Details

Time bar (total: 14.1s)

sample106.0ms

Algorithm
intervals
Results
55.0ms66×body10240exit
21.0ms267×body80valid
4.0ms4×body1280valid
2.0ms4×body640valid
1.0ms3×body320valid
1.0ms4×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1129
2199
done199

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.0b
(+ 1.0 (exp x))
0.3b
(log (+ 1.0 (exp x)))

rewrite54.0ms

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 add-exp-log log-div associate--l+
3×flip3-+ add-cbrt-cube flip-+ distribute-lft-out
2×associate--l-
1×+-commutative sub-neg flip3-- diff-log rem-log-exp sum-log log-pow flip--
Counts
3 → 45
Calls
3 calls:
25.0ms
(- (log (+ 1.0 (exp x))) (* x y))
13.0ms
(+ 1.0 (exp x))
14.0ms
(log (+ 1.0 (exp x)))

series179.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(- (log (+ 1.0 (exp x))) (* x y))
9.0ms
(+ 1.0 (exp x))
99.0ms
(log (+ 1.0 (exp x)))

simplify2.5s

Counts
54 → 54
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
092575
1208544
2499514
31201508
42613506
done5000506

prune206.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b
(* 1/2 (pow x 2))
0.0b
(+ (* 1/2 (pow x 2)) (+ x 2.0))
4.9b
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×add-exp-log add-log-exp
9×add-cube-cbrt *-un-lft-identity
8×associate-*r*
6×log-prod add-cbrt-cube
5×pow1
4×unpow-prod-down log-div unswap-sqr
3×flip3-+ associate-*l* prod-exp associate--l+ sum-log flip-+
2×associate--l- unpow2 sqr-pow
1×+-commutative pow-to-exp sub-neg associate-+r+ flip3-- diff-log rem-log-exp pow-exp log-pow *-commutative flip-- cbrt-unprod
Counts
4 → 71
Calls
4 calls:
28.0ms
(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
25.0ms
(* 1/2 (pow x 2))
41.0ms
(+ (* 1/2 (pow x 2)) (+ x 2.0))
49.0ms
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
28.0ms
(* 1/2 (pow x 2))
36.0ms
(+ (* 1/2 (pow x 2)) (+ x 2.0))
83.0ms
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify2.6s

Counts
83 → 83
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01521207
13721091
210061009
33541985
done5001982

prune300.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow x 2) (pow 2.0 2))
0.0b
(* x (+ (* x 0.25) 0.5))
0.0b
(+ (log 2.0) (* (/ (pow x 2) (pow 2.0 2)) -1/2))
4.0b
(+ (* x (+ (* x 0.25) 0.5)) (+ (log 2.0) (* (/ (pow x 2) (pow 2.0 2)) -1/2)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
54×unpow-prod-down
45×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
18×add-exp-log unpow2 sqr-pow
9×div-exp add-log-exp
8×associate-/r* add-cbrt-cube associate-/l*
7×flip3-+ flip-+
6×pow1 pow-to-exp associate-*r/ pow-exp
5×associate-+l+
4×frac-add sum-log
3×log-prod associate-*r* associate-*l*
2×+-commutative distribute-rgt-in distribute-lft-in
1×cbrt-undiv associate-+r+ frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 155
Calls
4 calls:
23.0ms
(/ (pow x 2) (pow 2.0 2))
50.0ms
(* x (+ (* x 0.25) 0.5))
18.0ms
(+ (log 2.0) (* (/ (pow x 2) (pow 2.0 2)) -1/2))
47.0ms
(+ (* x (+ (* x 0.25) 0.5)) (+ (log 2.0) (* (/ (pow x 2) (pow 2.0 2)) -1/2)))

series643.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ (pow x 2) (pow 2.0 2))
105.0ms
(* x (+ (* x 0.25) 0.5))
413.0ms
(+ (log 2.0) (* (/ (pow x 2) (pow 2.0 2)) -1/2))
66.0ms
(+ (* x (+ (* x 0.25) 0.5)) (+ (log 2.0) (* (/ (pow x 2) (pow 2.0 2)) -1/2)))

simplify1.2s

Counts
167 → 167
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02762925
16422618
222752247
done50022236

prune603.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.7b
(pow (- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y)) 3)
4.9b
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
11.8b
(cbrt (pow (- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y)) 3))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×add-log-exp
6×pow1 add-exp-log unpow-prod-down cube-prod
5×add-cbrt-cube
4×cube-div
3×pow-unpow log-prod sum-log
2×cube-mult log-div cbrt-div flip3-- flip3-+ unpow3 flip-- flip-+ sqr-pow
1×+-commutative pow-to-exp associate-+r+ pow-pow pow1/3 rem-log-exp pow-exp log-pow rem-cbrt-cube rem-cube-cbrt
Counts
4 → 75
Calls
4 calls:
28.0ms
(+ (* 1/2 (pow x 2)) (+ x 2.0))
20.0ms
(pow (- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y)) 3)
27.0ms
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
9.0ms
(cbrt (pow (- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y)) 3))

series416.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* 1/2 (pow x 2)) (+ x 2.0))
252.0ms
(pow (- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y)) 3)
52.0ms
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
84.0ms
(cbrt (pow (- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y)) 3))

simplify1.1s

Counts
87 → 87
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01812150
14861907
215641701
done50001658

prune246.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1109
done109

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.9s2465×body10240exit
646.0ms8447×body80valid
84.0ms134×body1280valid
82.0ms225×body640valid
42.0ms186×body320valid
13.0ms100×body160valid