Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	65×	body	1280	valid
8.0ms	83×	body	10240	exit
6.0ms	60×	body	640	valid
2.0ms	88×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	16×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
5.2b	(- (exp x) 1.0)

rewrite35.0ms

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:

21.0ms	(/ (exp x) (- (exp x) 1.0))
12.0ms	(- (exp x) 1.0)

series42.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify2.2s

Counts

73 → 73

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	117	900
1	239	790
2	511	706
3	1486	679
done	5001	650

prune140.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (fma x (* x (fma x 1/6 1/2)) x))
0.0b	(fma x (* x (fma x 1/6 1/2)) x)
0.1b	(* x (fma x 1/6 1/2))
0.1b	(fma x 1/6 1/2)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/ (exp x) (fma x (* x (fma x 1/6 1/2)) x))
0.0ms	(fma x (* x (fma x 1/6 1/2)) x)
7.0ms	(* x (fma x 1/6 1/2))
0.0ms	(fma x 1/6 1/2)

series170.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (exp x) (fma x (* x (fma x 1/6 1/2)) x))
32.0ms	(fma x (* x (fma x 1/6 1/2)) x)
58.0ms	(* x (fma x 1/6 1/2))
32.0ms	(fma x 1/6 1/2)

simplify883.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	128	1105
1	244	1076
2	612	964
3	1836	964
done	5002	964

prune193.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/12 x (/ 1 x))

series47.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(fma 1/12 x (/ 1 x))

simplify3.0s

Counts

13 → 13

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	16	108
1	21	105
2	44	93
3	145	93
4	446	93
5	1793	93
done	5001	93

prune28.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
5.2b	(- 1 (/ 1.0 (exp x)))

rewrite68.0ms

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:

6.0ms	(/ 1.0 (exp x))
32.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
21.0ms	(- 1 (/ 1.0 (exp x)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1.0 (exp x))
47.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
36.0ms	(- 1 (/ 1.0 (exp x)))

simplify3.1s

Counts

154 → 154

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	257	3113
1	540	2570
2	1217	2026
3	4025	1756
done	5000	1755

prune167.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
done	9	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

370.0ms	2241×	body	1280	valid
262.0ms	2552×	body	10240	exit
169.0ms	1643×	body	640	valid
57.0ms	2880×	body	80	valid
55.0ms	834×	body	320	valid
17.0ms	402×	body	160	valid