Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4574
6	1116
5	522
4	251
3	115
2	52
1	23
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(* (- x y) (+ y x))
17.7b	(/ (* (- x y) (+ y x)) (fma x x (* y y)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

0.0ms	(fma x x (* y y))
30.0ms	(* (- x y) (+ y x))
32.0ms	(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series220.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma x x (* y y))
59.0ms	(* (- x y) (+ y x))
104.0ms	(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify2.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	2980
1	385
0	123

prune442.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune20.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(/ (- x y) (/ (fma x x (* y y)) (+ y x)))
16.8b	(/ (fma x x (* y y)) (+ y x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
161×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`flip3--` `div-sub` `fma-udef` `flip--`

Counts

3 → 178

Calls

3 calls:

0.0ms	(fma x x (* y y))
44.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ y x)))
18.0ms	(/ (fma x x (* y y)) (+ y x))

series281.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma x x (* y y))
128.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ y x)))
98.0ms	(/ (fma x x (* y y)) (+ y x))

simplify2.3s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	4156
1	720
0	239

prune845.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(* x (- x y))
0.0b	(* y (- x y))
17.7b	(/ (+ (* y (- x y)) (* x (- x y))) (fma x x (* y y)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `distribute-lft-in`
12×	`times-frac` `associate-*r/`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
8×	`pow1`
6×	`flip3--` `associate-l` `flip--` `associate-/l/`
4×	`expm1-log1p-u` `sub-neg` `distribute-rgt-out` `frac-add` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

4 → 141

Calls

4 calls:

0.0ms	(fma x x (* y y))
37.0ms	(* x (- x y))
22.0ms	(* y (- x y))
49.0ms	(/ (+ (* y (- x y)) (* x (- x y))) (fma x x (* y y)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma x x (* y y))
62.0ms	(* x (- x y))
65.0ms	(* y (- x y))
79.0ms	(/ (+ (* y (- x y)) (* x (- x y))) (fma x x (* y y)))

simplify2.6s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
2	3181
1	570
0	229

prune680.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes123.0ms

Accuracy

79.1% (4.4b remaining)

Error of 4.9b against oracle of 0.4b and baseline of 21.6b

bsearch104.0ms

Steps

Iters	Range	Point
8	1.4224717713323527e-167	8.131351164067834e-164	7.961862811311691e-164
4	-1.857850302800927e-158	-9.802288210601573e-159	-1.2218614719090495e-158
9	-2.741116183037804e+158	-4.389998254864137e+150	-5.797856225877881e+150

Iters

Range

Point

1.4224717713323527e-167

8.131351164067834e-164

7.961862811311691e-164

-1.857850302800927e-158

-9.802288210601573e-159

-1.2218614719090495e-158

-2.741116183037804e+158

-4.389998254864137e+150

-5.797856225877881e+150

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample1.0s

Algorithm

intervals

Results

563.0ms	8000×	body	80	valid
193.0ms	8000×	pre	80	true