Details

Time bar (total: 16.9s)

sample161.0ms

Algorithm
intervals
Results
92.0ms139×body1280valid
29.0ms66×body640valid
19.0ms16×body2560valid
6.0ms21×body320valid
2.0ms7×body160valid
1.0ms7×body80valid

simplify19.0ms

Calls
1 calls:
Slowest
18.0ms
(- (cos (+ x eps)) (cos x))

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize30.0ms

Local error

Found 2 expressions with local error:

2.5b
(cos (+ x eps))
0.8b
(- (cos (+ x eps)) (cos x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 cos-sum add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
10.0ms
(- (cos (+ x eps)) (cos x))
3.0ms
(cos (+ x eps))

series87.0ms

Calls
2 calls:
Slowest
68.0ms
(- (cos (+ x eps)) (cos x))
19.0ms
(cos (+ x eps))

simplify668.0ms

Calls
13 calls:
Slowest
337.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
168.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
64.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
28.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
12.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune389.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

2.5b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b
(/ (+ x (+ eps x)) 2)
0.0b
(+ x (+ eps x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×insert-posit16 add-log-exp
3×associate-*r* associate-*l* associate-/l*
2×flip3-+ flip-+ associate-/l/
1×+-commutative associate-+r+ clear-num frac-2neg pow-prod-down prod-exp *-commutative cbrt-unprod div-inv sin-mult
Calls
4 calls:
Slowest
14.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ eps x)) 2))
6.0ms
(/ (+ x (+ eps x)) 2)
1.0ms
(+ x (+ eps x))

series151.0ms

Calls
4 calls:
Slowest
79.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
28.0ms
(sin (/ (+ x (+ eps x)) 2))
24.0ms
(/ (+ x (+ eps x)) 2)
20.0ms
(+ x (+ eps x))

simplify2.0s

Calls
25 calls:
Slowest
510.0ms
(- (* x x) (* (+ eps x) (+ eps x)))
490.0ms
(+ (pow x 3) (pow (+ eps x) 3))
335.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
156.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
115.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))

prune735.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

2.5b
(sin (/ (+ x (+ eps x)) 2))
2.5b
(sin (/ (+ x (+ eps x)) 2))
2.5b
(sin (/ (+ x (+ eps x)) 2))
0.6b
(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod
1×pow1/3
Calls
4 calls:
Slowest
4.0ms
(sin (/ (+ x (+ eps x)) 2))
3.0ms
(sin (/ (+ x (+ eps x)) 2))
3.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(cbrt (sin (/ (+ x (+ eps x)) 2)))

series182.0ms

Calls
4 calls:
Slowest
99.0ms
(cbrt (sin (/ (+ x (+ eps x)) 2)))
33.0ms
(sin (/ (+ x (+ eps x)) 2))
29.0ms
(sin (/ (+ x (+ eps x)) 2))
21.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify1.1s

Calls
15 calls:
Slowest
246.0ms
(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
140.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
137.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
108.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
56.0ms
(sin (* 1/2 (+ (* 2 x) eps)))

prune768.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b
(sin (/ (+ x (+ eps x)) 2))
0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))
0.6b
(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×pow1 add-cbrt-cube add-exp-log insert-posit16 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)))

series511.0ms

Calls
4 calls:
Slowest
164.0ms
(cbrt (sin (/ eps 2)))
160.0ms
(cbrt (sin (/ eps 2)))
153.0ms
(cbrt (sin (/ eps 2)))
34.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify953.0ms

Calls
21 calls:
Slowest
252.0ms
(- (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)))))
188.0ms
(- (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)))))
187.0ms
(- (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)))))
131.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
54.0ms
(sin (* 1/2 (+ (* 2 x) eps)))

prune746.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

regimes347.0ms

Accuracy

93.9% (1.0b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 16.2b

bsearch213.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.5s4464×body1280valid
1.7s1853×body640valid
989.0ms617×body2560valid
289.0ms661×body320valid
84.0ms323×body160valid
10.0ms82×body80valid