Details

Time bar (total: 25.3s)

sample278.0ms

Algorithm
intervals
Results
171.0ms109×body1280valid
40.0ms56×body640valid
33.0ms16×body2560valid
11.0ms21×body320valid
7.0ms43×body80valid
3.0ms11×body160valid

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(- (sin (+ x eps)) (sin x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize22.0ms

Local error

Found 2 expressions with local error:

2.1b
(sin (+ x eps))
1.8b
(- (sin (+ x eps)) (sin x))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity sin-sum add-log-exp
2×pow1 +-commutative add-cbrt-cube associate--l+ add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-sin flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
51.0ms
(- (sin (+ x eps)) (sin x))
9.0ms
(sin (+ x eps))

series91.0ms

Calls
2 calls:
Slowest
70.0ms
(- (sin (+ x eps)) (sin x))
21.0ms
(sin (+ x eps))

simplify908.0ms

Calls
15 calls:
Slowest
456.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
231.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
77.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
30.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
21.0ms
(- (sin (+ x eps)) (sin x))

prune332.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (* (cos eps) (sin x)) (sin x))
0.1b
(* (cos eps) (sin x))
0.1b
(* (sin eps) (cos x))
0.1b
(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
19×add-sqr-sqrt
12×associate-*l*
11×add-log-exp
10×add-cube-cbrt
9×associate-*r*
8×pow1 add-cbrt-cube add-exp-log
6×distribute-lft-out distribute-lft-out--
4×distribute-rgt-out-- insert-posit16
3×sin-cos-mult unswap-sqr
2×associate-+r+ sum-log sub-neg flip3-- diff-log pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-- difference-of-squares
1×+-commutative associate-+r- flip3-+ flip-+
Calls
4 calls:
Slowest
111.0ms
(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
45.0ms
(- (* (cos eps) (sin x)) (sin x))
13.0ms
(* (cos eps) (sin x))
11.0ms
(* (sin eps) (cos x))

series439.0ms

Calls
4 calls:
Slowest
208.0ms
(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
92.0ms
(- (* (cos eps) (sin x)) (sin x))
75.0ms
(* (cos eps) (sin x))
64.0ms
(* (sin eps) (cos x))

simplify3.9s

Calls
63 calls:
Slowest
381.0ms
(* (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos x) (cos x)) (cos x)))
364.0ms
(* (exp (* (sin eps) (cos x))) (exp (- (* (cos eps) (sin x)) (sin x))))
363.0ms
(* (* (* (cos eps) (cos eps)) (cos eps)) (* (* (sin x) (sin x)) (sin x)))
362.0ms
(* (exp (* (sin eps) (cos x))) (/ (exp (* (cos eps) (sin x))) (exp (sin x))))
281.0ms
(+ (* (+ (sin (- eps x)) (sin (+ eps x))) (+ (* (* (cos eps) (sin x)) (* (cos eps) (sin x))) (+ (* (sin x) (sin x)) (* (* (cos eps) (sin x)) (sin x))))) (* 2 (- (pow (* (cos eps) (sin x)) 3) (pow (sin x) 3))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (cos eps) 1)
0.1b
(* (sin x) (- (cos eps) 1))
0.1b
(* (sin eps) (cos x))
0.1b
(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt
10×associate-*r* associate-*l*
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
5×sub-neg
4×distribute-rgt-in associate-+r+ distribute-lft-in associate-*r/ insert-posit16 distribute-lft-out difference-of-squares
3×flip3-- sin-cos-mult flip--
2×difference-of-sqr-1 pow-prod-down frac-add prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
1×+-commutative sum-log flip3-+ diff-log flip-+
Calls
4 calls:
Slowest
71.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
25.0ms
(* (sin x) (- (cos eps) 1))
22.0ms
(* (sin eps) (cos x))
7.0ms
(- (cos eps) 1)

series350.0ms

Calls
4 calls:
Slowest
159.0ms
(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
81.0ms
(* (sin eps) (cos x))
70.0ms
(* (sin x) (- (cos eps) 1))
39.0ms
(- (cos eps) 1)

simplify3.6s

Calls
63 calls:
Slowest
495.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (- (cos eps) 1) (- (cos eps) 1)) (- (cos eps) 1)))
416.0ms
(- (* 1/24 (pow eps 4)) (+ (* 1/2 (pow eps 2)) (* 1/720 (pow eps 6))))
358.0ms
(* (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos x) (cos x)) (cos x)))
290.0ms
(* (exp (* (sin eps) (cos x))) (exp (* (sin x) (- (cos eps) 1))))
203.0ms
(- eps (+ (* 1/6 (pow eps 3)) (* 1/2 (* (pow x 2) eps))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

2.9b
(log (exp (- (cos eps) 1)))
2.9b
(- (cos eps) 1)
0.1b
(exp (- (cos eps) 1))
0.1b
(* (sin eps) (cos x))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×*-un-lft-identity
14×exp-prod
9×add-cube-cbrt add-log-exp
8×log-pow
7×pow1 add-exp-log
6×add-cbrt-cube difference-of-squares
5×log-prod
4×exp-sum insert-posit16
3×sub-neg difference-of-sqr-1 associate-*r* associate-*l* distribute-lft-out--
2×exp-diff diff-log rem-log-exp rem-exp-log
1×log-div flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod sin-cos-mult flip-- unswap-sqr
Calls
4 calls:
Slowest
30.0ms
(exp (- (cos eps) 1))
17.0ms
(log (exp (- (cos eps) 1)))
12.0ms
(- (cos eps) 1)
11.0ms
(* (sin eps) (cos x))

series168.0ms

Calls
4 calls:
Slowest
64.0ms
(exp (- (cos eps) 1))
49.0ms
(* (sin eps) (cos x))
33.0ms
(- (cos eps) 1)
22.0ms
(log (exp (- (cos eps) 1)))

simplify2.2s

Calls
57 calls:
Slowest
461.0ms
(- (* 1/24 (pow eps 4)) (+ (* 1/2 (pow eps 2)) (* 1/720 (pow eps 6))))
388.0ms
(- (* 1/24 (pow eps 4)) (+ (* 1/2 (pow eps 2)) (* 1/720 (pow eps 6))))
324.0ms
(* (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos x) (cos x)) (cos x)))
187.0ms
(- eps (+ (* 1/6 (pow eps 3)) (* 1/2 (* (pow x 2) eps))))
153.0ms
(- (+ (* 1/6 (pow eps 4)) 1) (* 1/2 (pow eps 2)))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch5.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
4.4s3388×body1280valid
1.4s606×body2560valid
1.4s1801×body640valid
358.0ms743×body320valid
191.0ms348×body160valid
149.0ms1114×body80valid