Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify7.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite65.0ms

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:

12.0ms	(+ (* x x) (* y y))
52.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series105.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) (* y y))
73.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.0s

Counts

53 → 53

Iterations

Useful iterations: done (1.0s)

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

prune194.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite134.0ms

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:

23.0ms	(/ (+ x y) (hypot x y))
74.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
28.0ms	(/ (- x y) (hypot x y))

series363.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (+ x y) (hypot x y))
130.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
110.0ms	(/ (- x y) (hypot x y))

simplify1.4s

Counts

145 → 145

Iterations

Useful iterations: done (1.4s)

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

prune402.0ms

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 181

Calls

4 calls:

61.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
28.0ms	(/ (- x y) (hypot x y))
24.0ms	(/ (- x y) (hypot x y))
20.0ms	(/ (- x y) (hypot x y))

series518.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
121.0ms	(/ (- x y) (hypot x y))
132.0ms	(/ (- x y) (hypot x y))
115.0ms	(/ (- x y) (hypot x y))

simplify1.5s

Counts

193 → 193

Iterations

Useful iterations: 2 (388.0ms)

Iter	Nodes	Cost
0	147	2787
1	437	2709
2	1541	2473
done	5000	2473

prune757.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot x y))
0.7b	(cbrt (+ x y))
0.7b	(cbrt (+ x y))
0.7b	(cbrt (+ x y))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (hypot x y))
8.0ms	(cbrt (+ x y))
7.0ms	(cbrt (+ x y))
8.0ms	(cbrt (+ x y))

series679.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (hypot x y))
163.0ms	(cbrt (+ x y))
179.0ms	(cbrt (+ x y))
197.0ms	(cbrt (+ x y))

simplify2.1s

Counts

73 → 73

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	78	631
1	160	594
2	331	562
3	740	547
4	2043	547
done	5000	541

prune397.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	50
1	14	50
done	14	50

end0.0ms

sample993.0ms

Algorithm

intervals

Results

450.0ms	8000×	body	80	valid
252.0ms	8000×	pre	80	true