Details

Time bar (total: 23.5s)

sample196.0ms

Algorithm
intervals
Results
117.0ms141×body1280valid
38.0ms68×body640valid
20.0ms12×body2560valid
6.0ms18×body320valid
3.0ms12×body160valid
1.0ms5×body80valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(- (cos (+ x eps)) (cos x))

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize31.0ms

Local error

Found 2 expressions with local error:

4.5b
(cos (+ x eps))
0.7b
(- (cos (+ x eps)) (cos x))

rewrite35.0ms

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
Counts
2 → 26
Calls
2 calls:
Slowest
21.0ms
(- (cos (+ x eps)) (cos x))
14.0ms
(cos (+ x eps))

series101.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
75.0ms
(- (cos (+ x eps)) (cos x))
26.0ms
(cos (+ x eps))

simplify554.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
204.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
158.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
59.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
47.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
20.0ms
(- (cos (+ x eps)) (cos x))

prune311.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize54.0ms

Local error

Found 4 expressions with local error:

4.1b
(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))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16
3×sum-log distribute-lft-out
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 64
Calls
4 calls:
Slowest
83.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
57.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
38.0ms
(sin (/ (+ x (+ eps x)) 2))
10.0ms
(+ x (+ eps x))

series294.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
90.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
33.0ms
(sin (/ (+ x (+ eps x)) 2))
30.0ms
(+ x (+ eps x))

simplify3.2s

Counts
36 → 76
Calls
36 calls:
Slowest
725.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
509.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
358.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
349.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
231.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune875.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize41.0ms

Local error

Found 2 expressions with local error:

4.1b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt *-un-lft-identity sin-sum associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×insert-posit16 add-log-exp
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
2 → 30
Calls
2 calls:
Slowest
71.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
16.0ms
(sin (+ x (* eps 1/2)))

series136.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
50.0ms
(sin (+ x (* eps 1/2)))

simplify1.9s

Counts
18 → 36
Calls
18 calls:
Slowest
610.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (sin (+ x (* eps 1/2))) (sin (+ x (* eps 1/2)))) (sin (+ x (* eps 1/2)))))
475.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (sin (+ x (* eps 1/2))) (sin (+ x (* eps 1/2)))) (sin (+ x (* eps 1/2)))))
260.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
166.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
59.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))

prune380.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
0.2b
(* (sin x) (cos (* eps 1/2)))
0.2b
(* (cos x) (sin (* eps 1/2)))
0.1b
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16
3×*-commutative
2×flip3-+ associate-*r/ flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in sin-cos-mult
Counts
4 → 74
Calls
4 calls:
Slowest
101.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
35.0ms
(* (cos x) (sin (* eps 1/2)))
33.0ms
(* (sin x) (cos (* eps 1/2)))
29.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
213.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
139.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
78.0ms
(* (sin x) (cos (* eps 1/2)))
70.0ms
(* (cos x) (sin (* eps 1/2)))

simplify4.6s

Counts
47 → 86
Calls
47 calls:
Slowest
658.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))
474.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))
423.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
412.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))
281.0ms
(+ (* (* (sin x) (cos (* eps 1/2))) (* (sin x) (cos (* eps 1/2)))) (- (* (* (cos x) (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (* (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.3s4478×body1280valid
2.1s1915×body640valid
1.3s613×body2560valid
351.0ms623×body320valid
83.0ms292×body160valid
10.0ms79×body80valid