Details

sample70.0ms

Algorithm

intervals

Results

24.0ms	53×	body	1280	valid
13.0ms	137×	body	80	valid
11.0ms	32×	body	640	valid
9.0ms	23×	body	320	valid
2.0ms	11×	body	160	valid

simplify228.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
2.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

29.0ms	(/ (+ x 1) (- x 1))
8.0ms	(/ x (+ x 1))
106.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series223.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (+ x 1) (- x 1))
38.0ms	(/ x (+ x 1))
144.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.8s

Counts

762 → 762

Iterations

Iter	Nodes
done	2000
2	2000
1	1369
0	584

prune2.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ 1 (/ (- x 1) (+ x 1)))
0.0b	(/ (- x 1) (+ x 1))
2.7b	(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

4919×	`times-frac`
4462×	`*-un-lft-identity`
3232×	`add-sqr-sqrt`
2251×	`add-cube-cbrt`
1926×	`prod-diff`
743×	`distribute-lft-out`
484×	`difference-of-squares`
355×	`associate-/r/`
241×	`distribute-lft-out--`
237×	`difference-of-sqr-1`
188×	`div-inv`
168×	`flip3-+` `flip-+`
42×	`associate-/r*`
19×	`add-exp-log`
18×	`fma-neg`
13×	`add-cbrt-cube` `associate-/l*`
9×	`div-exp`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 2232

Calls

4 calls:

20.0ms	(/ x (+ x 1))
31.0ms	(/ 1 (/ (- x 1) (+ x 1)))
16.0ms	(/ (- x 1) (+ x 1))
77.0ms	(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ x (+ x 1))
39.0ms	(/ 1 (/ (- x 1) (+ x 1)))
42.0ms	(/ (- x 1) (+ x 1))
131.0ms	(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))

simplify3.5s

Counts

2244 → 2244

Iterations

Iter	Nodes
done	2000
1	2000
0	1611

prune9.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

13.9b	(/ (+ x 1) (fma x x -1))
13.9b	(/ (- (+ x 1)) (fma x x -1))
28.8b	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
31.8b	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/l*`
12×	`distribute-lft-out`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `neg-mul-1` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv` `distribute-neg-frac`
1×	`neg-sub0` `div-sub` `distribute-frac-neg`

Counts

4 → 128

Calls

4 calls:

29.0ms	(/ (+ x 1) (fma x x -1))
24.0ms	(/ (- (+ x 1)) (fma x x -1))
0.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
0.0ms	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (+ x 1) (fma x x -1))
43.0ms	(/ (- (+ x 1)) (fma x x -1))
177.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
242.0ms	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	2006
3	2006
2	1034
1	394
0	175

prune903.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

28.8b	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
28.8b	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
28.8b	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
31.8b	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

0.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
0.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
0.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
0.0ms	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
152.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
183.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (+ x 1) (/ (- (+ x 1)) (fma x x -1))))
233.0ms	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	2072
4	2072
3	1430
2	367
1	116
0	55

prune651.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch136.0ms

Steps

Iters	Range		Point
10	0.001953933407705698	32640636.358721357	12225.500062890518
7	-16883.399250034305	-988.0224752747107	-11515.964231250555

simplify14.0ms

Iterations

Iter	Nodes
done	47
3	47
2	43
1	35
0	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	1700×	body	1280	valid
462.0ms	1280×	body	640	valid
444.0ms	4072×	body	80	valid
162.0ms	625×	body	320	valid
83.0ms	323×	body	160	valid