Details

sample56.0ms

Algorithm

intervals

Results

15.0ms	62×	body	1280	valid
11.0ms	71×	body	10240	exit
7.0ms	48×	body	640	valid
6.0ms	30×	body	320	valid
3.0ms	100×	body	80	valid
1.0ms	16×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.8b	(- (exp x) 1.0)

rewrite50.0ms

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×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 67

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)

series77.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (exp x) (- (exp x) 1.0))
27.0ms	(- (exp x) 1.0)

simplify642.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	897
1	253
0	117

prune255.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

9.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
0.0ms	(fma 1/12 x 1/2)

series73.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
51.0ms	(fma 1/12 x 1/2)

simplify2.3s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
3	3869
2	503
1	115
0	42

prune170.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.8b	(- 1 (/ 1.0 (exp x)))

rewrite74.0ms

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` `clear-num` `frac-2neg` `flip3--` `associate-/r/` `flip--`
1×	`rec-exp` `sub-neg` `diff-log` `1-exp` `pow-flip` `inv-pow`

Counts

3 → 145

Calls

3 calls:

36.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
13.0ms	(/ 1.0 (exp x))
15.0ms	(- 1 (/ 1.0 (exp x)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
24.0ms	(/ 1.0 (exp x))
42.0ms	(- 1 (/ 1.0 (exp x)))

simplify2.2s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	2401
1	609
0	257

prune365.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x 1/12 1/2)
0.2b	(/ 1 (pow x 3))
0.2b	(/ (- (/ 1 x) (fma x 1/12 1/2)) x)
40.3b	(/ (+ (pow (fma x 1/12 1/2) 3) (/ 1 (pow x 3))) (fma (fma x 1/12 1/2) (fma x 1/12 1/2) (/ (- (/ 1 x) (fma x 1/12 1/2)) x)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

83×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
16×	`associate-/l*`
12×	`unpow-prod-down` `cube-prod` `difference-of-squares`
11×	`div-inv`
10×	`add-cbrt-cube`
8×	`div-exp` `distribute-lft-out` `distribute-lft-out--`
4×	`expm1-log1p-u` `cube-mult` `pow1` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow` `associate-/l/`
3×	`pow-to-exp` `cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-exp`
1×	`flip3-+` `flip3--` `div-sub` `flip-+` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

4 → 176

Calls

4 calls:

1.0ms	(fma x 1/12 1/2)
14.0ms	(/ 1 (pow x 3))
48.0ms	(/ (- (/ 1 x) (fma x 1/12 1/2)) x)
139.0ms	(/ (+ (pow (fma x 1/12 1/2) 3) (/ 1 (pow x 3))) (fma (fma x 1/12 1/2) (fma x 1/12 1/2) (/ (- (/ 1 x) (fma x 1/12 1/2)) x)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma x 1/12 1/2)
64.0ms	(/ 1 (pow x 3))
33.0ms	(/ (- (/ 1 x) (fma x 1/12 1/2)) x)
94.0ms	(/ (+ (pow (fma x 1/12 1/2) 3) (/ 1 (pow x 3))) (fma (fma x 1/12 1/2) (fma x 1/12 1/2) (/ (- (/ 1 x) (fma x 1/12 1/2)) x)))

simplify1.4s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	2672
1	574
0	252

prune937.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes98.0ms

Accuracy

96.5% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 21.2b

bsearch1.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2638×	body	10240	exit
705.0ms	2167×	body	1280	valid
374.0ms	1677×	body	640	valid
108.0ms	891×	body	320	valid
95.0ms	2836×	body	80	valid
35.0ms	431×	body	160	valid