Details

Time bar (total: 18.4s)

sample169.0ms

Algorithm
intervals
Results
80.0ms148×body1280valid
39.0ms24×body320valid
22.0ms19×body2560valid
17.0ms49×body640valid
3.0ms14×body160valid
0.0ms2×body80valid

simplify8.0ms

Calls
1 calls:
Slowest
8.0ms
(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize16.0ms

Local error

Found 2 expressions with local error:

2.9b
(cos (+ x eps))
1.1b
(- (cos (+ x eps)) (cos x))

rewrite9.0ms

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
7.0ms
(- (cos (+ x eps)) (cos x))
2.0ms
(cos (+ x eps))

series78.0ms

Calls
2 calls:
Slowest
66.0ms
(- (cos (+ x eps)) (cos x))
12.0ms
(cos (+ x eps))

simplify1.5s

Calls
33 calls:
Slowest
359.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
167.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
83.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
78.0ms
(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (sqrt (cos x)) (sqrt (cos x)))))
53.0ms
(fma 1 (cos (+ x eps)) (- (* (cos x) 1)))

prune519.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite33.0ms

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
18.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
10.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
3.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series221.0ms

Calls
4 calls:
Slowest
95.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
93.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
21.0ms
(sin (/ (+ x (+ eps x)) 2))
12.0ms
(+ x (+ eps x))

simplify1.4s

Calls
22 calls:
Slowest
397.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
166.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
141.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
126.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
62.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune839.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 3 expressions with local error:

2.9b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite31.0ms

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
22.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series139.0ms

Calls
3 calls:
Slowest
91.0ms
(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
28.0ms
(sin (/ (+ x (+ eps x)) 2))
20.0ms
(+ x (+ eps x))

simplify1.3s

Calls
15 calls:
Slowest
391.0ms
(* (* (* (* -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))))
338.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
144.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
68.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
66.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune613.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (* -2 (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
0.2b
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.1b
(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube add-exp-log
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt log1p-expm1-u
4×expm1-log1p-u insert-posit16 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
15.0ms
(* (* -2 (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series285.0ms

Calls
4 calls:
Slowest
144.0ms
(* (* -2 (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (sin (/ eps 2)))
67.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
45.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
29.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.7s

Calls
20 calls:
Slowest
419.0ms
(* (* (* (* -2 (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (* -2 (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))) (* -2 (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
328.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
173.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
114.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
80.0ms
(+ x (+ (* 1/2 (pow x 2)) (* 1/2 eps)))

prune779.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.5b

regimes222.0ms

Accuracy

97.9% (0.3b remaining)

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

bsearch244.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.2s4469×body1280valid
1.6s636×body2560valid
1.1s1820×body640valid
269.0ms713×body320valid
79.0ms290×body160valid
9.0ms72×body80valid