Details

Time bar (total: 17.1s)

sample217.0ms

Algorithm
intervals
Results
104.0ms124×body1280valid
45.0ms28×body2560valid
43.0ms63×body640valid
10.0ms27×body320valid
3.0ms12×body160valid
0.0ms2×body80valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize50.0ms

Local error

Found 2 expressions with local error:

2.5b
(cos (+ x eps))
1.4b
(- (cos (+ x eps)) (cos x))

rewrite18.0ms

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
12.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series71.0ms

Calls
2 calls:
Slowest
50.0ms
(- (cos (+ x eps)) (cos x))
21.0ms
(cos (+ x eps))

simplify1.4s

Calls
33 calls:
Slowest
287.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
219.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
74.0ms
(fma 1 (cos (+ x eps)) (- (* (cos x) 1)))
69.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
60.0ms
(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune522.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 3 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult
Calls
3 calls:
Slowest
17.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series121.0ms

Calls
3 calls:
Slowest
71.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
39.0ms
(sin (/ (+ x (+ eps x)) 2))
11.0ms
(+ x (+ eps x))

simplify839.0ms

Calls
18 calls:
Slowest
167.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
142.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
138.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
53.0ms
(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
50.0ms
(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune597.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
0.3b
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.2b
(expm1 (sin (/ (+ x (+ eps x)) 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef
Calls
4 calls:
Slowest
9.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
3.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
0.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))

series321.0ms

Calls
4 calls:
Slowest
135.0ms
(* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
94.0ms
(log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))
58.0ms
(expm1 (sin (/ (+ x (+ eps x)) 2)))
34.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.4s

Calls
22 calls:
Slowest
195.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
193.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
178.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
166.0ms
(* (* (* (log1p (expm1 (sin (/ (+ x (+ eps x)) 2)))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (log1p (expm1 (sin (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
77.0ms
(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune855.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b
(sin (/ (+ x (+ eps x)) 2))
0.7b
(cbrt (sin (/ eps 2)))
0.7b
(cbrt (sin (/ eps 2)))
0.7b
(cbrt (sin (/ eps 2)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
Calls
4 calls:
Slowest
6.0ms
(sin (/ (+ x (+ eps x)) 2))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))

series455.0ms

Calls
4 calls:
Slowest
149.0ms
(cbrt (sin (/ eps 2)))
141.0ms
(cbrt (sin (/ eps 2)))
132.0ms
(cbrt (sin (/ eps 2)))
32.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.0s

Calls
21 calls:
Slowest
274.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
251.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
224.0ms
(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
107.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
36.0ms
(sin (* 1/2 (+ (* 2 x) eps)))

prune822.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

regimes287.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.0b

bsearch178.0ms

end0.0ms

sample7.8s

Algorithm
intervals
Results
4.6s4432×body1280valid
1.4s1855×body640valid
1.2s658×body2560valid
291.0ms712×body320valid
67.0ms275×body160valid
8.0ms68×body80valid