Details

sample250.0ms

Algorithm

intervals

Results

144.0ms	99×	body	1280	valid
60.0ms	85×	body	640	valid
14.0ms	38×	body	320	valid
6.0ms	256×	pre	80	true
5.0ms	25×	body	160	valid
1.0ms	9×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.1b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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:

30.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
8.0ms	(log (+ 1.0 x))
11.0ms	(log (- 1.0 x))

series745.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
59.0ms	(log (+ 1.0 x))
455.0ms	(log (- 1.0 x))

simplify3.2s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.5s)

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

prune363.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 58.2b

localize26.0ms

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

rewrite27.0ms

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:

18.0ms	(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
6.0ms	(log (- 1.0 x))

series271.0ms

Counts

2 → 6

Calls

2 calls:

199.0ms	(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
71.0ms	(log (- 1.0 x))

simplify2.7s

Counts

59 → 59

Iterations

Useful iterations: done (2.7s)

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

prune283.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite119.0ms

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:

57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
53.0ms	(/ (- (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))))

series240.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
167.0ms	(/ (- (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

162 → 162

Iterations

Useful iterations: done (1.2s)

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

prune747.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

56.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
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))))))
24.0ms	(/ (- (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))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
207.0ms	(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)))))
276.0ms	(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))))))
172.0ms	(/ (- (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

190 → 190

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	351	4568
1	770	4308
2	1832	3776
done	5001	3747

prune793.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes93.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	18	32
done	18	32

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.3s	3432×	body	1280	valid
1.4s	2508×	body	640	valid
317.0ms	1191×	body	320	valid
129.0ms	8000×	pre	80	true
98.0ms	655×	body	160	valid
14.0ms	214×	body	80	valid