Details

sample31.0ms

Algorithm

intervals

Results

21.0ms

478×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	2
1	8	2
2	8	2

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (* x x) (* y y))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `fma-def` `*-un-lft-identity` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 14

Calls

1 calls:

3.0ms

(+ (* x x) (* y y))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(+ (* x x) (* y y))

simplify45.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	109	74
1	511	64
2	1427	61
3	5001	60

prune37.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x y)
0.0b	(hypot x y)
0.0b	(* (hypot x y) (hypot x y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`hypot-udef`
5×	`add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `pow-prod-down` `prod-exp` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

0.0ms	(hypot x y)
0.0ms	(hypot x y)
3.0ms	(* (hypot x y) (hypot x y))

series162.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(hypot x y)
45.0ms	(hypot x y)
66.0ms	(* (hypot x y) (hypot x y))

simplify48.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	84	173
1	290	146
2	1254	137
3	5002	134

prune102.0ms

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	(fma x x (* y y))
0.0b	(* (sqrt (fma x x (* y y))) (hypot x y))
6.7b	(sqrt (fma x x (* y y)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`hypot-udef` `fma-udef` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-unprod` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 61

Calls

4 calls:

0.0ms	(hypot x y)
0.0ms	(fma x x (* y y))
5.0ms	(* (sqrt (fma x x (* y y))) (hypot x y))
1.0ms	(sqrt (fma x x (* y y)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot x y)
33.0ms	(fma x x (* y y))
107.0ms	(* (sqrt (fma x x (* y y))) (hypot x y))
47.0ms	(sqrt (fma x x (* y y)))

simplify39.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	113	315
1	406	201
2	1214	171
3	5001	168

prune164.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (hypot x y) (cbrt (hypot x y))) (cbrt (hypot x y))) (cbrt (hypot x y)))
0.6b	(cbrt (hypot x y))
0.6b	(cbrt (hypot x y))
0.6b	(cbrt (hypot x y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-exp-log`
12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-up`
1×	`associate-l` `*-commutative`

Counts

4 → 66

Calls

4 calls:

35.0ms	(* (* (* (hypot x y) (cbrt (hypot x y))) (cbrt (hypot x y))) (cbrt (hypot x y)))
0.0ms	(cbrt (hypot x y))
0.0ms	(cbrt (hypot x y))
1.0ms	(cbrt (hypot x y))

series386.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* (* (hypot x y) (cbrt (hypot x y))) (cbrt (hypot x y))) (cbrt (hypot x y)))
111.0ms	(cbrt (hypot x y))
106.0ms	(cbrt (hypot x y))
111.0ms	(cbrt (hypot x y))

simplify81.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	191	525
1	741	447
2	3857	381
3	5001	348

prune334.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2

end0.0ms

sample768.0ms

Algorithm

intervals

Results

545.0ms

14063×

body

valid