Details

sample87.0ms

Algorithm

intervals

Results

19.0ms	25×	body	320	valid
19.0ms	85×	body	10240	exit
18.0ms	59×	body	1280	valid
14.0ms	67×	body	640	valid
4.0ms	90×	body	80	valid
1.0ms	15×	body	160	valid

simplify5.0ms

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: 42.3b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

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:

39.0ms	(/ (exp x) (- (exp x) 1.0))
13.0ms	(- (exp x) 1.0)

series88.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (exp x) (- (exp x) 1.0))
27.0ms	(- (exp x) 1.0)

simplify3.1s

Counts

73 → 73

Iterations

Useful iterations: done (3.0s)

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

prune180.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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))

series66.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

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

simplify4.4s

Counts

13 → 13

Iterations

Useful iterations: 2 (7.0ms)

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

prune64.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.7b	(- 1 (/ 1.0 (exp x)))

rewrite101.0ms

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:

49.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
7.0ms	(/ 1.0 (exp x))
39.0ms	(- 1 (/ 1.0 (exp x)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
25.0ms	(/ 1.0 (exp x))
47.0ms	(- 1 (/ 1.0 (exp x)))

simplify4.7s

Counts

154 → 154

Iterations

Useful iterations: 3 (2.9s)

Iter	Nodes	Cost
0	257	3113
1	540	2570
2	1217	2026
3	4012	1756
done	5000	1756

prune271.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1.0 x (* (pow x 2) (- (* 0.16666666666666666 x) 0.5)))
0.0b	(/ 1 (fma 1.0 x (* (pow x 2) (- (* 0.16666666666666666 x) 0.5))))
0.1b	(* (pow x 2) (- (* 0.16666666666666666 x) 0.5))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
9×	`times-frac`
8×	`associate-l`
7×	`add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow1` `unpow-prod-down` `unswap-sqr`
3×	`expm1-log1p-u` `associate-r` `prod-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`sub-neg` `associate-*r/` `div-exp` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `1-exp` `pow-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `inv-pow`

Counts

3 → 84

Calls

3 calls:

1.0ms	(fma 1.0 x (* (pow x 2) (- (* 0.16666666666666666 x) 0.5)))
11.0ms	(/ 1 (fma 1.0 x (* (pow x 2) (- (* 0.16666666666666666 x) 0.5))))
42.0ms	(* (pow x 2) (- (* 0.16666666666666666 x) 0.5))

series250.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma 1.0 x (* (pow x 2) (- (* 0.16666666666666666 x) 0.5)))
61.0ms	(/ 1 (fma 1.0 x (* (pow x 2) (- (* 0.16666666666666666 x) 0.5))))
132.0ms	(* (pow x 2) (- (* 0.16666666666666666 x) 0.5))

simplify4.0s

Counts

93 → 93

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	177	1621
1	351	1483
2	911	1317
3	3669	1245
done	5001	1191

prune253.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

93.4% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 7.8b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	39
1	30	39
done	30	39

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	2186×	body	1280	valid
788.0ms	2464×	body	10240	exit
312.0ms	1693×	body	640	valid
110.0ms	839×	body	320	valid
102.0ms	2870×	body	80	valid
32.0ms	414×	body	160	valid