Details

Time bar (total: 9.3s)

sample150.0ms

Algorithm
intervals
Results
94.0ms111×body1280valid
31.0ms77×body640valid
7.0ms37×body320valid
3.0ms256×pre80true
2.0ms22×body160valid
0.0ms9×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115
done115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.3b
(log (- 1.0 x))
6.5b
(log (+ 1.0 x))

rewrite28.0ms

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:
16.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.0ms
(log (- 1.0 x))
4.0ms
(log (+ 1.0 x))

series216.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
43.0ms
(log (- 1.0 x))
46.0ms
(log (+ 1.0 x))

simplify45.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0452686
11669638
25002623
done5002623

prune216.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.1b

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 x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.3b
(log (- 1.0 x))

rewrite65.0ms

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 associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv flip3-- div-sub flip-- 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 → 165
Calls
3 calls:
36.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
15.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.0ms
(log (- 1.0 x))

series246.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
145.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
44.0ms
(log (- 1.0 x))

simplify87.0ms

Counts
174 → 174
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09281453
138371286
250011286
done50011286

prune495.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

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* add-log-exp
4×expm1-log1p-u log-pow cbrt-unprod log1p-expm1-u difference-of-squares
3×cbrt-undiv associate-/r* div-inv
2×associate-*r/ pow-prod-down *-commutative associate-/l/
1×+-commutative flip3-- fma-def frac-2neg flip3-+ div-sub clear-num sum-log flip-- flip-+
Counts
4 → 282
Calls
4 calls:
8.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
35.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
55.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series357.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
55.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
60.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
132.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify102.0ms

Counts
294 → 294
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08242553
135112263
250022260
done50022260

prune858.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

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

rewrite158.0ms

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 associate-*l* associate-/l*
5×flip3-- flip--
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
1×pow-flip inv-pow
Counts
4 → 389
Calls
4 calls:
36.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
34.0ms
(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
31.0ms
(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
135.0ms
(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
131.0ms
(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify80.0ms

Counts
401 → 401
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010536079
150015411
done50015411

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes48.0ms

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
02519
12519
done2519

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.8s3353×body1280valid
990.0ms2497×body640valid
263.0ms1328×body320valid
96.0ms8000×pre80true
68.0ms625×body160valid
9.0ms197×body80valid