Details

Time bar (total: 7.1s)

sample150.0ms

Algorithm
intervals
Results
91.0ms104×body1280valid
37.0ms93×body640valid
6.0ms31×body320valid
4.0ms256×pre80true
2.0ms19×body160valid
0.0ms9×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 61.0b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.9b
(log (+ 1.0 x))
5.9b
(log (- 1.0 x))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×log-div
2×flip3-- div-sub flip--
1×frac-2neg flip3-+ clear-num flip-+ div-inv
Counts
3 → 9
Calls
3 calls:
3.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms
(log (+ 1.0 x))
2.0ms
(log (- 1.0 x))

series216.0ms

Counts
3 → 9
Calls
3 calls:
127.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms
(log (+ 1.0 x))
47.0ms
(log (- 1.0 x))

simplify36.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0345243
11342235
25001217

prune77.0ms

Filtered
18 candidates to 18 candidates (100.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New14418
Fresh000
Picked011
Done000
Total14519

Merged error: 58.6b

Counts
19 → 5

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))))))
5.9b
(log (- 1.0 x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-*r/
6×unpow2 sqr-pow
5×associate-*r*
4×log-div times-frac
3×clear-num
2×flip3-- frac-2neg div-sub associate-/r* flip-- div-inv associate-/l*
1×un-div-inv *-commutative
Counts
3 → 21
Calls
3 calls:
5.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
3.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
2.0ms
(log (- 1.0 x))

series237.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
137.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
46.0ms
(log (- 1.0 x))

simplify39.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0369259
11454243
25001238

prune111.0ms

Filtered
30 candidates to 27 candidates (90.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New29130
Fresh123
Picked101
Done011
Total31435

Merged error: 0.0b

Counts
35 → 4

localize14.0ms

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))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×associate-*r/
12×unpow2 sqr-pow
10×associate-*r*
8×times-frac
5×clear-num
4×associate-/r* associate-/l*
3×frac-2neg div-sub *-commutative div-inv
2×+-commutative fma-def un-div-inv associate-/l/ associate--r+
1×flip3-- flip3-+ flip-- flip-+
Counts
4 → 41
Calls
4 calls:
7.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
5.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
5.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
5.0ms
(/ (- (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))))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
49.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
127.0ms
(/ (- (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))))))

simplify38.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0240277
11012275
25002273

prune180.0ms

Filtered
53 candidates to 44 candidates (83.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New50353
Fresh022
Picked101
Done101
Total52557

Merged error: 0.0b

Counts
57 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (- (log 1.0) (* 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.0b
(- (/ (- (log 1.0) (* 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (* 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)))))))
29.1b
(/ (* 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))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
90×frac-sub
86×associate-/l/
56×associate-/l*
49×associate-*r/
42×unpow2 sqr-pow
39×clear-num
35×associate-*r*
34×frac-2neg
28×times-frac
20×flip3-- flip--
14×associate-/r* div-inv
7×un-div-inv *-commutative
2×div-sub sub-div
1×associate--l- sub-neg distribute-rgt-out-- fma-neg prod-diff
Counts
4 → 138
Calls
4 calls:
5.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
4.0ms
(/ (- (log 1.0) (* 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
18.0ms
(- (/ (- (log 1.0) (* 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (* 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)))))))
7.0ms
(/ (* 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))))))

series566.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
113.0ms
(/ (- (log 1.0) (* 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
264.0ms
(- (/ (- (log 1.0) (* 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (* 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)))))))
137.0ms
(/ (* 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))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
016535436
150025112

prune455.0ms

Filtered
150 candidates to 104 candidates (69.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1482150
Fresh224
Picked011
Done000
Total1505155

Merged error: 0b

Counts
155 → 5

regimes24.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
11824

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.8s3334×body1280valid
1.0s2560×body640valid
245.0ms1236×body320valid
102.0ms8000×pre80true
72.0ms656×body160valid
10.0ms214×body80valid