Details

Time bar (total: 12.3s)

sample154.0ms

Algorithm
intervals
Results
96.0ms110×body1280valid
36.0ms93×body640valid
6.0ms32×body320valid
4.0ms256×pre80true
2.0ms19×body160valid
0.0ms2×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: 62.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.5b
(log (- 1.0 x))
4.6b
(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:
11.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms
(log (- 1.0 x))
2.0ms
(log (+ 1.0 x))

series212.0ms

Counts
3 → 9
Calls
3 calls:
123.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
47.0ms
(log (- 1.0 x))
42.0ms
(log (+ 1.0 x))

simplify575.0ms

Counts
84 → 84
Iterations

Useful iterations: done (573.0ms)

IterNodesCost
01921243
14531173
214361093
done50001075

prune213.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 60.4b

localize17.0ms

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)))))
4.5b
(log (- 1.0 x))

rewrite46.0ms

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))

series240.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
140.0ms
(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
49.0ms
(log (- 1.0 x))

simplify959.0ms

Counts
176 → 176
Iterations

Useful iterations: 2 (506.0ms)

IterNodesCost
03973124
19602862
230152559
done50012559

prune710.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

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)))))

rewrite84.0ms

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)))
15.0ms
(/ (- (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)))))

series232.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
124.0ms
(/ (- (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)))))

simplify772.0ms

Counts
279 → 279
Iterations

Useful iterations: 2 (387.0ms)

IterNodesCost
03205262
17794805
223874264
done50014264

prune864.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 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
(/ 1 (/ (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b
(/ (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
322×times-frac
248×add-sqr-sqrt
196×*-un-lft-identity
148×add-cube-cbrt
136×associate-*r*
112×unpow-prod-down
63×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
32×distribute-lft-out--
30×associate-/r*
26×div-exp
25×pow1
21×add-cbrt-cube
20×prod-exp
16×log-pow difference-of-squares
12×pow-to-exp pow-exp
11×associate-/r/
8×div-inv
6×cbrt-undiv flip3-- associate-*l* flip-- associate-/l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp associate-*r/ pow-prod-down clear-num *-commutative associate-/l/
1×pow-flip div-sub inv-pow
Counts
4 → 392
Calls
4 calls:
26.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
13.0ms
(/ 1 (/ (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
12.0ms
(/ (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
127.0ms
(/ 1 (/ (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
121.0ms
(/ (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify1.1s

Counts
404 → 404
Iterations

Useful iterations: 2 (637.0ms)

IterNodesCost
045711972
1109511129
2318310204
done500110204

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01431
11531
done1531

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.8s3349×body1280valid
1.0s2528×body640valid
253.0ms1277×body320valid
101.0ms8000×pre80true
68.0ms619×body160valid
12.0ms227×body80valid