Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

463×

body

valid

simplify281.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	14	6
1	29	4
2	50	4
3	70	3
4	82	3
5	125	3
6	229	3
7	321	3
8	336	3
9	436	3
10	790	3
11	3492	3
12	5001	3

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(fma 3 (* y y) (* x x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 3 (* y y) (* x x))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(fma 3 (* y y) (* x x))

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	59
1	84	52
2	267	52
3	1089	52
4	5002	52

prune28.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 3 (* y y) (* x x))
0.2b	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
8.5b	(sqrt (fma 3 (* y y) (* x x)))
8.5b	(sqrt (fma 3 (* y y) (* x x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 91

Calls

4 calls:

0.0ms	(fma 3 (* y y) (* x x))
9.0ms	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma 3 (* y y) (* x x))
32.0ms	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
55.0ms	(sqrt (fma 3 (* y y) (* x x)))
53.0ms	(sqrt (fma 3 (* y y) (* x x)))

simplify128.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	127	542
1	462	484
2	2877	464
3	5002	449

prune196.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma 3 (* y y) (* x x)))) (sqrt (sqrt (fma 3 (* y y) (* x x)))))
8.5b	(sqrt (fma 3 (* y y) (* x x)))
8.5b	(sqrt (fma 3 (* y y) (* x x)))
8.5b	(sqrt (fma 3 (* y y) (* x x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1`
19×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 122

Calls

4 calls:

12.0ms	(* (sqrt (sqrt (fma 3 (* y y) (* x x)))) (sqrt (sqrt (fma 3 (* y y) (* x x)))))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sqrt (sqrt (fma 3 (* y y) (* x x)))) (sqrt (sqrt (fma 3 (* y y) (* x x)))))
59.0ms	(sqrt (fma 3 (* y y) (* x x)))
54.0ms	(sqrt (fma 3 (* y y) (* x x)))
60.0ms	(sqrt (fma 3 (* y y) (* x x)))

simplify163.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 3 (152.0ms)

Iter	Nodes	Cost
0	141	798
1	530	731
2	3156	710
3	5001	683

prune269.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (fma 3 (* y y) (* x x)))
9.0b	(cbrt (fma 3 (* y y) (* x x)))
9.0b	(cbrt (fma 3 (* y y) (* x x)))
9.0b	(cbrt (fma 3 (* y y) (* x x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(sqrt (fma 3 (* y y) (* x x)))
0.0ms	(cbrt (fma 3 (* y y) (* x x)))
0.0ms	(cbrt (fma 3 (* y y) (* x x)))
1.0ms	(cbrt (fma 3 (* y y) (* x x)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt (fma 3 (* y y) (* x x)))
131.0ms	(cbrt (fma 3 (* y y) (* x x)))
136.0ms	(cbrt (fma 3 (* y y) (* x x)))
132.0ms	(cbrt (fma 3 (* y y) (* x x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	105	418
1	278	384
2	1034	378
3	5001	362

prune309.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	3

end0.0ms

sample861.0ms

Algorithm

intervals

Results

641.0ms

14325×

body

valid