Details

Time bar (total: 12.8s)

sample149.0ms

Algorithm
intervals
Results
87.0ms98×body1280valid
38.0ms94×body640valid
8.0ms40×body320valid
4.0ms256×pre80true
2.0ms16×body160valid
0.0ms8×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1109
2119
done119

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.8b
(log (- 1.0 x))
5.9b
(log (+ 1.0 x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-sqr-sqrt
16×times-frac
15×pow1 add-cube-cbrt
12×log-pow
9×log-prod
7×add-exp-log
6×log-div
5×add-cbrt-cube
4×associate-/r* associate-/l*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×flip3-- div-sub rem-log-exp flip--
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 75
Calls
3 calls:
7.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms
(log (- 1.0 x))
2.0ms
(log (+ 1.0 x))

series216.0ms

Counts
3 → 9
Calls
3 calls:
126.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
48.0ms
(log (- 1.0 x))
42.0ms
(log (+ 1.0 x))

simplify588.0ms

Counts
84 → 84
Iterations

Useful iterations: done (586.0ms)

IterNodesCost
01921243
14531173
214361093
done50011075

prune225.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 58.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.8b
(log (- 1.0 x))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
83×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
49×*-un-lft-identity
47×add-cube-cbrt
29×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×pow1 div-exp prod-exp add-cbrt-cube
6×pow-to-exp pow-exp
5×log-prod log-pow
4×log-div associate-/l*
3×expm1-log1p-u flip3-- associate-*l* associate-/r* flip-- log1p-expm1-u add-log-exp
2×cbrt-undiv div-sub associate-/r/ cbrt-unprod div-inv
1×frac-2neg associate-*r/ rem-log-exp pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 167
Calls
3 calls:
26.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
9.0ms
(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms
(log (- 1.0 x))

series241.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
143.0ms
(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
48.0ms
(log (- 1.0 x))

simplify1.3s

Counts
176 → 176
Iterations

Useful iterations: 2 (762.0ms)

IterNodesCost
03973124
19602862
230202559
done50012559

prune520.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
158×add-sqr-sqrt
136×associate-*r*
112×unpow-prod-down
94×*-un-lft-identity
82×add-cube-cbrt
51×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
20×prod-exp
19×div-exp
15×add-cbrt-cube
12×pow-to-exp pow-exp
11×pow1
8×distribute-lft-out--
6×associate-*l* associate-/l*
4×log-pow cbrt-unprod difference-of-squares
3×cbrt-undiv expm1-log1p-u associate-/r* log1p-expm1-u div-inv add-log-exp
2×flip3-- associate-*r/ pow-prod-down associate-/r/ *-commutative flip-- associate-/l/
1×frac-2neg div-sub clear-num
Counts
3 → 270
Calls
3 calls:
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
26.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
13.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series228.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
121.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify881.0ms

Counts
279 → 279
Iterations

Useful iterations: 2 (422.0ms)

IterNodesCost
03205262
17794805
223874264
done50014264

prune868.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(cbrt (pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
0.0b
(pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)
0.0b
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
170×times-frac
157×add-sqr-sqrt
139×*-un-lft-identity
104×unpow-prod-down
91×add-cube-cbrt
68×associate-*r*
54×cbrt-prod
48×cube-prod
32×add-exp-log distribute-lft-out--
26×sqr-pow
24×unpow2
23×pow1
17×unswap-sqr
16×log-pow difference-of-squares
14×add-cbrt-cube
11×div-exp
10×prod-exp associate-/r/
8×pow-exp
7×pow-to-exp
6×flip3-- flip-- div-inv associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-*l* associate-/r*
2×cube-div cube-mult unpow3 cbrt-unprod associate-/l/ rem-cube-cbrt
1×cbrt-div pow-pow frac-2neg pow1/3 div-sub associate-*r/ pow-prod-down clear-num *-commutative rem-cbrt-cube
Counts
4 → 294
Calls
4 calls:
25.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
15.0ms
(cbrt (pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
11.0ms
(pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)
13.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
122.0ms
(cbrt (pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
175.0ms
(pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)
130.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.3s

Counts
306 → 306
Iterations

Useful iterations: 2 (712.0ms)

IterNodesCost
043612021
1113511048
2365810123
done500110123

prune874.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01734
11834
done1834

end0.0ms

sample4.5s

Algorithm
intervals
Results
3.0s3430×body1280valid
995.0ms2468×body640valid
255.0ms1275×body320valid
106.0ms8000×pre80true
69.0ms618×body160valid
10.0ms209×body80valid