Details

sample154.0ms

Algorithm

intervals

Results

100.0ms	116×	body	1280	valid
27.0ms	68×	body	640	valid
7.0ms	39×	body	320	valid
3.0ms	256×	pre	80	true
3.0ms	27×	body	160	valid
0.0ms	6×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5
done	11	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.9b	(log (+ 1.0 x))
8.0b	(log (- 1.0 x))

rewrite31.0ms

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:

17.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms	(log (+ 1.0 x))
7.0ms	(log (- 1.0 x))

series210.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (+ 1.0 x))
46.0ms	(log (- 1.0 x))

simplify44.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	452	686
1	1669	638
2	5001	623
done	5001	623

prune224.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.8b

localize14.0ms

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))))))
8.0b	(log (- 1.0 x))

rewrite70.0ms

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:

39.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
16.0ms	(/ (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))

series238.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
135.0ms	(/ (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))

simplify92.0ms

Counts

174 → 174

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	928	1453
1	3837	1286
2	5001	1286
done	5001	1286

prune500.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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) (+ (* 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))))))

rewrite155.0ms

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×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`

Counts

3 → 268

Calls

3 calls:

39.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
39.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
60.0ms	(/ (- (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))))))

series233.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
56.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
126.0ms	(/ (- (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))))))

simplify91.0ms

Counts

277 → 277

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	753	2429
1	3174	2138
2	5001	2135
done	5001	2135

prune778.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.0b	(sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.1b	(/ (sqrt (- (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))))))
0.1b	(* (sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (sqrt (- (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)))))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
65×	`sqrt-prod`
58×	`times-frac`
42×	`add-cube-cbrt`
31×	`associate-r`
20×	`distribute-lft-out--`
18×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div` `log-pow` `difference-of-squares`
9×	`associate-l` `associate-/l*`
6×	`unswap-sqr`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 161

Calls

4 calls:

39.0ms	(sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
39.0ms	(sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
44.0ms	(/ (sqrt (- (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))))))
128.0ms	(* (sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (sqrt (- (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)))))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
122.0ms	(sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
299.0ms	(/ (sqrt (- (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))))))
127.0ms	(* (sqrt (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (sqrt (- (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)))))))

simplify89.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	617	4395
1	2584	4013
2	5001	3896
done	5001	3896

prune538.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.4b 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)

Iter	Nodes	Cost
0	18	16
1	18	16
done	18	16

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	3413×	body	1280	valid
1.0s	2556×	body	640	valid
232.0ms	1207×	body	320	valid
99.0ms	8000×	pre	80	true
66.0ms	616×	body	160	valid
9.0ms	208×	body	80	valid