Details

sample44.0ms

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	113	14
4	229	14
5	461	14
6	822	14
7	1308	14
8	3296	14
done	5000	14

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite73.0ms

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:

17.0ms	(+ (* x x) (* y y))
53.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* x x) (* y y))
96.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.2s

Counts

53 → 53

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	95	874
1	317	764
2	1517	635
done	5000	627

prune183.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 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))

rewrite186.0ms

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:

27.0ms	(/ (+ x y) (hypot x y))
114.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
36.0ms	(/ (- x y) (hypot x y))

series389.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(/ (+ x y) (hypot x y))
123.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
159.0ms	(/ (- x y) (hypot x y))

simplify1.7s

Counts

145 → 145

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	167	2187
1	472	2127
2	1644	1919
done	5000	1918

prune427.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite209.0ms

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:

25.0ms	(/ (hypot x y) (+ x y))
120.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
22.0ms	(/ 1 (/ (hypot x y) (+ x y)))
22.0ms	(/ (- x y) (hypot x y))

series487.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (hypot x y) (+ x y))
118.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))
116.0ms	(/ 1 (/ (hypot x y) (+ x y)))
109.0ms	(/ (- x y) (hypot x y))

simplify1.8s

Counts

308 → 308

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	339	5542
1	924	4833
2	2486	4298
done	5002	4271

prune870.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))
0.0b	(pow (/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y)) 3)
0.0b	(/ (hypot x y) (+ x y))

rewrite437.0ms

Algorithm

rewrite-expression-head

Rules

2529×	`times-frac`
1701×	`*-un-lft-identity`
1357×	`add-sqr-sqrt`
959×	`add-cube-cbrt`
289×	`unpow-prod-down` `cube-prod`
199×	`distribute-lft-out--` `difference-of-squares`
172×	`distribute-lft-out`
125×	`associate-/r/`
103×	`associate-/l*`
71×	`div-inv`
57×	`flip3-+` `flip-+`
30×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/r*`
16×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`pow-unpow` `frac-2neg` `div-sub` `clear-num` `associate-/l/`
1×	`cube-div` `cube-mult` `pow-to-exp` `flip3--` `pow-pow` `unpow3` `flip--` `sqr-pow`

Counts

4 → 1175

Calls

4 calls:

68.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
33.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
160.0ms	(pow (/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y)) 3)
22.0ms	(/ (hypot x y) (+ x y))

series540.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
139.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
133.0ms	(pow (/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y)) 3)
105.0ms	(/ (hypot x y) (+ x y))

simplify2.7s

Counts

1187 → 1187

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	1080	39880
1	4445	37483
done	5000	37391

prune3.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample946.0ms

Algorithm

intervals

Results

483.0ms	8000×	body	80	valid
186.0ms	8000×	pre	80	true