Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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: 19.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite41.0ms

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:

8.0ms	(+ (* x x) (* y y))
31.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series92.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x x) (* y y))
62.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify806.0ms

Counts

53 → 53

Iterations

Useful iterations: done (804.0ms)

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

prune138.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x y)
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)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

0.0ms	(hypot x y)
18.0ms	(/ (- x y) (hypot x y))
21.0ms	(/ (+ x y) (hypot x y))
53.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot x y)
91.0ms	(/ (- x y) (hypot x y))
90.0ms	(/ (+ x y) (hypot x y))
95.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify1.0s

Counts

158 → 158

Iterations

Useful iterations: done (997.0ms)

Iter	Nodes	Cost
0	172	2247
1	478	2185
2	1652	1971
done	5001	1970

prune321.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

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:

17.0ms	(/ (- x y) (hypot x y))
11.0ms	(/ (hypot x y) (+ x y))
20.0ms	(/ 1 (/ (hypot x y) (+ x y)))
80.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- x y) (hypot x y))
91.0ms	(/ (hypot x y) (+ x y))
92.0ms	(/ 1 (/ (hypot x y) (+ x y)))
95.0ms	(* (/ (- x y) (hypot x y)) (/ 1 (/ (hypot x y) (+ x y))))

simplify1.2s

Counts

308 → 308

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	339	5542
1	924	4833
2	2466	4298
done	5001	4271

prune531.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

0.0ms	(hypot x y)
24.0ms	(/ (* (- x y) (/ (+ x y) (hypot x y))) (hypot x y))
20.0ms	(/ (+ x y) (hypot x y))
41.0ms	(* (- x y) (/ (+ x y) (hypot x y)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot x y)
92.0ms	(/ (* (- x y) (/ (+ x y) (hypot x y))) (hypot x y))
92.0ms	(/ (+ x y) (hypot x y))
89.0ms	(* (- x y) (/ (+ x y) (hypot x y)))

simplify1.0s

Counts

130 → 130

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	153	1766
1	404	1704
2	1680	1484
done	5001	1479

prune259.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes49.0ms

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	10	17
1	14	17
done	14	17

end0.0ms

sample505.0ms

Algorithm

intervals

Results

225.0ms	8000×	body	80	valid
97.0ms	8000×	pre	80	true