Details

Time bar (total: 24.5s)

sample219.0ms

Algorithm
intervals
Results
122.0ms136×body1280valid
42.0ms68×body640valid
31.0ms16×body2560valid
10.0ms25×body320valid
2.0ms8×body160valid
0.0ms3×body80valid

simplify16.0ms

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

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize30.0ms

Local error

Found 2 expressions with local error:

2.5b
(cos (+ x eps))
0.9b
(- (cos (+ x eps)) (cos x))

rewrite36.0ms

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))
15.0ms
(cos (+ x eps))

series133.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
102.0ms
(- (cos (+ x eps)) (cos x))
30.0ms
(cos (+ x eps))

simplify550.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
203.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
169.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
57.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
16.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune366.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

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

rewrite220.0ms

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
91.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
64.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
41.0ms
(sin (/ (+ x (+ eps x)) 2))
23.0ms
(+ x (+ eps x))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
108.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
42.0ms
(sin (/ (+ x (+ eps x)) 2))
34.0ms
(+ x (+ eps x))

simplify2.9s

Counts
36 → 76
Calls
36 calls:
Slowest
635.0ms
(* (* (* -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)))))
479.0ms
(* (* (* -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)))))
385.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
249.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
237.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))

prune817.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.5b

localize44.0ms

Local error

Found 3 expressions with local error:

2.6b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
0.0b
(* -2 (sin (* eps 1/2)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×*-un-lft-identity associate-*r* add-cube-cbrt
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sin-sum insert-posit16 add-log-exp
2×*-commutative
1×distribute-rgt-in distribute-lft-in unswap-sqr
Counts
3 → 49
Calls
3 calls:
Slowest
54.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
26.0ms
(* -2 (sin (* eps 1/2)))
16.0ms
(sin (+ x (* eps 1/2)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
85.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
46.0ms
(* -2 (sin (* eps 1/2)))
31.0ms
(sin (+ x (* eps 1/2)))

simplify2.6s

Counts
31 → 58
Calls
31 calls:
Slowest
584.0ms
(* (* (* (* -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)))))
509.0ms
(* (* (* (* -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)))))
404.0ms
(- (* 1/24 (pow eps 3)) (+ (* 1/1920 (pow eps 5)) eps))
268.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
188.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))

prune588.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* -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)))
0.1b
(* (cos x) (sin (* eps 1/2)))
0.1b
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

rewrite225.0ms

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
144.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
30.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
30.0ms
(* (sin x) (cos (* eps 1/2)))
19.0ms
(* (cos x) (sin (* eps 1/2)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
161.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
91.0ms
(* (cos x) (sin (* eps 1/2)))
77.0ms
(* (sin x) (cos (* eps 1/2)))

simplify4.4s

Counts
47 → 86
Calls
47 calls:
Slowest
577.0ms
(* (* (* (* -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))))))
419.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
415.0ms
(* (* (* (* -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))))))
375.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))
264.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes205.0ms

Accuracy

0% (0.3b remaining)

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

bsearch8.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.4s4571×body1280valid
1.7s1819×body640valid
1.1s600×body2560valid
352.0ms668×body320valid
73.0ms268×body160valid
10.0ms74×body80valid