Details

Time bar (total: 22.5s)

sample134.0ms

Algorithm
intervals
Results
84.0ms85×body10240exit
25.0ms270×body80valid
5.0ms5×body1280valid
4.0ms6×body640valid
3.0ms8×body320valid
1.0ms5×body160valid

simplify31.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
31.0ms
(- (log (+ 1 (exp x))) (* x y))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×log-prod
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt
4×pow1 log-div associate--l+ add-exp-log
3×flip3-+ add-cbrt-cube flip-+ insert-posit16 distribute-lft-out
2×associate--l-
1×+-commutative sum-log sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Counts
3 → 48
Calls
3 calls:
Slowest
8.0ms
(- (log (+ 1 (exp x))) (* x y))
8.0ms
(+ 1 (exp x))
4.0ms
(log (+ 1 (exp x)))

series163.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
83.0ms
(- (log (+ 1 (exp x))) (* x y))
69.0ms
(log (+ 1 (exp x)))
10.0ms
(+ 1 (exp x))

simplify603.0ms

Counts
25 → 57
Calls
25 calls:
Slowest
76.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
66.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
64.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
62.0ms
(/ (+ 1 (exp x)) (exp (* x y)))
54.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune601.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(log (sqrt (+ 1 (exp x))))
1.2b
(log (sqrt (+ 1 (exp x))))
0.0b
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
0.0b
(+ 1 (exp x))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod *-un-lft-identity
9×add-log-exp
8×add-sqr-sqrt pow1 log-div sqrt-div add-cube-cbrt sqrt-prod
6×add-exp-log log-pow
5×flip3-+ flip-+
4×associate--l- add-cbrt-cube insert-posit16
3×distribute-lft-out
2×associate-+r- sum-log sqrt-pow1 pow1/2 diff-log rem-log-exp associate-+l-
1×+-commutative sub-neg flip3-- associate--l+ flip--
Counts
4 → 74
Calls
4 calls:
Slowest
60.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
5.0ms
(+ 1 (exp x))
4.0ms
(log (sqrt (+ 1 (exp x))))
4.0ms
(log (sqrt (+ 1 (exp x))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
132.0ms
(log (sqrt (+ 1 (exp x))))
126.0ms
(log (sqrt (+ 1 (exp x))))
13.0ms
(+ 1 (exp x))

simplify2.5s

Counts
43 → 86
Calls
43 calls:
Slowest
282.0ms
(/ (* (sqrt (+ 1 (exp x))) (sqrt (+ 1 (exp x)))) (exp (* x y)))
262.0ms
(/ (exp (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x)))))) (exp (* x y)))
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))))
225.0ms
(- (+ (* 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))))
198.0ms
(log (sqrt (+ (pow 1 3) (pow (exp x) 3))))

prune978.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 3 expressions with local error:

6.3b
(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))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
6×log-prod
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 log-div add-exp-log
3×sum-log flip3-+ add-cbrt-cube associate--l+ flip-+ insert-posit16
2×associate--l-
1×+-commutative associate-+r+ sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Counts
3 → 47
Calls
3 calls:
Slowest
30.0ms
(- (log (+ (* x (* x 1/2)) (+ x 2))) (* x y))
26.0ms
(+ (* x (* x 1/2)) (+ x 2))
18.0ms
(log (+ (* x (* x 1/2)) (+ x 2)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
89.0ms
(- (log (+ (* x (* x 1/2)) (+ x 2))) (* x y))
37.0ms
(log (+ (* x (* x 1/2)) (+ x 2)))
30.0ms
(+ (* x (* x 1/2)) (+ x 2))

simplify3.5s

Counts
23 → 56
Calls
23 calls:
Slowest
405.0ms
(* (exp (* x (* x 1/2))) (exp (+ x 2)))
355.0ms
(log (+ (pow (* x (* x 1/2)) 3) (pow (+ x 2) 3)))
328.0ms
(log (+ (pow (* x (* x 1/2)) 3) (pow (+ x 2) 3)))
306.0ms
(- (+ (log 1/2) (* 2 (/ 1 x))) (+ (* 2 (log (/ 1 x))) (* x y)))
285.0ms
(- (+ (log 1/2) (+ (* 2 (/ 1 (pow x 2))) (* 2 (/ 1 x)))) (* 2 (log (/ 1 x))))

prune586.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

6.1b
(sqrt (+ (* x (* x 1/2)) (+ x 2)))
6.1b
(sqrt (+ (* x (* x 1/2)) (+ x 2)))
0.7b
(log (sqrt (+ (* x (* x 1/2)) (+ x 2))))
0.7b
(log (sqrt (+ (* x (* x 1/2)) (+ x 2))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt log-prod sqrt-prod
10×pow1 *-un-lft-identity add-cube-cbrt
8×sqrt-div
6×add-exp-log log-pow
4×log-div sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 flip-+ insert-posit16 add-log-exp
2×rem-sqrt-square rem-log-exp
Counts
4 → 72
Calls
4 calls:
Slowest
60.0ms
(sqrt (+ (* x (* x 1/2)) (+ x 2)))
37.0ms
(sqrt (+ (* x (* x 1/2)) (+ x 2)))
20.0ms
(log (sqrt (+ (* x (* x 1/2)) (+ x 2))))
19.0ms
(log (sqrt (+ (* x (* x 1/2)) (+ x 2))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(log (sqrt (+ (* x (* x 1/2)) (+ x 2))))
222.0ms
(log (sqrt (+ (* x (* x 1/2)) (+ x 2))))
97.0ms
(sqrt (+ (* x (* x 1/2)) (+ x 2)))
91.0ms
(sqrt (+ (* x (* x 1/2)) (+ x 2)))

simplify6.4s

Counts
46 → 84
Calls
46 calls:
Slowest
407.0ms
(log (sqrt (+ (pow (* x (* x 1/2)) 3) (pow (+ x 2) 3))))
389.0ms
(- (+ (/ 1 (* (pow x 2) (pow (sqrt 1/2) 2))) (+ (* 1/2 (/ 1 (* x (pow (sqrt 1/2) 2)))) (log (sqrt 1/2)))) (+ (log (/ 1 x)) (* 1/4 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 4))))))
388.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
369.0ms
(log (sqrt (+ (pow (* x (* x 1/2)) 3) (pow (+ x 2) 3))))
365.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes75.0ms

Accuracy

0% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 0.9b

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.7s2514×body10240exit
829.0ms8413×body80valid
198.0ms250×body640valid
136.0ms126×body1280valid
134.0ms204×body320valid
25.0ms126×body160valid