Details

Time bar (total: 18.7s)

sample227.0ms

Algorithm
intervals
Results
142.0ms108×body1280valid
46.0ms76×body640valid
13.0ms43×body320valid
5.0ms256×pre80true
3.0ms19×body160valid
1.0ms10×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.0b
(log (- 1.0 x))
6.1b
(log (+ 1.0 x))

rewrite62.0ms

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:
45.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.0ms
(log (- 1.0 x))
6.0ms
(log (+ 1.0 x))

series306.0ms

Counts
3 → 9
Calls
3 calls:
153.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
70.0ms
(log (- 1.0 x))
83.0ms
(log (+ 1.0 x))

simplify3.4s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01921243
14531173
213211093
346501039
done50001039

prune361.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 59.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
6.0b
(log (- 1.0 x))

rewrite31.0ms

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:
23.0ms
(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
7.0ms
(log (- 1.0 x))

series229.0ms

Counts
2 → 6
Calls
2 calls:
175.0ms
(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
54.0ms
(log (- 1.0 x))

simplify2.3s

Counts
59 → 59
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01811508
14231463
212441364
345241346
done50001343

prune326.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 1 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
20×add-sqr-sqrt
18×times-frac
12×add-cube-cbrt
8×distribute-lft-out--
6×associate-/l*
5×pow1
4×log-pow difference-of-squares
3×add-exp-log associate-/r* add-cbrt-cube
2×associate-/l/
1×cbrt-undiv expm1-log1p-u flip3-- frac-2neg div-sub div-exp clear-num flip-- log1p-expm1-u div-inv add-log-exp
Counts
1 → 44
Calls
1 calls:
42.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

series181.0ms

Counts
1 → 3
Calls
1 calls:
181.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

simplify1.2s

Counts
47 → 47
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01002108
12242075
25971948
321631945
done50021943

prune250.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0)))))
0.0b
(log1p (expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))))
0.0b
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
22×add-sqr-sqrt
18×times-frac
14×add-cube-cbrt
8×distribute-lft-out--
7×pow1
6×associate-/l*
5×add-exp-log add-cbrt-cube
4×log-pow log1p-expm1-u difference-of-squares
3×expm1-log1p-u associate-/r* add-log-exp
2×associate-/l/
1×cbrt-undiv log1p-udef expm1-log1p flip3-- frac-2neg div-sub log1p-expm1 div-exp clear-num flip-- div-inv expm1-udef
Counts
3 → 66
Calls
3 calls:
0.0ms
(expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0)))))
0.0ms
(log1p (expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))))
51.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

series642.0ms

Counts
3 → 9
Calls
3 calls:
190.0ms
(expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0)))))
282.0ms
(log1p (expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))))
169.0ms
(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

simplify1.7s

Counts
75 → 75
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01383066
13013001
27762744
326662728
done50002722

prune379.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

0% (0.4b 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
11832
done1832

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.3s3379×body1280valid
1.5s2514×body640valid
391.0ms1262×body320valid
248.0ms8000×pre80true
101.0ms629×body160valid
15.0ms216×body80valid