Details

sample48.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	52	14
3	115	14
4	249	14
5	516	14
6	1111	14
7	4552	14
done	5000	14

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
20.2b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

16.0ms	(+ (* x x) (* y y))
65.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series195.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(+ (* x x) (* y y))
124.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify3.0s

Counts

53 → 53

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	95	874
1	352	767
2	2743	639
done	5000	635

prune342.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
58×	`times-frac`
39×	`add-cube-cbrt`
19×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`associate-r`
9×	`associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `flip3--` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

3 → 136

Calls

3 calls:

37.0ms	(/ (- x y) (hypot x y))
34.0ms	(/ (+ x y) (hypot x y))
95.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series442.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(/ (- x y) (hypot x y))
144.0ms	(/ (+ x y) (hypot x y))
155.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify3.4s

Counts

145 → 145

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	167	2187
1	501	2127
2	2869	1937
done	5000	1919

prune811.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

251×	`times-frac`
194×	`*-un-lft-identity`
173×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
64×	`add-exp-log`
59×	`associate-r`
34×	`add-cbrt-cube`
30×	`div-exp`
25×	`associate-/r*` `distribute-lft-out`
19×	`associate-l`
18×	`associate-/r/`
14×	`cbrt-undiv` `prod-exp`
12×	`div-inv`
11×	`associate-/l*`
10×	`unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`rec-exp` `1-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`frac-times` `flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `flip--` `inv-pow`

Counts

4 → 296

Calls

4 calls:

34.0ms	(/ (- x y) (hypot x y))
157.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
21.0ms	(/ (hypot x y) (+ x y))
33.0ms	(/ 1 (/ (hypot x y) (+ x y)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- x y) (hypot x y))
158.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
162.0ms	(/ (hypot x y) (+ x y))
160.0ms	(/ 1 (/ (hypot x y) (+ x y)))

simplify959.0ms

Counts

308 → 308

Iterations

Useful iterations: done (938.0ms)

Iter	Nodes	Cost
0	339	5542
1	1088	4863
done	5000	4477

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (hypot x y))
0.2b	(/ (/ (- x y) (hypot x y)) (sqrt (hypot x y)))
0.3b	(* (/ (/ (- x y) (hypot x y)) (sqrt (hypot x y))) (/ (+ x y) (sqrt (hypot x y))))
0.5b	(/ (+ x y) (sqrt (hypot x y)))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

514×	`times-frac`
386×	`add-sqr-sqrt`
354×	`*-un-lft-identity`
242×	`add-cube-cbrt`
155×	`sqrt-prod`
118×	`associate-l`
43×	`distribute-lft-out--` `difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-r` `associate-/l*`
18×	`div-inv`
15×	`associate-/r*` `unswap-sqr`
14×	`cbrt-undiv` `div-exp`
13×	`distribute-lft-out`
6×	`pow1` `prod-exp` `cbrt-unprod`
5×	`associate-/l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`frac-times` `flip3--` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 434

Calls

4 calls:

40.0ms	(/ (- x y) (hypot x y))
48.0ms	(/ (/ (- x y) (hypot x y)) (sqrt (hypot x y)))
247.0ms	(* (/ (/ (- x y) (hypot x y)) (sqrt (hypot x y))) (/ (+ x y) (sqrt (hypot x y))))
47.0ms	(/ (+ x y) (sqrt (hypot x y)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- x y) (hypot x y))
190.0ms	(/ (/ (- x y) (hypot x y)) (sqrt (hypot x y)))
163.0ms	(* (/ (/ (- x y) (hypot x y)) (sqrt (hypot x y))) (/ (+ x y) (sqrt (hypot x y))))
168.0ms	(/ (+ x y) (sqrt (hypot x y)))

simplify1.2s

Counts

446 → 446

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	455	10368
1	1406	9772
done	5001	9118

prune2.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	14	17
done	14	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

698.0ms	8000×	body	80	valid
324.0ms	8000×	pre	80	true