Details

Time bar (total: 15.2s)

sample129.0ms

Algorithm
intervals
Results
65.0ms66×body10240exit
37.0ms263×body80valid
6.0ms5×body1280valid
5.0ms9×body640valid
2.0ms5×body320valid
1.0ms3×body160valid

simplify30.0ms

Calls
1 calls:
Slowest
29.0ms
(- (log (+ 1 (exp x))) (* x y))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(log (+ 1 (exp x)))
0.0b
(- (log (+ 1 (exp x))) (* x y))
0.0b
(+ 1 (exp x))

rewrite10.0ms

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
6.0ms
(- (log (+ 1 (exp x))) (* x y))
2.0ms
(+ 1 (exp x))
1.0ms
(log (+ 1 (exp x)))

series133.0ms

Calls
3 calls:
Slowest
87.0ms
(log (+ 1 (exp x)))
39.0ms
(- (log (+ 1 (exp x))) (* x y))
6.0ms
(+ 1 (exp x))

simplify512.0ms

Calls
21 calls:
Slowest
72.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
54.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
51.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
49.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
39.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))

prune536.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
0.7b
(cbrt (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))
0.3b
(log (+ 1 (exp x)))
0.3b
(log (+ 1 (exp x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1
12×log-prod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-exp-log
6×add-cbrt-cube
4×log-div associate-*r* associate-*l* log-pow insert-posit16 add-log-exp
3×distribute-rgt-in distribute-lft-in
2×flip3-+ rem-log-exp flip-+
1×cbrt-prod pow2 pow-plus pow1/3 pow3 pow-prod-down prod-exp *-commutative pow-prod-up rem-cbrt-cube cbrt-unprod
Calls
4 calls:
Slowest
17.0ms
(cbrt (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))
13.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
2.0ms
(log (+ 1 (exp x)))
2.0ms
(log (+ 1 (exp x)))

series275.0ms

Calls
4 calls:
Slowest
93.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
68.0ms
(cbrt (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))
63.0ms
(log (+ 1 (exp x)))
51.0ms
(log (+ 1 (exp x)))

simplify1.1s

Calls
44 calls:
Slowest
274.0ms
(+ (* 1/4 (* (log 2) (pow x 2))) (+ (* (log 2) x) (+ (* 1/4 (pow x 2)) (pow (log 2) 2))))
77.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
55.0ms
(* (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))) (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))
48.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
46.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize19.0ms

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)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
24×log-prod
16×*-un-lft-identity
15×sqrt-prod
14×add-sqr-sqrt
13×add-cube-cbrt
8×associate-+r+ sqrt-div
7×pow1
6×log-div associate-+l+ associate--l+ add-exp-log add-log-exp
5×flip3-+ log-pow flip-+
4×add-cbrt-cube insert-posit16
3×pow1/2
2×sum-log rem-log-exp associate-+l- distribute-lft-out
1×+-commutative rem-sqrt-square associate-+r- sub-neg diff-log
Calls
4 calls:
Slowest
24.0ms
(+ (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)))

series301.0ms

Calls
4 calls:
Slowest
97.0ms
(log (sqrt (+ 1 (exp x))))
92.0ms
(log (sqrt (+ 1 (exp x))))
91.0ms
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))
20.0ms
(sqrt (+ 1 (exp x)))

simplify2.4s

Calls
57 calls:
Slowest
395.0ms
(- (+ (* 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))))
336.0ms
(- (+ (* 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))))
241.0ms
(- (+ (* 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))))
227.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
116.0ms
(* (sqrt (+ 1 (exp x))) (exp (- (log (sqrt (+ 1 (exp x)))) (* x y))))

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

7.6b
(log (+ (* (* x x) 1/2) (+ x 2)))
0.0b
(- (log (+ (* (* x x) 1/2) (+ x 2))) (* x y))
0.0b
(* (* x x) 1/2)
0.0b
(+ (* (* x x) 1/2) (+ x 2))

rewrite29.0ms

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
12.0ms
(- (log (+ (* (* x x) 1/2) (+ x 2))) (* x y))
9.0ms
(log (+ (* (* x x) 1/2) (+ x 2)))
5.0ms
(+ (* (* x x) 1/2) (+ x 2))
3.0ms
(* (* x x) 1/2)

series107.0ms

Calls
4 calls:
Slowest
60.0ms
(- (log (+ (* (* x x) 1/2) (+ x 2))) (* x y))
27.0ms
(log (+ (* (* x x) 1/2) (+ x 2)))
10.0ms
(* (* x x) 1/2)
9.0ms
(+ (* (* x x) 1/2) (+ x 2))

simplify2.8s

Calls
25 calls:
Slowest
289.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ -1 x))))
270.0ms
(log (+ (pow (* (* x x) 1/2) 3) (pow (+ x 2) 3)))
267.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ 1 x))))
265.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ 1 x))) (* x y)))
258.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ -1 x))) (* x y)))

prune645.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes116.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.0s2412×body10240exit
792.0ms8367×body80valid
534.0ms138×body1280valid
165.0ms283×body640valid
64.0ms203×body320valid
21.0ms101×body160valid