Details

Time bar (total: 28.8s)

sample252.0ms

Algorithm
intervals
Results
142.0ms111×body1280valid
53.0ms29×body2560valid
31.0ms55×body640valid
10.0ms20×body320valid
4.0ms32×body80valid
3.0ms9×body160valid

simplify8.0ms

Calls
1 calls:
Slowest
8.0ms
(- (sin (+ x eps)) (sin x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube sin-sum add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
64.0ms
(- (sin (+ x eps)) (sin x))
15.0ms
(sin (+ x eps))

series83.0ms

Calls
2 calls:
Slowest
54.0ms
(- (sin (+ x eps)) (sin x))
29.0ms
(sin (+ x eps))

simplify2.3s

Calls
33 calls:
Slowest
276.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
192.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
187.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
183.0ms
(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
180.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))

prune408.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
6×add-cube-cbrt
5×pow1 add-cbrt-cube add-exp-log
3×expm1-log1p-u sum-log fma-def associate-*r* associate-*l* insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Calls
3 calls:
Slowest
22.0ms
(+ x (+ eps x))
19.0ms
(cos (/ (+ x (+ eps x)) 2))
17.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series166.0ms

Calls
3 calls:
Slowest
102.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
36.0ms
(cos (/ (+ x (+ eps x)) 2))
27.0ms
(+ x (+ eps x))

simplify1.9s

Calls
25 calls:
Slowest
458.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
392.0ms
(cos (* 1/2 (+ (* 2 x) eps)))
382.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
236.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
72.0ms
(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune606.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize28.0ms

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)))

rewrite212.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
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
73.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))
57.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
43.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
37.0ms
(cos (/ (+ x (+ eps x)) 2))

series272.0ms

Calls
4 calls:
Slowest
122.0ms
(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
68.0ms
(exp (cos (/ (+ x (+ eps x)) 2)))
43.0ms
(cos (/ (+ x (+ eps x)) 2))
39.0ms
(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify2.7s

Calls
36 calls:
Slowest
422.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
382.0ms
(* (* (* (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))))
365.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
247.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
236.0ms
(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize52.0ms

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)))

rewrite166.0ms

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×expm1-log1p-u rem-log-exp associate-*l* pow-exp insert-posit16 log1p-expm1-u 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
63.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
42.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
39.0ms
(cos (/ (+ x (+ eps x)) 2))
21.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))

series437.0ms

Calls
4 calls:
Slowest
196.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
111.0ms
(pow E (cos (/ (+ x (+ eps x)) 2)))
101.0ms
(log (pow E (cos (/ (+ x (+ eps x)) 2))))
28.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify7.6s

Calls
42 calls:
Slowest
622.0ms
(log (pow (* (cbrt E) (cbrt E)) (cos (/ (+ x (+ eps x)) 2))))
542.0ms
(* (log (pow E (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
536.0ms
(log (pow (sqrt E) (cos (/ (+ x (+ eps x)) 2))))
488.0ms
(+ (log (log (pow E (cos (/ (+ x (+ eps x)) 2))))) (log (sin (/ eps 2))))
459.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes207.0ms

Accuracy

98.3% (0.3b remaining)

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

bsearch155.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
4.2s3252×body1280valid
2.4s1804×body640valid
1.3s653×body2560valid
352.0ms767×body320valid
210.0ms1142×body80valid
162.0ms382×body160valid