Details

Time bar (total: 16.1s)

sample131.0ms

Algorithm
intervals
Results
79.0ms81×body10240exit
25.0ms270×body80valid
7.0ms11×body640valid
5.0ms5×body1280valid
2.0ms6×body320valid

simplify33.0ms

Calls
1 calls:
Slowest
33.0ms
(- (log (+ 1 (exp x))) (* x y))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.7b
(log (+ 1 (exp x)))
0.0b
(+ 1 (exp x))
0.0b
(- (log (+ 1 (exp x))) (* x y))

rewrite31.0ms

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
26.0ms
(- (log (+ 1 (exp x))) (* x y))
2.0ms
(log (+ 1 (exp x)))
2.0ms
(+ 1 (exp x))

series98.0ms

Calls
3 calls:
Slowest
46.0ms
(- (log (+ 1 (exp x))) (* x y))
46.0ms
(log (+ 1 (exp x)))
6.0ms
(+ 1 (exp x))

simplify834.0ms

Calls
32 calls:
Slowest
82.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
76.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
71.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
47.0ms
(fma 1 (log (+ 1 (exp x))) (- (* y x)))
43.0ms
(fma (* (cbrt (log (+ 1 (exp x)))) (cbrt (log (+ 1 (exp x))))) (cbrt (log (+ 1 (exp x)))) (- (* y x)))

prune642.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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)))))
0.7b
(log (+ 1 (exp x)))
0.7b
(log (+ 1 (exp x)))

rewrite23.0ms

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
11.0ms
(cbrt (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))
6.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
2.0ms
(log (+ 1 (exp x)))
2.0ms
(log (+ 1 (exp x)))

series297.0ms

Calls
4 calls:
Slowest
78.0ms
(log (+ 1 (exp x)))
74.0ms
(log (+ 1 (exp x)))
73.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
72.0ms
(cbrt (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))

simplify1.2s

Calls
46 calls:
Slowest
269.0ms
(+ (* 1/4 (* (log 2) (pow x 2))) (+ (* (log 2) x) (+ (* 1/4 (pow x 2)) (pow (log 2) 2))))
111.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
111.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
83.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
57.0ms
(* (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))) (* (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (log (+ 1 (exp x)))))

prune987.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b
(log (sqrt (+ 1 (exp x))))
1.4b
(log (sqrt (+ 1 (exp x))))
0.0b
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))
0.0b
(- (log (sqrt (+ 1 (exp x)))) (* x y))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
30×log-prod
21×*-un-lft-identity
18×add-sqr-sqrt add-cube-cbrt
15×sqrt-prod
13×associate-+r+ log-pow
12×associate--l+
11×pow1
10×prod-diff
8×log-div sqrt-div
7×add-log-exp
6×associate-+l+ pow1/2 add-exp-log
5×fma-def flip3-+ fma-neg flip-+
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×associate--l- sum-log sub-neg diff-log rem-log-exp associate-+l- distribute-lft-out
1×+-commutative associate-+r- flip3-- flip--
Calls
4 calls:
Slowest
14.0ms
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))
11.0ms
(- (log (sqrt (+ 1 (exp x)))) (* x y))
2.0ms
(log (sqrt (+ 1 (exp x))))
2.0ms
(log (sqrt (+ 1 (exp x))))

series341.0ms

Calls
4 calls:
Slowest
96.0ms
(+ (log (sqrt (+ 1 (exp x)))) (- (log (sqrt (+ 1 (exp x)))) (* x y)))
94.0ms
(log (sqrt (+ 1 (exp x))))
86.0ms
(- (log (sqrt (+ 1 (exp x)))) (* x y))
65.0ms
(log (sqrt (+ 1 (exp x))))

simplify2.8s

Calls
79 calls:
Slowest
347.0ms
(- (+ (* 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))))
189.0ms
(- (+ (* 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))))
187.0ms
(- (+ (* 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))))
187.0ms
(- (+ (* 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))))
120.0ms
(* (sqrt (+ 1 (exp x))) (exp (- (log (sqrt (+ 1 (exp x)))) (* x y))))

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 2 expressions with local error:

6.3b
(log (fma (fma x 1/2 1) x 2))
0.0b
(- (log (fma (fma x 1/2 1) x 2)) (* x y))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt log-prod *-un-lft-identity add-cube-cbrt
5×pow1
4×fma-neg prod-diff
3×associate--l+ add-exp-log log-pow add-log-exp
2×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log rem-log-exp flip--
Calls
2 calls:
Slowest
12.0ms
(- (log (fma (fma x 1/2 1) x 2)) (* x y))
2.0ms
(log (fma (fma x 1/2 1) x 2))

series90.0ms

Calls
2 calls:
Slowest
46.0ms
(log (fma (fma x 1/2 1) x 2))
43.0ms
(- (log (fma (fma x 1/2 1) x 2)) (* x y))

simplify2.2s

Calls
24 calls:
Slowest
459.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ 1 x))) (* x y)))
359.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ 1 x))))
303.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ -1 x))) (* x y)))
280.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ -1 x))))
100.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune431.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes93.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.7s2446×body10240exit
1.1s8435×body80valid
150.0ms150×body1280valid
133.0ms235×body640valid
109.0ms187×body320valid
22.0ms98×body160valid