Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	75×	body	1280	valid
8.0ms	75×	body	10240	exit
6.0ms	54×	body	640	valid
2.0ms	89×	body	80	valid
1.0ms	18×	body	320	valid
1.0ms	20×	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: 41.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
4.9b	(- (exp x) 1.0)

rewrite15.0ms

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)

series43.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify3.6s

Counts

73 → 73

Iterations

Useful iterations: 3 (462.0ms)

Iter	Nodes	Cost
0	117	900
1	250	790
2	807	697
3	4495	679
done	5000	679

prune145.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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))

series48.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

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

simplify1.4s

Counts

13 → 13

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	16	108
1	21	105
2	47	93
3	123	93
4	389	93
5	1524	93
done	5000	93

prune30.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
4.9b	(- 1 (/ 1.0 (exp x)))

rewrite35.0ms

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))
16.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
10.0ms	(- 1 (/ 1.0 (exp x)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(/ 1.0 (exp x))
47.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
37.0ms	(- 1 (/ 1.0 (exp x)))

simplify1.1s

Counts

154 → 154

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	257	3113
1	571	2650
2	1776	2026
done	5000	2020

prune185.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma 1/12 x (/ 1 x)))
0.1b	(fma 1/12 x (/ 1 x))
0.1b	(fma 1/12 x (/ 1 x))
0.2b	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (fma 1/12 x (/ 1 x)))
0.0ms	(fma 1/12 x (/ 1 x))
0.0ms	(fma 1/12 x (/ 1 x))
7.0ms	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

series171.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (fma 1/12 x (/ 1 x)))
48.0ms	(fma 1/12 x (/ 1 x))
43.0ms	(fma 1/12 x (/ 1 x))
48.0ms	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

simplify2.8s

Counts

98 → 98

Iterations

Useful iterations: 3 (406.0ms)

Iter	Nodes	Cost
0	80	1388
1	150	930
2	546	827
3	3244	790
done	5000	790

prune158.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

96.2% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 21.7b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

397.0ms	2294×	body	1280	valid
281.0ms	2571×	body	10240	exit
173.0ms	1611×	body	640	valid
58.0ms	2923×	body	80	valid
55.0ms	789×	body	320	valid
17.0ms	383×	body	160	valid