Details

sample21.0ms

Algorithm

intervals

Results

12.0ms

441×

body

valid

simplify275.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 2

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:

1.0ms

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

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

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

simplify51.0ms

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

prune24.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.1b

Counts

15 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3 (* y y) (* x x))
0.2b	(* (sqrt (fma 3 (* y y) (* x x))) (sqrt (fma 3 (* y y) (* x x))))
5.1b	(sqrt (fma 3 (* y y) (* x x)))
5.1b	(sqrt (fma 3 (* y y) (* x x)))

rewrite11.0ms

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:

1.0ms	(fma 3 (* y y) (* x x))
6.0ms	(* (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)))

series174.0ms

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

simplify130.0ms

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

prune161.0ms

Filtered

103 candidates to 62 candidates (60.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Merged error: 0.0b

Counts

106 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3) (sqrt (sqrt (fma 3 (* y y) (* x x)))))
0.7b	(pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3)
5.1b	(sqrt (fma 3 (* y y) (* x x)))
5.1b	(sqrt (fma 3 (* y y) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
70×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`associate-l` `unswap-sqr`
23×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqrt-pow1`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 145

Calls

4 calls:

14.0ms	(* (pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3) (sqrt (sqrt (fma 3 (* y y) (* x x)))))
4.0ms	(pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3)
2.0ms	(sqrt (fma 3 (* y y) (* x x)))
2.0ms	(sqrt (fma 3 (* y y) (* x x)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3) (sqrt (sqrt (fma 3 (* y y) (* x x)))))
159.0ms	(pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3)
56.0ms	(sqrt (fma 3 (* y y) (* x x)))
53.0ms	(sqrt (fma 3 (* y y) (* x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	324	1492
1	1447	1194
2	5001	1060

prune240.0ms

Filtered

157 candidates to 78 candidates (49.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	4	157
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	156	9	165

Merged error: 0.0b

Counts

165 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3/2)
5.1b	(sqrt (fma 3 (* y y) (* x x)))
5.1b	(sqrt (fma 3 (* y y) (* x x)))
5.1b	(sqrt (fma 3 (* y y) (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`unpow-prod-down`
7×	`sqrt-pow1`
5×	`add-exp-log` `pow-pow` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow`
1×	`pow-to-exp` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

4.0ms	(pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3/2)
2.0ms	(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)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(pow (sqrt (sqrt (fma 3 (* y y) (* x x)))) 3/2)
54.0ms	(sqrt (fma 3 (* y y) (* x x)))
51.0ms	(sqrt (fma 3 (* y y) (* x x)))
54.0ms	(sqrt (fma 3 (* y y) (* x x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	196	524
1	581	494
2	2276	494
3	5002	489

prune229.0ms

Filtered

87 candidates to 66 candidates (75.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	87	9	96

Merged error: 0.0b

Counts

96 → 9

regimes133.0ms

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

sample615.0ms

Algorithm

intervals

Results

394.0ms

14185×

body

valid