Details

Time bar (total: 20.8s)

sample262.0ms

Algorithm
intervals
Results
144.0ms113×body1280valid
49.0ms66×body640valid
33.0ms18×body2560valid
16.0ms26×body320valid
4.0ms12×body160valid
3.0ms21×body80valid

simplify16.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize38.0ms

Local error

Found 2 expressions with local error:

5.8b
(sin (+ x eps))
1.5b
(- (sin (+ x eps)) (sin x))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube sin-sum add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 26
Calls
2 calls:
Slowest
47.0ms
(- (sin (+ x eps)) (sin x))
18.0ms
(sin (+ x eps))

series96.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
75.0ms
(- (sin (+ x eps)) (sin x))
21.0ms
(sin (+ x eps))

simplify749.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
327.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
253.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
56.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
39.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
14.0ms
(- (sin (+ x eps)) (sin x))

prune299.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

5.6b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite90.0ms

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
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 62
Calls
4 calls:
Slowest
40.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
23.0ms
(cos (/ (+ x (+ eps x)) 2))
16.0ms
(+ x (+ eps x))
11.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(* 2 (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
117.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
43.0ms
(+ x (+ eps x))
41.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.9s

Counts
35 → 74
Calls
35 calls:
Slowest
612.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
448.0ms
(* (* (* 2 2) 2) (* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
367.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
350.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
192.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune643.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize55.0ms

Local error

Found 4 expressions with local error:

5.6b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.3b
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×log-prod associate-*r*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 59
Calls
4 calls:
Slowest
61.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
41.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
41.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
24.0ms
(cos (/ (+ x (+ eps x)) 2))

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
62.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
38.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
26.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.9s

Counts
36 → 71
Calls
36 calls:
Slowest
725.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
370.0ms
(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
289.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
216.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
200.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune930.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize62.0ms

Local error

Found 4 expressions with local error:

5.6b
(cos (/ (+ x (+ eps x)) 2))
5.6b
(cos (/ (+ x (+ eps x)) 2))
0.8b
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
0.8b
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod log-pow
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 sqrt-pow1
6×exp-prod add-exp-log sqrt-prod
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow1/2 rem-log-exp
Counts
4 → 58
Calls
4 calls:
Slowest
74.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
52.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
25.0ms
(cos (/ (+ x (+ eps x)) 2))
24.0ms
(cos (/ (+ x (+ eps x)) 2))

series254.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
88.0ms
(log (sqrt (exp (cos (/ (+ x (+ eps x)) 2)))))
40.0ms
(cos (/ (+ x (+ eps x)) 2))
38.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.1s

Counts
34 → 70
Calls
34 calls:
Slowest
320.0ms
(- (log (sqrt E)) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
316.0ms
(- (log (sqrt E)) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
309.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
283.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
71.0ms
(log (sqrt (exp (cos (* 1/2 (+ (* 2 x) eps))))))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes152.0ms

Accuracy

95.1% (0.7b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 15.0b

bsearch231.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
3.8s3347×body1280valid
1.2s1795×body640valid
1.1s644×body2560valid
265.0ms739×body320valid
164.0ms1100×body80valid
126.0ms375×body160valid