Details

sample235.0ms

Algorithm

intervals

Results

132.0ms	95×	body	1280	valid
59.0ms	92×	body	640	valid
14.0ms	44×	body	320	valid
6.0ms	256×	pre	80	true
3.0ms	18×	body	160	valid
1.0ms	7×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.9b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.5b	(log (- 1.0 x))
5.7b	(log (+ 1.0 x))

rewrite27.0ms

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` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

13.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms	(log (- 1.0 x))
6.0ms	(log (+ 1.0 x))

series252.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
56.0ms	(log (- 1.0 x))
52.0ms	(log (+ 1.0 x))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	191	1243
1	457	1174
2	1839	1096
done	5000	1069

prune386.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
5.5b	(log (- 1.0 x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`times-frac` `add-cube-cbrt`
7×	`pow1`
5×	`log-prod` `add-exp-log` `log-pow`
4×	`log-div` `add-cbrt-cube` `associate-/l*`
3×	`associate-/r*`
2×	`expm1-log1p-u` `flip3--` `div-sub` `log1p-expm1-u` `flip--` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 53

Calls

2 calls:

21.0ms	(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
5.0ms	(log (- 1.0 x))

series248.0ms

Counts

2 → 6

Calls

2 calls:

193.0ms	(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
56.0ms	(log (- 1.0 x))

simplify811.0ms

Counts

59 → 59

Iterations

Useful iterations: done (808.0ms)

Iter	Nodes	Cost
0	180	1508
1	427	1463
2	1641	1365
done	5000	1362

prune451.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

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 (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
89×	`add-sqr-sqrt`
68×	`associate-r`
59×	`*-un-lft-identity`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
27×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`div-exp` `prod-exp`
9×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
4×	`log-pow` `difference-of-squares`
3×	`associate-/r` `associate-l*`
2×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

2 → 156

Calls

2 calls:

31.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
36.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

series232.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
152.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

simplify1.8s

Counts

162 → 162

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	313	3610
1	825	3377
2	3718	2983
done	5002	2978

prune839.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(cbrt (pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) 3))
0.0b	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
0.0b	(pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) 3)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

170×	`times-frac`
157×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
100×	`unpow-prod-down`
91×	`add-cube-cbrt`
68×	`associate-r`
50×	`cbrt-prod`
44×	`cube-prod`
32×	`add-exp-log` `distribute-lft-out--`
26×	`sqr-pow`
24×	`unpow2`
23×	`pow1`
17×	`unswap-sqr`
16×	`log-pow` `difference-of-squares`
14×	`add-cbrt-cube`
11×	`div-exp`
10×	`prod-exp`
8×	`pow-exp`
7×	`pow-to-exp`
6×	`div-inv` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-l*`
2×	`cube-div` `cube-mult` `unpow3` `cbrt-unprod` `rem-cube-cbrt` `associate-/l/`
1×	`cbrt-div` `clear-num` `pow-pow` `frac-2neg` `flip3--` `pow1/3` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `rem-cbrt-cube` `flip--`

Counts

4 → 284

Calls

4 calls:

49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
13.0ms	(cbrt (pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) 3))
18.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
14.0ms	(pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) 3)

series596.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
158.0ms	(cbrt (pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) 3))
142.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
212.0ms	(pow (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) 3)

simplify613.0ms

Counts

296 → 296

Iterations

Useful iterations: done (597.0ms)

Iter	Nodes	Cost
0	418	11031
1	1258	10212
done	5001	9396

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes42.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	20	35
1	21	35
done	21	35

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.7s	3451×	body	1280	valid
1.7s	2454×	body	640	valid
512.0ms	8000×	pre	80	true
397.0ms	1269×	body	320	valid
109.0ms	615×	body	160	valid
17.0ms	211×	body	80	valid