Details

sample42.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2065
8	2065
7	1738
6	803
5	457
4	220
3	107
2	50
1	23
0	9

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`associate-/r*` `times-frac` `flip3--` `flip--`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/r/` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 49

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
45.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(+ (* x x) (* y y))
108.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	2010
3	2010
2	1458
1	338
0	97

prune449.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) (* y y))
0.0b	(/ 1 (/ (fma x x (* y y)) (- (* x x) (* y y))))
18.9b	(/ (fma x x (* y y)) (- (* x x) (* y y)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
63×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`associate-/r*`
17×	`difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

3 → 153

Calls

3 calls:

23.0ms	(- (* x x) (* y y))
32.0ms	(/ 1 (/ (fma x x (* y y)) (- (* x x) (* y y))))
16.0ms	(/ (fma x x (* y y)) (- (* x x) (* y y)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(- (* x x) (* y y))
92.0ms	(/ 1 (/ (fma x x (* y y)) (- (* x x) (* y y))))
81.0ms	(/ (fma x x (* y y)) (- (* x x) (* y y)))

simplify1.2s

Counts

162 → 162

Iterations

Iter	Nodes
done	2004
3	2004
2	1752
1	550
0	224

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* 1 (+ y x)) (hypot y x))
0.0b	(* (/ (* 1 (+ y x)) (hypot y x)) (- x y))
0.2b	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
55×	`distribute-rgt-in` `add-sqr-sqrt` `distribute-lft-in`
54×	`prod-diff`
53×	`*-un-lft-identity`
52×	`prod-exp`
51×	`add-cube-cbrt`
49×	`add-cbrt-cube`
28×	`div-exp`
21×	`cbrt-unprod`
20×	`associate-l`
15×	`times-frac`
13×	`associate-*r/`
12×	`cbrt-undiv`
11×	`frac-times` `1-exp`
10×	`pow1`
6×	`sub-neg` `flip3--` `associate-r` `flip--`
5×	`rec-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`*-commutative` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 196

Calls

3 calls:

21.0ms	(/ (* 1 (+ y x)) (hypot y x))
61.0ms	(* (/ (* 1 (+ y x)) (hypot y x)) (- x y))
144.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))

series370.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(/ (* 1 (+ y x)) (hypot y x))
108.0ms	(* (/ (* 1 (+ y x)) (hypot y x)) (- x y))
123.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))

simplify1.1s

Counts

205 → 205

Iterations

Iter	Nodes
done	2001
2	2001
1	988
0	310

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (* 1 (+ y x)) (hypot y x)) (- x y))
0.2b	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))
0.2b	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))
0.2b	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log`
143×	`distribute-rgt-in` `distribute-lft-in`
138×	`prod-exp`
126×	`prod-diff`
116×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
112×	`add-cube-cbrt`
109×	`add-cbrt-cube`
69×	`div-exp`
52×	`cbrt-unprod`
46×	`associate-l`
30×	`times-frac`
29×	`frac-times` `associate-*r/`
28×	`1-exp`
26×	`cbrt-undiv`
21×	`pow1`
15×	`rec-exp`
14×	`sub-neg` `flip3--` `flip--`
10×	`pow-prod-down` `associate-*l/`
8×	`associate-r`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 389

Calls

4 calls:

49.0ms	(* (/ (* 1 (+ y x)) (hypot y x)) (- x y))
119.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))
101.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))
92.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (/ (* 1 (+ y x)) (hypot y x)) (- x y))
122.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))
144.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))
136.0ms	(* (/ 1 (hypot y x)) (* (/ (* 1 (+ y x)) (hypot y x)) (- x y)))

simplify1.3s

Counts

401 → 401

Iterations

Iter	Nodes
done	2003
2	2003
1	935
0	289

prune6.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes82.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

900.0ms	8000×	body	80	valid
669.0ms	8000×	pre	80	true