Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

443×

body

valid

simplify269.0ms

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:

0.1b	(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))

series30.0ms

Counts

1 → 3

Calls

1 calls:

30.0ms

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

simplify49.0ms

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

prune32.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3 (* y y) (* x x))
0.3b	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
6.3b	(sqrt (fma 3 (* y y) (* x x)))
6.3b	(sqrt (fma 3 (* y y) (* x x)))

rewrite18.0ms

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))
13.0ms	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))
2.0ms	(sqrt (fma 3 (* y y) (* x x)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(fma 3 (* y y) (* x x))
31.0ms	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
54.0ms	(sqrt (fma 3 (* y y) (* x x)))
53.0ms	(sqrt (fma 3 (* y y) (* x x)))

simplify127.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (119.0ms)

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

prune196.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (fabs (cbrt (fma 3 (* y y) (* x x)))) (sqrt (fma 3 (* y y) (* x x)))) (sqrt (cbrt (fma 3 (* y y) (* x x)))))
6.3b	(sqrt (fma 3 (* y y) (* x x)))
6.8b	(cbrt (fma 3 (* y y) (* x x)))
6.8b	(cbrt (fma 3 (* y y) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod` `associate-r` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 67

Calls

4 calls:

30.0ms	(* (* (fabs (cbrt (fma 3 (* y y) (* x x)))) (sqrt (fma 3 (* y y) (* x x)))) (sqrt (cbrt (fma 3 (* y y) (* x x)))))
2.0ms	(sqrt (fma 3 (* y y) (* x x)))
1.0ms	(cbrt (fma 3 (* y y) (* x x)))
1.0ms	(cbrt (fma 3 (* y y) (* x x)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (* (fabs (cbrt (fma 3 (* y y) (* x x)))) (sqrt (fma 3 (* y y) (* x x)))) (sqrt (cbrt (fma 3 (* y y) (* x x)))))
54.0ms	(sqrt (fma 3 (* y y) (* x x)))
119.0ms	(cbrt (fma 3 (* y y) (* x x)))
122.0ms	(cbrt (fma 3 (* y y) (* x x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	277	842
1	1186	759
2	5001	747

prune264.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (cbrt (fma 3 (* y y) (* x x)))))
6.3b	(sqrt (fma 3 (* y y) (* x x)))
6.8b	(cbrt (fma 3 (* y y) (* x x)))
6.8b	(cbrt (fma 3 (* y y) (* x x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cbrt-prod`
10×	`pow1`
9×	`associate-r`
6×	`add-exp-log` `sqrt-pow1` `associate-l` `add-cbrt-cube` `unswap-sqr`
4×	`expm1-log1p-u` `pow1/2` `pow1/3` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-prod-up`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

19.0ms	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (cbrt (fma 3 (* y y) (* x x)))))
1.0ms	(sqrt (fma 3 (* y y) (* x x)))
1.0ms	(cbrt (fma 3 (* y y) (* x x)))
1.0ms	(cbrt (fma 3 (* y y) (* x x)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (cbrt (fma 3 (* y y) (* x x)))))
56.0ms	(sqrt (fma 3 (* y y) (* x x)))
122.0ms	(cbrt (fma 3 (* y y) (* x x)))
121.0ms	(cbrt (fma 3 (* y y) (* x x)))

simplify98.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	220	806
1	750	767
2	3176	760
3	5001	731

prune274.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes129.0ms

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

sample597.0ms

Algorithm

intervals

Results

299.0ms

14173×

body

valid