Details

sample20.0ms

Algorithm

intervals

Results

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

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	51	14
3	98	14
4	207	14
5	410	14
6	754	14
7	1776	14
done	5001	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(* (- x y) (+ x y))
16.7b	(/ (* (- x y) (+ x y)) (fma x x (* y y)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

0.0ms	(fma x x (* y y))
17.0ms	(* (- x y) (+ x y))
9.0ms	(/ (* (- x y) (+ x y)) (fma x x (* y y)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma x x (* y y))
43.0ms	(* (- x y) (+ x y))
71.0ms	(/ (* (- x y) (+ x y)) (fma x x (* y y)))

simplify644.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	119	1145
1	363	1100
2	1931	956
done	5000	956

prune210.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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 y x)
32.0ms	(* (/ (- x y) (hypot y x)) (/ (+ x y) (hypot y x)))
9.0ms	(/ (- x y) (hypot y x))
9.0ms	(/ (+ x y) (hypot y x))

series320.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y x)
92.0ms	(* (/ (- x y) (hypot y x)) (/ (+ x y) (hypot y x)))
92.0ms	(/ (- x y) (hypot y x))
90.0ms	(/ (+ x y) (hypot y x))

simplify684.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (149.0ms)

Iter	Nodes	Cost
0	172	2247
1	493	2185
2	1949	1971
done	5000	1971

prune352.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

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:

56.0ms	(* (/ (- x y) (hypot y x)) (/ 1 (/ (hypot y x) (+ x y))))
9.0ms	(/ 1 (/ (hypot y x) (+ x y)))
9.0ms	(/ (- x y) (hypot y x))
5.0ms	(/ (hypot y x) (+ x y))

series363.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.5s

Counts

308 → 308

Iterations

Useful iterations: 2 (391.0ms)

Iter	Nodes	Cost
0	339	5542
1	1006	4995
2	3816	4298
done	5001	4298

prune592.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

3387×	`times-frac`
2189×	`*-un-lft-identity`
1725×	`add-sqr-sqrt`
1285×	`add-cube-cbrt`
700×	`cbrt-prod`
694×	`unpow-prod-down` `cube-prod`
232×	`distribute-lft-out`
220×	`distribute-lft-out--` `difference-of-squares`
158×	`associate-/r/`
154×	`div-inv`
77×	`flip3-+` `flip-+`
21×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
7×	`associate-/r*`
5×	`pow1` `pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow1/3` `div-sub` `flip--` `rem-cbrt-cube`

Counts

4 → 1509

Calls

4 calls:

70.0ms	(pow (/ (/ (- x y) (hypot y x)) (/ (hypot y x) (+ x y))) 3)
92.0ms	(cbrt (pow (/ (/ (- x y) (hypot y x)) (/ (hypot y x) (+ x y))) 3))
9.0ms	(/ (- x y) (hypot y x))
6.0ms	(/ (hypot y x) (+ x y))

series402.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (/ (/ (- x y) (hypot y x)) (/ (hypot y x) (+ x y))) 3)
111.0ms	(cbrt (pow (/ (/ (- x y) (hypot y x)) (/ (hypot y x) (+ x y))) 3))
91.0ms	(/ (- x y) (hypot y x))
96.0ms	(/ (hypot y x) (+ x y))

simplify490.0ms

Counts

1521 → 1521

Iterations

Useful iterations: done (410.0ms)

Iter	Nodes	Cost
0	1523	58951
done	5000	51937

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes34.0ms

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

sample499.0ms

Algorithm

intervals

Results

244.0ms	8000×	body	80	valid
109.0ms	8000×	pre	80	true