Details

sample62.0ms

Algorithm

intervals

Results

21.0ms	48×	body	1280	valid
12.0ms	131×	body	80	valid
11.0ms	34×	body	640	valid
8.0ms	28×	body	320	valid
2.0ms	15×	body	160	valid

simplify137.0ms

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: 29.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
4.4b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite157.0ms

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:

16.0ms	(/ x (+ x 1))
42.0ms	(/ (+ x 1) (- x 1))
64.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ x (+ x 1))
35.0ms	(/ (+ x 1) (- x 1))
87.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.6s

Counts

762 → 762

Iterations

Iter	Nodes
done	2001
2	2001
1	1369
0	584

prune8.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
0.1b	(* (/ 1 (- x 1)) (+ x 1))
29.5b	(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
32.3b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
54×	`associate-l`
52×	`*-un-lft-identity`
46×	`times-frac`
28×	`add-cube-cbrt`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`difference-of-squares`
8×	`pow1` `associate-r` `prod-exp`
6×	`difference-of-sqr-1` `distribute-lft-out--` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 140

Calls

4 calls:

26.0ms	(* (/ 1 (- x 1)) (+ x 1))
32.0ms	(* (/ 1 (- x 1)) (+ x 1))
0.0ms	(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ 1 (- x 1)) (+ x 1))
35.0ms	(* (/ 1 (- x 1)) (+ x 1))
86.0ms	(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
123.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify1.1s

Counts

152 → 152

Iterations

Iter	Nodes
done	2020
3	2020
2	1445
1	534
0	157

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

14.1b	(/ (+ x 1) (fma x x -1))
14.1b	(/ (+ x 1) (fma x x -1))
29.8b	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (- (+ x 1)) (/ (+ x 1) (fma x x -1))))
32.3b	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `associate-/l*`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `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`

Counts

4 → 94

Calls

4 calls:

23.0ms	(/ (+ x 1) (fma x x -1))
23.0ms	(/ (+ 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)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (+ x 1) (fma x x -1))
37.0ms	(/ (+ x 1) (fma x x -1))
136.0ms	(fma (/ x (fma x (* x x) 1)) (- (fma x x 1) x) (* (- (+ x 1)) (/ (+ x 1) (fma x x -1))))
209.0ms	(fma (- (+ x 1)) (/ (+ x 1) (fma x x -1)) (* (/ (+ x 1) (fma x x -1)) (+ x 1)))

simplify937.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	2002
3	2002
2	703
1	248
0	111

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
14.6b	(/ (fma x x -1) (* (- x 1) (- x 1)))
29.5b	(fma x (/ 1 (+ x 1)) (- (/ (fma x x -1) (* (- x 1) (- x 1)))))
32.3b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`associate-l`
26×	`times-frac`
18×	`add-exp-log` `add-cube-cbrt`
14×	`add-cbrt-cube`
10×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`frac-times` `pow1` `difference-of-squares`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `associate-r` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `difference-of-sqr-1` `associate-l/` `cbrt-unprod` `associate-/l` `distribute-lft-out--` `unswap-sqr`
2×	`flip3-+` `flip-+` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `rec-exp` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `1-exp` `pow-prod-down` `-commutative` `distribute-lft-out`

Counts

4 → 113

Calls

4 calls:

26.0ms	(* (/ 1 (- x 1)) (+ x 1))
13.0ms	(/ (fma x x -1) (* (- x 1) (- x 1)))
0.0ms	(fma x (/ 1 (+ x 1)) (- (/ (fma x x -1) (* (- x 1) (- x 1)))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ 1 (- x 1)) (+ x 1))
61.0ms	(/ (fma x x -1) (* (- x 1) (- x 1)))
109.0ms	(fma x (/ 1 (+ x 1)) (- (/ (fma x x -1) (* (- x 1) (- x 1)))))
154.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify750.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2000
2	2000
1	643
0	212

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch167.0ms

Steps

Iters	Range		Point
10	186.95626557948964	3373396396890550.5	12311.34325898398
9	-24078.920296370652	-0.35383103211093586	-13167.552073147652

simplify13.0ms

Iterations

Iter	Nodes
done	59
3	59
2	57
1	49
0	31

end0.0ms

sample2.2s

Algorithm

intervals

Results

980.0ms	1698×	body	1280	valid
456.0ms	1267×	body	640	valid
381.0ms	4118×	body	80	valid
163.0ms	626×	body	320	valid
68.0ms	291×	body	160	valid