Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	67×	body	1280	valid
11.0ms	87×	body	10240	exit
5.0ms	48×	body	640	valid
5.0ms	103×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.1b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify1.4s

Counts

73 → 73

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	117	900
1	235	790
2	530	706
3	1717	679
done	5001	678

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.1b	(fma 1/6 (pow x 3) x)
10.8b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

3.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series152.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
81.0ms	(fma 1/6 (pow x 3) x)
28.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify931.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	95	1024
1	177	1003
2	488	909
3	1705	909
done	5000	909

prune202.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (sqrt (exp x)))
0.0b	(/ (sqrt (exp x)) (/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (sqrt (exp x))))
0.1b	(fma 1/6 (pow x 3) x)
10.8b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
156×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
144×	`sqrt-prod`
28×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`associate-/r/`

Counts

4 → 238

Calls

4 calls:

4.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (sqrt (exp x)))
11.0ms	(/ (sqrt (exp x)) (/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (sqrt (exp x))))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (sqrt (exp x)))
46.0ms	(/ (sqrt (exp x)) (/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) (sqrt (exp x))))
81.0ms	(fma 1/6 (pow x 3) x)
29.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify978.0ms

Counts

250 → 250

Iterations

Useful iterations: 2 (401.0ms)

Iter	Nodes	Cost
0	314	8352
1	657	7835
2	2508	7295
done	5000	7295

prune573.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
4.1b	(- 1 (/ 1.0 (exp x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

3.0ms	(/ 1.0 (exp x))
18.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
11.0ms	(- 1 (/ 1.0 (exp x)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ 1.0 (exp x))
51.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
42.0ms	(- 1 (/ 1.0 (exp x)))

simplify3.2s

Counts

154 → 154

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	257	3113
1	536	2570
2	1248	2062
3	4489	1861
done	5001	1861

prune183.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes67.0ms

Accuracy

94.1% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 11.6b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	23	35
done	23	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

401.0ms	2224×	body	1280	valid
308.0ms	2499×	body	10240	exit
188.0ms	1625×	body	640	valid
69.0ms	844×	body	320	valid
63.0ms	2881×	body	80	valid
20.0ms	427×	body	160	valid