Details

Time bar (total: 9.7s)

sample52.0ms

Algorithm
intervals
Results
28.0ms67×body10240exit
10.0ms271×body80valid
2.0ms7×body640valid
1.0ms5×body320valid
1.0ms1×body1280valid
0.0ms4×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089
1129
2199
done199

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.5b
(log (+ 1.0 (exp x)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
8×log-prod *-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-div associate--l+
3×pow1 add-exp-log add-log-exp
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Counts
2 → 33
Calls
2 calls:
5.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))

series122.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(- (log (+ 1.0 (exp x))) (* x y))
64.0ms
(log (+ 1.0 (exp x)))

simplify2.3s

Counts
39 → 39
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
083463
1179437
2438415
31247409
44510407
done5000407

prune94.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
0.0b
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
0.0b
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
16×add-log-exp
7×sum-log
4×add-sqr-sqrt add-cube-cbrt associate-+l+ associate-+r+ *-un-lft-identity
3×pow1 add-exp-log sub-neg log-prod diff-log add-cbrt-cube
2×+-commutative distribute-rgt-in distribute-lft-in flip3-+ flip-+
1×flip3-- associate--l+ flip--
Counts
3 → 46
Calls
3 calls:
4.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
66.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
15.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

series453.0ms

Counts
3 → 9
Calls
3 calls:
327.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
69.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
57.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

simplify1.6s

Counts
55 → 55
Iterations

Useful iterations: 3 (410.0ms)

IterNodesCost
0961299
12721211
29691122
343811016
done50001016

prune151.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.5b
(log (+ 1.0 (exp x)))
0.7b
(pow (- (log (+ 1.0 (exp x))) (* x y)) 3)
14.7b
(cbrt (pow (- (log (+ 1.0 (exp x))) (* x y)) 3))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×cbrt-prod add-sqr-sqrt add-cube-cbrt
8×log-prod
6×pow1 add-exp-log unpow-prod-down cube-prod
5×add-cbrt-cube add-log-exp
4×cube-div log-div associate--l+
3×pow-unpow flip3-- flip--
2×associate--l- cube-mult cbrt-div flip3-+ unpow3 flip-+ distribute-lft-out sqr-pow
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log rem-log-exp pow-exp log-pow rem-cbrt-cube rem-cube-cbrt
Counts
4 → 81
Calls
4 calls:
5.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))
4.0ms
(pow (- (log (+ 1.0 (exp x))) (* x y)) 3)
4.0ms
(cbrt (pow (- (log (+ 1.0 (exp x))) (* x y)) 3))

series309.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (log (+ 1.0 (exp x))) (* x y))
61.0ms
(log (+ 1.0 (exp x)))
128.0ms
(pow (- (log (+ 1.0 (exp x))) (* x y)) 3)
60.0ms
(cbrt (pow (- (log (+ 1.0 (exp x))) (* x y)) 3))

simplify446.0ms

Counts
93 → 93
Iterations

Useful iterations: done (444.0ms)

IterNodesCost
01551610
13631365
211771255
done50011241

prune217.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (log 2.0) 2)
1.0b
(pow (log 2.0) 2)
1.0b
(pow (log 2.0) 3)
8.0b
(cbrt (+ (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))) (+ (pow (log 2.0) 3) (* 1.5 (* (pow (log 2.0) 2) x)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
11×pow1
9×pow-unpow
7×add-exp-log
6×cbrt-div
5×flip3-+ add-cbrt-cube flip-+
4×cube-prod associate-*r/ frac-add log-pow add-log-exp
3×cbrt-prod pow-to-exp pow-pow pow-exp sqr-pow
2×unpow2
1×cube-mult pow1/3 unpow3 rem-cube-cbrt
Counts
4 → 80
Calls
4 calls:
2.0ms
(pow (log 2.0) 2)
1.0ms
(pow (log 2.0) 2)
1.0ms
(pow (log 2.0) 3)
38.0ms
(cbrt (+ (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))) (+ (pow (log 2.0) 3) (* 1.5 (* (pow (log 2.0) 2) x)))))

series620.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(pow (log 2.0) 2)
0.0ms
(pow (log 2.0) 2)
0.0ms
(pow (log 2.0) 3)
620.0ms
(cbrt (+ (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))) (+ (pow (log 2.0) 3) (* 1.5 (* (pow (log 2.0) 2) x)))))

simplify1.1s

Counts
86 → 86
Iterations

Useful iterations: 2 (301.0ms)

IterNodesCost
01892179
15871928
228131798
done50011798

prune260.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes81.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1109
done109

end0.0ms

sample1.7s

Algorithm
intervals
Results
999.0ms2440×body10240exit
313.0ms8379×body80valid
73.0ms271×body640valid
50.0ms100×body1280valid
30.0ms190×body320valid
12.0ms123×body160valid