Details

sample73.0ms

Algorithm

intervals

Results

31.0ms	83×	body	1280	valid
15.0ms	95×	body	10240	exit
8.0ms	44×	body	640	valid
3.0ms	33×	body	320	valid
3.0ms	84×	body	80	valid
1.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.6b	(- (exp x) 1.0)

rewrite44.0ms

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:

19.0ms	(/ (exp x) (- (exp x) 1.0))
23.0ms	(- (exp x) 1.0)

series66.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (exp x) (- (exp x) 1.0))
22.0ms	(- (exp x) 1.0)

simplify704.0ms

Counts

73 → 73

Iterations

Useful iterations: done (701.0ms)

Iter	Nodes	Cost
0	117	900
1	254	793
2	896	708
done	5000	690

prune180.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)))
0.0b	(fma 1/6 (pow x 3) x)
9.3b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite14.0ms

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:

11.0ms	(/ (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))

series214.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
104.0ms	(fma 1/6 (pow x 3) x)
48.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify520.0ms

Counts

58 → 58

Iterations

Useful iterations: done (518.0ms)

Iter	Nodes	Cost
0	95	1024
1	193	1003
2	795	911
done	5000	909

prune200.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

12.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
1.0ms	(fma 1/12 x (/ 1 x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
80.0ms	(fma 1/12 x (/ 1 x))

simplify1.8s

Counts

34 → 34

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	41	329
1	108	314
2	360	286
3	1957	280
done	5000	279

prune125.0ms

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))))
4.7b	(- 1 (/ 1.0 (exp x)))

rewrite106.0ms

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:

13.0ms	(/ 1.0 (exp x))
43.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
37.0ms	(- 1 (/ 1.0 (exp x)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1.0 (exp x))
92.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
52.0ms	(- 1 (/ 1.0 (exp x)))

simplify2.8s

Counts

154 → 154

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	257	3113
1	608	2598
2	2403	2085
done	5000	1772

prune287.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

96.1% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 11.3b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	24	29
done	24	29

end0.0ms

sample2.9s

Algorithm

intervals

Results

782.0ms	2670×	body	10240	exit
737.0ms	2235×	body	1280	valid
564.0ms	855×	body	320	valid
317.0ms	1641×	body	640	valid
202.0ms	2863×	body	80	valid
33.0ms	407×	body	160	valid