Details

Time bar (total: 24.8s)

sample296.0ms

Algorithm
intervals
Results
131.0ms111×body1280valid
61.0ms29×body2560valid
42.0ms55×body640valid
33.0ms9×body160valid
10.0ms20×body320valid
5.0ms32×body80valid

simplify8.0ms

Calls
1 calls:
Slowest
7.0ms
(- (sin (+ x eps)) (sin x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize13.0ms

Local error

Found 2 expressions with local error:

3.4b
(sin (+ x eps))
1.4b
(- (sin (+ x eps)) (sin x))

rewrite70.0ms

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
Calls
2 calls:
Slowest
62.0ms
(- (sin (+ x eps)) (sin x))
7.0ms
(sin (+ x eps))

series80.0ms

Calls
2 calls:
Slowest
48.0ms
(- (sin (+ x eps)) (sin x))
32.0ms
(sin (+ x eps))

simplify823.0ms

Calls
13 calls:
Slowest
445.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
185.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
76.0ms
(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
57.0ms
(/ (exp (sin (+ x eps))) (exp (sin x)))
12.0ms
(+ (sqrt (sin (+ x eps))) (sqrt (sin x)))

prune266.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 3 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.3b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
5×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r* associate-*l* insert-posit16 distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Calls
3 calls:
Slowest
23.0ms
(cos (/ (+ x (+ eps x)) 2))
11.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
10.0ms
(+ x (+ eps x))

series172.0ms

Calls
3 calls:
Slowest
101.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
42.0ms
(+ x (+ eps x))
29.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify1.3s

Calls
23 calls:
Slowest
373.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
269.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
181.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
68.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
57.0ms
(cos (* 1/2 (+ (* 2 x) eps)))

prune583.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize41.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.6b
(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)))

rewrite201.0ms

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
Calls
4 calls:
Slowest
86.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
48.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
37.0ms
(cos (/ (+ x (+ eps x)) 2))
29.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))

series222.0ms

Calls
4 calls:
Slowest
99.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
48.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
41.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
33.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.2s

Calls
36 calls:
Slowest
347.0ms
(* (* (* (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))))
313.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
276.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
171.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
146.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))

prune981.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

3.1b
(cos (/ (+ x (+ eps x)) 2))
0.6b
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
0.3b
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b
(pow E (cos (/ (+ x (+ eps x)) 2)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×add-exp-log
7×pow1 log-prod
6×unpow-prod-down add-cbrt-cube
4×rem-log-exp associate-*l* pow-exp insert-posit16 add-log-exp
3×pow-unpow associate-*r*
2×pow-to-exp e-exp-1 log-pow sqr-pow
1×pow-pow pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
73.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
48.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
27.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
24.0ms
(cos (/ (+ x (+ eps x)) 2))

series312.0ms

Calls
4 calls:
Slowest
120.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
86.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
77.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
28.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify7.5s

Calls
42 calls:
Slowest
1.1s
(log (pow (* (cbrt E) (cbrt E)) (cos (/ (+ x (+ eps x)) 2))))
496.0ms
(log (pow E (/ (cos (/ (+ x (+ eps x)) 2)) 2)))
449.0ms
(log (pow (sqrt E) (cos (/ (+ x (+ eps x)) 2))))
448.0ms
(+ (log (log (pow E (cos (/ (+ x (+ eps x)) 2))))) (log (sin (/ eps 2))))
440.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))

prune817.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes224.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.2b

bsearch220.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
4.1s3252×body1280valid
1.8s1804×body640valid
1.4s653×body2560valid
324.0ms767×body320valid
225.0ms1142×body80valid
105.0ms382×body160valid