Details

Time bar (total: 15.9s)

sample112.0ms

Algorithm
intervals
Results
64.0ms83×body10240exit
22.0ms266×body80valid
6.0ms11×body640valid
5.0ms8×body1280valid
1.0ms4×body320valid
1.0ms4×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (log (+ 1 (exp x))) (* x y))

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.4b
(log (+ 1 (exp x)))
0.0b
(- (log (+ 1 (exp x))) (* x y))
0.0b
(+ 1 (exp x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×log-prod
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 log-div add-exp-log add-log-exp
3×flip3-+ add-cbrt-cube associate--l+ flip-+ insert-posit16
2×associate--l-
1×+-commutative sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Calls
3 calls:
Slowest
8.0ms
(- (log (+ 1 (exp x))) (* x y))
2.0ms
(log (+ 1 (exp x)))
1.0ms
(+ 1 (exp x))

series122.0ms

Calls
3 calls:
Slowest
61.0ms
(log (+ 1 (exp x)))
53.0ms
(- (log (+ 1 (exp x))) (* x y))
8.0ms
(+ 1 (exp x))

simplify405.0ms

Calls
21 calls:
Slowest
63.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
44.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
39.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
38.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
32.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))

prune487.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

3.7b
(log (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))))
3.6b
(- (* (exp x) (exp x)) (* 1 (exp x)))
0.5b
(log (+ (exp (+ (+ x x) x)) 1))
0.0b
(* (exp x) (exp x))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
9×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt
7×log-prod
6×add-cbrt-cube add-exp-log add-log-exp
4×log-div insert-posit16
3×associate-*r* associate-*l*
2×flip3-+ rem-log-exp log-pow flip-+
1×pow2 sub-neg pow-plus flip3-- distribute-rgt-out-- diff-log pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod flip-- distribute-lft-out
Calls
4 calls:
Slowest
23.0ms
(log (+ (exp (+ (+ x x) x)) 1))
12.0ms
(log (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))))
12.0ms
(* (exp x) (exp x))
10.0ms
(- (* (exp x) (exp x)) (* 1 (exp x)))

series241.0ms

Calls
4 calls:
Slowest
128.0ms
(log (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))))
63.0ms
(log (+ (exp (+ (+ x x) x)) 1))
28.0ms
(- (* (exp x) (exp x)) (* 1 (exp x)))
22.0ms
(* (exp x) (exp x))

simplify2.3s

Calls
39 calls:
Slowest
455.0ms
(log (- (* (* 1 1) (* 1 1)) (* (- (* (exp x) (exp x)) (* 1 (exp x))) (- (* (exp x) (exp x)) (* 1 (exp x))))))
397.0ms
(log (sqrt (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))))
299.0ms
(log (+ (pow (* 1 1) 3) (pow (- (* (exp x) (exp x)) (* 1 (exp x))) 3)))
121.0ms
(log (+ (pow (exp (+ (+ x x) x)) 3) (pow 1 3)))
111.0ms
(+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))

prune976.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(log (sqrt (+ 1 (exp x))))
1.0b
(log (sqrt (+ 1 (exp x))))
0.0b
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
0.0b
(sqrt (+ 1 (exp x)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
10×add-sqr-sqrt sqrt-div
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×log-div
7×add-log-exp
6×pow1 add-exp-log
5×flip3-+ flip-+
4×associate--l- add-cbrt-cube log-pow insert-posit16
3×pow1/2
2×associate-+r- diff-log rem-log-exp associate-+l-
1×rem-sqrt-square sum-log sub-neg flip3-- associate--l+ flip--
Calls
4 calls:
Slowest
61.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
3.0ms
(log (sqrt (+ 1 (exp x))))
3.0ms
(log (sqrt (+ 1 (exp x))))
2.0ms
(sqrt (+ 1 (exp x)))

series571.0ms

Calls
4 calls:
Slowest
217.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
158.0ms
(log (sqrt (+ 1 (exp x))))
142.0ms
(log (sqrt (+ 1 (exp x))))
53.0ms
(sqrt (+ 1 (exp x)))

simplify1.9s

Calls
43 calls:
Slowest
379.0ms
(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
269.0ms
(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
214.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
188.0ms
(- (+ (* 1/2 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (* 2 (log (sqrt 2))) (/ x (pow (sqrt 2) 2)))) (* 1/2 (/ (pow x 2) (pow (sqrt 2) 4))))
80.0ms
(/ (exp (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x)))))) (exp (* x y)))

prune949.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

8.0b
(log (+ (* (* x x) 1/2) (+ x 2)))
0.0b
(- (log (+ (* (* x x) 1/2) (+ x 2))) (* x y))
0.0b
(+ (* (* x x) 1/2) (+ x 2))
0.0b
(* (* x x) 1/2)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×add-sqr-sqrt log-prod *-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×log-div add-cbrt-cube insert-posit16
3×flip3-+ associate--l+ flip-+
2×associate--l-
1×+-commutative associate-+r+ sum-log sub-neg flip3-- diff-log rem-log-exp associate-*l* log-pow *-commutative flip--
Calls
4 calls:
Slowest
21.0ms
(- (log (+ (* (* x x) 1/2) (+ x 2))) (* x y))
8.0ms
(+ (* (* x x) 1/2) (+ x 2))
5.0ms
(log (+ (* (* x x) 1/2) (+ x 2)))
4.0ms
(* (* x x) 1/2)

series181.0ms

Calls
4 calls:
Slowest
61.0ms
(- (log (+ (* (* x x) 1/2) (+ x 2))) (* x y))
47.0ms
(log (+ (* (* x x) 1/2) (+ x 2)))
45.0ms
(* (* x x) 1/2)
28.0ms
(+ (* (* x x) 1/2) (+ x 2))

simplify2.8s

Calls
25 calls:
Slowest
290.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ 1 x))) (* x y)))
279.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ -1 x))) (* x y)))
270.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ -1 x))))
262.0ms
(log (+ (pow (* (* x x) 1/2) 3) (pow (+ x 2) 3)))
237.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ 1 x))))

prune632.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.1b

regimes63.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch7.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
2.0s2417×body10240exit
857.0ms8443×body80valid
596.0ms277×body640valid
142.0ms128×body1280valid
56.0ms184×body320valid
20.0ms105×body160valid