Details

sample18.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	51	14
3	97	14
4	206	14
5	402	14
6	733	14
7	1234	14
8	3218	14
done	5000	14

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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:

3.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) (* y y))
60.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify763.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (196.0ms)

Iter	Nodes	Cost
0	95	874
1	319	764
2	1467	635
done	5000	635

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

0.0ms	(hypot x y)
0.0ms	(hypot x y)
8.0ms	(/ (+ x y) (hypot x y))
30.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot x y)
45.0ms	(hypot x y)
90.0ms	(/ (+ x y) (hypot x y))
91.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify1.0s

Counts

128 → 128

Iterations

Useful iterations: 2 (406.0ms)

Iter	Nodes	Cost
0	145	1787
1	429	1739
2	1520	1547
done	5000	1547

prune263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
43×	`times-frac`
32×	`add-cube-cbrt`
31×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
9×	`pow1` `cbrt-undiv` `div-exp`
8×	`cbrt-prod` `prod-exp` `cbrt-unprod`
7×	`distribute-lft-out`
6×	`cube-div`
5×	`pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-l/` `associate-/r*` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `flip3-+` `pow1/3` `clear-num` `*-commutative` `rem-cbrt-cube` `flip-+`

Counts

4 → 151

Calls

4 calls:

8.0ms	(/ (+ x y) (hypot x y))
1.0ms	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
10.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
31.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (+ x y) (hypot x y))
102.0ms	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
98.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
88.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify862.0ms

Counts

163 → 163

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	195	2839
1	533	2504
2	2008	2285
done	5000	2260

prune395.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

22.0ms	(* (/ (- x y) (hypot x y)) (+ x y))
0.0ms	(hypot x y)
0.0ms	(hypot x y)
10.0ms	(/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y))

series262.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ (- x y) (hypot x y)) (+ x y))
46.0ms	(hypot x y)
45.0ms	(hypot x y)
86.0ms	(/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y))

simplify898.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	138	1431
1	474	1399
2	1745	1199
done	5001	1199

prune228.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
done	13	18

end0.0ms

sample451.0ms

Algorithm

intervals

Results

220.0ms	8000×	body	80	valid
102.0ms	8000×	pre	80	true