Details

Time bar (total: 14.1s)

sample151.0ms

Algorithm
intervals
Results
96.0ms108×body1280valid
34.0ms85×body640valid
6.0ms30×body320valid
3.0ms256×pre80true
2.0ms22×body160valid
1.0ms11×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: 60.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.4b
(log (+ 1.0 x))
5.5b
(log (- 1.0 x))

rewrite15.0ms

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:
8.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms
(log (+ 1.0 x))
3.0ms
(log (- 1.0 x))

series216.0ms

Counts
3 → 9
Calls
3 calls:
129.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
40.0ms
(log (+ 1.0 x))
47.0ms
(log (- 1.0 x))

simplify482.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (132.0ms)

IterNodesCost
01921243
14581173
217061093
done50011093

prune236.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 57.4b

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)))))
5.5b
(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))

series238.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
141.0ms
(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
46.0ms
(log (- 1.0 x))

simplify1.7s

Counts
176 → 176
Iterations

Useful iterations: 2 (390.0ms)

IterNodesCost
03973124
19702862
242562559
done50012559

prune519.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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)))))

rewrite82.0ms

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:
25.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
28.0ms
(* 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)))))

series230.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
125.0ms
(/ (- (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)))))

simplify1.7s

Counts
279 → 279
Iterations

Useful iterations: 2 (314.0ms)

IterNodesCost
03205262
17834805
234624264
done50004264

prune872.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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
(log1p (expm1 (/ (- (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)))))))
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)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
159×add-sqr-sqrt
136×associate-*r*
112×unpow-prod-down
95×*-un-lft-identity
83×add-cube-cbrt
52×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
20×prod-exp
19×div-exp
16×add-cbrt-cube
12×pow1 pow-to-exp pow-exp
8×distribute-lft-out--
6×associate-*l* associate-/l*
4×expm1-log1p-u log-pow cbrt-unprod log1p-expm1-u add-log-exp difference-of-squares
3×cbrt-undiv associate-/r* div-inv
2×flip3-- associate-*r/ pow-prod-down associate-/r/ *-commutative flip-- associate-/l/
1×log1p-udef frac-2neg div-sub log1p-expm1 clear-num
Counts
4 → 281
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)))
0.0ms
(log1p (expm1 (/ (- (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)))))))
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)))))

series486.0ms

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)))
255.0ms
(log1p (expm1 (/ (- (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)))))))
127.0ms
(/ (- (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)))))

simplify1.5s

Counts
293 → 293
Iterations

Useful iterations: 2 (331.0ms)

IterNodesCost
03315753
17965268
234604531
done50014531

prune964.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes42.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01633
11733
done1733

end0.0ms

sample4.5s

Algorithm
intervals
Results
3.0s3536×body1280valid
943.0ms2396×body640valid
244.0ms1238×body320valid
98.0ms8000×pre80true
67.0ms587×body160valid
12.0ms243×body80valid