Details

sample232.0ms

Algorithm

intervals

Results

144.0ms	114×	body	1280	valid
49.0ms	77×	body	640	valid
13.0ms	42×	body	320	valid
6.0ms	256×	pre	80	true
3.0ms	18×	body	160	valid
0.0ms	5×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.6b	(log (+ 1.0 x))
5.6b	(log (- 1.0 x))

rewrite70.0ms

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:

42.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
9.0ms	(log (+ 1.0 x))
13.0ms	(log (- 1.0 x))

series346.0ms

Counts

3 → 9

Calls

3 calls:

207.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
58.0ms	(log (+ 1.0 x))
80.0ms	(log (- 1.0 x))

simplify3.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	192	1243
1	453	1173
2	1322	1093
3	4635	1039
done	5000	1039

prune371.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.8b

localize19.0ms

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))))
5.6b	(log (- 1.0 x))

rewrite26.0ms

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:

17.0ms	(/ (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))

series237.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
79.0ms	(log (- 1.0 x))

simplify2.5s

Counts

59 → 59

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	181	1508
1	423	1463
2	1244	1364
3	4524	1346
done	5000	1343

prune267.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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

rewrite82.0ms

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-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

2 → 156

Calls

2 calls:

47.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
25.0ms	(/ (- (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))))

series186.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
126.0ms	(/ (- (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))))

simplify953.0ms

Counts

162 → 162

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	313	3610
1	693	3382
2	1657	2980
done	5000	2964

prune731.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

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-l` `associate-/r*`
2×	`cube-div` `cube-mult` `unpow3` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `rem-cbrt-cube`

Counts

4 → 284

Calls

4 calls:

72.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
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))))
28.0ms	(cbrt (pow (/ (- (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)))) 3))
40.0ms	(pow (/ (- (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)))) 3)

series560.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 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 -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
154.0ms	(cbrt (pow (/ (- (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)))) 3))
180.0ms	(pow (/ (- (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)))) 3)

simplify1.5s

Counts

296 → 296

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	418	11031
1	1005	10155
2	2706	9237
done	5000	9220

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	33
1	19	33
done	19	33

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.5s	3393×	body	1280	valid
1.5s	2463×	body	640	valid
404.0ms	1297×	body	320	valid
135.0ms	8000×	pre	80	true
100.0ms	630×	body	160	valid
15.0ms	217×	body	80	valid