Details

sample64.0ms

Algorithm

intervals

Results

35.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify5.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5047
7	1955
6	840
5	471
4	234
3	110
2	52
1	23
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite52.0ms

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:

16.0ms	(+ (* x x) (* y y))
35.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series142.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* x x) (* y y))
109.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5003
2	1513
1	338
0	97

prune264.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
18.8b	(sqrt (+ (* x x) (* y y)))
18.8b	(sqrt (+ (* x x) (* y y)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
90×	`times-frac`
55×	`add-cube-cbrt`
54×	`sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 189

Calls

4 calls:

26.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
92.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
12.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(sqrt (+ (* x x) (* y y)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
89.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
49.0ms	(sqrt (+ (* x x) (* y y)))
67.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.0s

Counts

201 → 201

Iterations

Iter	Nodes
done	5001
2	2356
1	611
0	201

prune824.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
105×	`times-frac`
64×	`add-cube-cbrt`
54×	`associate-l`
51×	`associate-r`
42×	`add-cbrt-cube` `add-exp-log`
13×	`cbrt-undiv` `div-exp` `distribute-lft-out`
12×	`prod-exp` `cbrt-unprod` `unswap-sqr`
10×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`frac-times` `associate-/r` `pow-prod-down` `associate-l/` `associate-r/` `-commutative`
2×	`associate-/l/`
1×	`clear-num` `frac-2neg` `flip3-+` `flip-+`

Counts

4 → 222

Calls

4 calls:

24.0ms	(/ (+ x y) (hypot x y))
37.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
40.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
58.0ms	(* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ x y) (hypot x y))
130.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
100.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
125.0ms	(* (/ (+ x y) (hypot x y)) (/ (- x y) (hypot x y)))

simplify2.0s

Counts

234 → 234

Iterations

Iter	Nodes
done	5004
2	2353
1	681
0	205

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ (+ x y) (hypot x y)) (cbrt (hypot x y))) (cbrt (hypot x y)))
0.6b	(cbrt (hypot x y))
0.6b	(cbrt (hypot x y))
0.6b	(cbrt (hypot x y))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

1776×	`times-frac`
1028×	`*-un-lft-identity`
776×	`add-sqr-sqrt` `add-cube-cbrt`
648×	`cbrt-prod`
126×	`distribute-lft-out`
100×	`associate-/l*`
50×	`div-inv`
13×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 768

Calls

4 calls:

42.0ms	(/ (/ (/ (+ x y) (hypot x y)) (cbrt (hypot x y))) (cbrt (hypot x y)))
1.0ms	(cbrt (hypot x y))
1.0ms	(cbrt (hypot x y))
1.0ms	(cbrt (hypot x y))

series688.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (/ (/ (+ x y) (hypot x y)) (cbrt (hypot x y))) (cbrt (hypot x y)))
140.0ms	(cbrt (hypot x y))
154.0ms	(cbrt (hypot x y))
157.0ms	(cbrt (hypot x y))

simplify2.6s

Counts

780 → 780

Iterations

Iter	Nodes
done	5003
1	2060
0	975

prune4.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
2	16
1	15
0	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
348.0ms	8000×	pre	80	true