Details

Time bar (total: 13.9s)

sample134.0ms

Algorithm
intervals
Results
78.0ms66×body10240exit
29.0ms263×body80valid
6.0ms9×body640valid
6.0ms5×body1280valid
2.0ms5×body320valid
1.0ms3×body160valid

simplify22.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b
(log1p (exp x))
0.0b
(- (log1p (exp x)) (* y x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u fma-neg prod-diff
2×pow1 log1p-udef add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- log1p-expm1 flip--
Calls
2 calls:
Slowest
4.0ms
(- (log1p (exp x)) (* y x))
0.0ms
(log1p (exp x))

series138.0ms

Calls
2 calls:
Slowest
75.0ms
(log1p (exp x))
62.0ms
(- (log1p (exp x)) (* y x))

simplify446.0ms

Calls
17 calls:
Slowest
79.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
78.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
52.0ms
(fma 1 (log1p (exp x)) (- (* x y)))
40.0ms
(- (log (+ (exp x) 1)) (* x y))
35.0ms
(/ (exp (log1p (exp x))) (exp (* y x)))

prune356.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 log-prod
4×log-div fma-neg prod-diff add-exp-log add-log-exp
3×expm1-log1p-u flip3-+ add-cbrt-cube associate--l+ log-pow flip-+ insert-posit16 log1p-expm1-u
2×associate--l-
1×+-commutative sub-neg log1p-def flip3-- diff-log rem-log-exp flip--
Calls
3 calls:
Slowest
11.0ms
(- (log (+ 1 (exp x))) (* x y))
2.0ms
(log (+ 1 (exp x)))
2.0ms
(+ 1 (exp x))

series113.0ms

Calls
3 calls:
Slowest
64.0ms
(log (+ 1 (exp x)))
40.0ms
(- (log (+ 1 (exp x))) (* x y))
9.0ms
(+ 1 (exp x))

simplify699.0ms

Calls
32 calls:
Slowest
82.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
62.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
58.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
54.0ms
(fma (* (cbrt (log (+ 1 (exp x)))) (cbrt (log (+ 1 (exp x))))) (cbrt (log (+ 1 (exp x)))) (- (* y x)))
49.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))

prune611.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

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)))

rewrite36.0ms

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×expm1-log1p-u log-div associate-*r* associate-*l* log-pow insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×log1p-def 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)))

series576.0ms

Calls
4 calls:
Slowest
381.0ms
(log (+ 1 (exp x)))
78.0ms
(log (+ 1 (exp x)))
66.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
51.0ms
(cbrt (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))

simplify1.3s

Calls
46 calls:
Slowest
336.0ms
(+ (* 1/4 (* (log 2) (pow x 2))) (+ (* (log 2) x) (+ (* 1/4 (pow x 2)) (pow (log 2) 2))))
88.0ms
(* (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))) (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))
78.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
73.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
60.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune909.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

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)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×log-prod
18×*-un-lft-identity
17×add-sqr-sqrt
15×add-cube-cbrt sqrt-prod
13×associate-+r+
9×pow1 log-pow
8×sqrt-div
6×log-div associate-+l+ associate--l+ add-exp-log add-log-exp
5×fma-def flip3-+ pow1/2 prod-diff flip-+
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×sum-log rem-log-exp associate-+l- distribute-lft-out
1×+-commutative rem-sqrt-square associate-+r- sub-neg diff-log hypot-1-def
Calls
4 calls:
Slowest
21.0ms
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))
2.0ms
(sqrt (+ 1 (exp x)))
2.0ms
(log (sqrt (+ 1 (exp x))))
2.0ms
(log (sqrt (+ 1 (exp x))))

series281.0ms

Calls
4 calls:
Slowest
111.0ms
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))
82.0ms
(log (sqrt (+ 1 (exp x))))
68.0ms
(log (sqrt (+ 1 (exp x))))
19.0ms
(sqrt (+ 1 (exp x)))

simplify2.4s

Calls
64 calls:
Slowest
348.0ms
(- (+ (* 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))))
276.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
208.0ms
(- (+ (* 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))))
196.0ms
(- (+ (* 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))))
95.0ms
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes148.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.3s2412×body10240exit
872.0ms8367×body80valid
521.0ms138×body1280valid
155.0ms283×body640valid
78.0ms203×body320valid
22.0ms101×body160valid