body80valid

simplify9.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize13.0ms

Local error

Found 2 expressions with local error:

3.3b
(cos (+ x eps))
1.3b
(- (cos (+ x eps)) (cos x))

rewrite41.0ms

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 cos-sum add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
39.0ms
(- (cos (+ x eps)) (cos x))
2.0ms
(cos (+ x eps))

series88.0ms

Calls
2 calls:
Slowest
69.0ms
(- (cos (+ x eps)) (cos x))
19.0ms
(cos (+ x eps))

simplify1.4s

Calls
33 calls:
Slowest
337.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
204.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
81.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (sqrt (cos x)) (sqrt (cos x)))))
62.0ms
(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
54.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x)))))

prune471.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u 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
19.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
11.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
3.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series320.0ms

Calls
4 calls:
Slowest
137.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
111.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms
(+ x (+ eps x))
31.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.4s

Calls
22 calls:
Slowest
307.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
223.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
153.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
124.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
67.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune775.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1 add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative associate-+r+ flip3-+ associate-*l* pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Calls
3 calls:
Slowest
19.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series187.0ms

Calls
3 calls:
Slowest
116.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
41.0ms
(+ x (+ eps x))
31.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.1s

Calls
15 calls:
Slowest
328.0ms
(* (* (* (* -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))))
285.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
132.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
90.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
62.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune524.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

3.7b
(sin (/ (+ x (+ eps x)) 2))
0.5b
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.2b
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.2b
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
1×log1p-udef expm1-log1p associate-*l* pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef
Calls
4 calls:
Slowest
8.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
3.0ms
(sin (/ (+ x (+ eps x)) 2))
0.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))

series323.0ms

Calls
4 calls:
Slowest
141.0ms
(* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
72.0ms
(expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))
63.0ms
(log1p (sin (/ (+ x (+ eps x)) 2)))
47.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.5s

Calls
20 calls:
Slowest
374.0ms
(* (* (* (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2))))) (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* -2 (expm1 (log1p (sin (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
274.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
166.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
113.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
85.0ms
(- (+ x (* 1/2 eps)) (* 1/2 (pow x 2)))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

regimes260.0ms

Accuracy

97.7% (0.3b remaining)

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

bsearch215.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.8s4536×body1280valid
1.5s1816×body640valid
1.1s618×body2560valid
325.0ms677×body320valid
107.0ms263×body160valid
12.0ms90×body80valid