Details

Time bar (total: 28.7s)

sample108.0ms

Algorithm
intervals
Results
51.0ms71×body10240exit
36.0ms266×body80valid
3.0ms11×body320valid
3.0ms5×body1280valid
2.0ms5×body640valid
1.0ms6×body160valid

simplify21.0ms

Calls
1 calls:
Slowest
21.0ms
(- (log (+ 1 (exp x))) (* x y))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×log-prod
4×add-sqr-sqrt log-div *-un-lft-identity add-cube-cbrt
3×pow1 associate--l+ add-exp-log add-log-exp
2×associate--l- flip3-+ add-cbrt-cube flip-+ insert-posit16
1×sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Calls
2 calls:
Slowest
10.0ms
(- (log (+ 1 (exp x))) (* x y))
2.0ms
(log (+ 1 (exp x)))

series104.0ms

Calls
2 calls:
Slowest
61.0ms
(log (+ 1 (exp x)))
43.0ms
(- (log (+ 1 (exp x))) (* x y))

simplify340.0ms

Calls
18 calls:
Slowest
42.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
37.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
37.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
33.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
29.0ms
(- (log (+ (exp x) 1)) (* x y))

prune356.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

1.7b
(log (sqrt (+ 1 (exp x))))
1.7b
(log (sqrt (+ 1 (exp x))))
0.0b
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
8×log-div sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×sqrt-prod add-log-exp
5×pow1 add-exp-log
4×associate--l- flip3-+ log-pow flip-+
3×add-cbrt-cube insert-posit16
2×associate-+r- pow1/2 diff-log rem-log-exp associate-+l-
1×sum-log sub-neg flip3-- associate--l+ flip--
Calls
3 calls:
Slowest
35.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
2.0ms
(log (sqrt (+ 1 (exp x))))
1.0ms
(log (sqrt (+ 1 (exp x))))

series244.0ms

Calls
3 calls:
Slowest
91.0ms
(log (sqrt (+ 1 (exp x))))
80.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
72.0ms
(log (sqrt (+ 1 (exp x))))

simplify1.5s

Calls
34 calls:
Slowest
298.0ms
(- (+ (* 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))))
280.0ms
(- (+ (* 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))))
225.0ms
(- (+ (* 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))))
99.0ms
(/ (exp (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x)))))) (exp (* x y)))
48.0ms
(log (sqrt (+ (pow 1 3) (pow (exp x) 3))))

prune653.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

15.1b
(/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
1.0b
(log (+ 1 (exp x)))
1.0b
(log (+ 1 (exp x)))
1.0b
(log (+ 1 (exp x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
28×*-un-lft-identity
24×times-frac
20×add-cube-cbrt
12×difference-of-squares
9×log-prod add-exp-log
8×associate-/l*
7×pow1
6×log-div add-cbrt-cube
4×difference-cubes unpow-prod-down flip3-+ cube-prod flip-+ insert-posit16 distribute-lft-out-- add-log-exp
3×associate-/r* rem-log-exp log-pow
2×associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp div-inv flip--
Calls
4 calls:
Slowest
46.0ms
(/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
2.0ms
(log (+ 1 (exp x)))
1.0ms
(log (+ 1 (exp x)))
1.0ms
(log (+ 1 (exp x)))

series314.0ms

Calls
4 calls:
Slowest
137.0ms
(/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
69.0ms
(log (+ 1 (exp x)))
54.0ms
(log (+ 1 (exp x)))
53.0ms
(log (+ 1 (exp x)))

simplify16.8s

Calls
94 calls:
Slowest
642.0ms
(- (* (pow (log (+ 1 (exp x))) 3) (pow (log (+ 1 (exp x))) 3)) (* (pow (* x y) 3) (pow (* x y) 3)))
580.0ms
(/ (* (* (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (* (* (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))))
484.0ms
(/ (sqrt (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (* (cbrt (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))) (cbrt (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))))
481.0ms
(/ (sqrt (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
469.0ms
(/ (sqrt (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (sqrt (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ (log 2) (* x (+ (* x 1/8) 1/2))) (* x y))
0.0b
(+ (log 2) (* x (+ (* x 1/8) 1/2)))
0.0b
(* x (+ (* x 1/8) 1/2))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×pow1 add-cbrt-cube associate-*r* add-exp-log insert-posit16
2×distribute-rgt-in associate-+r+ sum-log distribute-lft-in flip3-+ diff-log associate-*r/ flip-+
1×+-commutative sub-neg flip3-- associate--l+ *-commutative flip--
Calls
3 calls:
Slowest
27.0ms
(- (+ (log 2) (* x (+ (* x 1/8) 1/2))) (* x y))
8.0ms
(+ (log 2) (* x (+ (* x 1/8) 1/2)))
6.0ms
(* x (+ (* x 1/8) 1/2))

series79.0ms

Calls
3 calls:
Slowest
35.0ms
(* x (+ (* x 1/8) 1/2))
26.0ms
(- (+ (log 2) (* x (+ (* x 1/8) 1/2))) (* x y))
17.0ms
(+ (log 2) (* x (+ (* x 1/8) 1/2)))

simplify1.5s

Calls
22 calls:
Slowest
290.0ms
(+ (* (* x 1/8) (* x 1/8)) (- (* 1/2 1/2) (* (* x 1/8) 1/2)))
243.0ms
(/ (exp (+ (log 2) (* x (+ (* x 1/8) 1/2)))) (exp (* x y)))
211.0ms
(/ (* 2 (exp (* x (+ (* x 1/8) 1/2)))) (exp (* x y)))
198.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
123.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))

prune519.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes98.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 1.0b

bsearch3.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.4s2427×body10240exit
994.0ms8356×body80valid
521.0ms123×body1280valid
169.0ms251×body640valid
64.0ms189×body320valid
23.0ms115×body160valid