Details

sample89.0ms

Algorithm

intervals

Results

24.0ms	108×	body	10240	exit
20.0ms	70×	body	1280	valid
15.0ms	94×	body	80	valid
11.0ms	54×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	11×	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: 40.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.1b	(- (exp x) 1.0)

rewrite65.0ms

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:

37.0ms	(/ (exp x) (- (exp x) 1.0))
24.0ms	(- (exp x) 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (exp x) (- (exp x) 1.0))
44.0ms	(- (exp x) 1.0)

simplify3.2s

Counts

73 → 73

Iterations

Useful iterations: done (3.2s)

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

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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))

rewrite10.0ms

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:

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

series85.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
64.0ms	(fma 1/12 x (/ 1 x))

simplify1.1s

Counts

34 → 34

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	41	329
1	92	303
2	256	286
3	1199	280
done	5001	279

prune115.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
3.0b	(- 1 (/ 1.0 (exp x)))

rewrite78.0ms

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:

10.0ms	(/ 1.0 (exp x))
43.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
19.0ms	(- 1 (/ 1.0 (exp x)))

series125.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1.0 (exp x))
70.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify5.5s

Counts

154 → 154

Iterations

Useful iterations: done (5.5s)

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

prune264.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 1 (sqrt (/ 1.0 (exp x)))))
0.0b	(/ 1.0 (exp x))
0.0b	(/ 1.0 (exp x))
2.6b	(- 1 (sqrt (/ 1.0 (exp x))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
87×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
62×	`times-frac`
48×	`prod-diff` `sqrt-prod`
11×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`distribute-lft-out`
6×	`div-inv` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `frac-2neg` `fma-neg` `clear-num`
2×	`associate-/r/` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `flip3-+` `diff-log` `1-exp` `flip--` `flip-+` `inv-pow`

Counts

4 → 174

Calls

4 calls:

37.0ms	(/ 1 (+ 1 (sqrt (/ 1.0 (exp x)))))
10.0ms	(/ 1.0 (exp x))
13.0ms	(/ 1.0 (exp x))
46.0ms	(- 1 (sqrt (/ 1.0 (exp x))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ 1 (+ 1 (sqrt (/ 1.0 (exp x)))))
19.0ms	(/ 1.0 (exp x))
27.0ms	(/ 1.0 (exp x))
80.0ms	(- 1 (sqrt (/ 1.0 (exp x))))

simplify3.8s

Counts

186 → 186

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	300	3956
1	596	3111
2	1236	2592
3	3886	2475
done	5000	2471

prune541.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

96.1% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 21.6b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2611×	body	10240	exit
679.0ms	2244×	body	1280	valid
347.0ms	1654×	body	640	valid
106.0ms	2886×	body	80	valid
96.0ms	770×	body	320	valid
35.0ms	447×	body	160	valid