Details

Time bar (total: 14.8s)

sample208.0ms

Algorithm
intervals
Results
121.0ms103×body1280valid
50.0ms85×body640valid
13.0ms45×body320valid
5.0ms256×pre80true
3.0ms18×body160valid
0.0ms5×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.7b
(log (- 1.0 x))
5.8b
(log (+ 1.0 x))

rewrite54.0ms

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:
23.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
20.0ms
(log (- 1.0 x))
7.0ms
(log (+ 1.0 x))

series224.0ms

Counts
3 → 9
Calls
3 calls:
124.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
48.0ms
(log (- 1.0 x))
52.0ms
(log (+ 1.0 x))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01921243
14601173
218241095
done50001070

prune235.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
5.7b
(log (- 1.0 x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt times-frac
7×pow1
5×add-exp-log log-prod log-pow
4×log-div add-cbrt-cube associate-/l*
3×associate-/r*
2×expm1-log1p-u flip3-- div-sub flip-- log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp rem-log-exp clear-num div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 53
Calls
2 calls:
17.0ms
(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
6.0ms
(log (- 1.0 x))

series190.0ms

Counts
2 → 6
Calls
2 calls:
138.0ms
(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
52.0ms
(log (- 1.0 x))

simplify732.0ms

Counts
59 → 59
Iterations

Useful iterations: done (730.0ms)

IterNodesCost
01811508
14291463
216451366
done50011361

prune281.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 2 expressions with local error:

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 (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
98×times-frac
89×add-sqr-sqrt
68×associate-*r*
59×*-un-lft-identity
56×unpow-prod-down
47×add-cube-cbrt
27×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×div-exp prod-exp
9×add-cbrt-cube
8×pow1 distribute-lft-out--
6×pow-to-exp pow-exp associate-/l*
4×log-pow difference-of-squares
3×associate-*l* associate-/r*
2×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num *-commutative flip--
Counts
2 → 156
Calls
2 calls:
49.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
39.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

series232.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
163.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

simplify1.7s

Counts
162 → 162
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03133610
18233382
237322980
done50012976

prune677.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
242×times-frac
179×add-sqr-sqrt
161×*-un-lft-identity
113×add-cube-cbrt
68×associate-*r*
56×unpow-prod-down
39×add-exp-log
32×distribute-lft-out--
30×associate-/r*
24×unpow2 sqr-pow
22×pow1
17×div-exp unswap-sqr
16×log-pow difference-of-squares
15×add-cbrt-cube
11×associate-/r/
10×prod-exp
7×div-inv
6×pow-to-exp pow-exp associate-/l*
5×cbrt-undiv flip3-- flip--
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num cbrt-unprod
1×pow-flip associate-*r/ pow-prod-down *-commutative inv-pow
Counts
3 → 277
Calls
3 calls:
58.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
28.0ms
(/ 1 (/ (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
24.0ms
(/ (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series348.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
134.0ms
(/ 1 (/ (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
144.0ms
(/ (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))) (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify760.0ms

Counts
286 → 286
Iterations

Useful iterations: done (743.0ms)

IterNodesCost
044910075
111969438
done50008847

prune987.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes86.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01732
12032
done2032

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.0s3302×body1280valid
1.6s2624×body640valid
379.0ms1248×body320valid
338.0ms215×body80valid
147.0ms611×body160valid
130.0ms8000×pre80true