Details

sample38.0ms

Algorithm

intervals

Results

22.0ms

443×

body

valid

simplify283.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

6.0ms	(+ (* x x) (* y y))
9.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series61.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify102.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	196	257
1	953	206
2	3765	190
3	5001	186

prune81.0ms

Filtered

39 candidates to 30 candidates (76.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	35	6	41

Merged error: 0.0b

Counts

41 → 6

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(+ (+ (fma x x (* y y)) (* y y)) (* y y))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 18

Calls

1 calls:

5.0ms

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

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

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

simplify66.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	115	156
1	525	127
2	2218	115
3	5001	112

prune52.0ms

Filtered

21 candidates to 17 candidates (81.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	17	4	21
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 0.0b

Counts

27 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(fma (sqrt (+ (fma x x (* y y)) (* y y))) (sqrt (+ (fma x x (* y y)) (* y y))) (* y y))
7.7b	(sqrt (+ (fma x x (* y y)) (* y y)))
7.7b	(sqrt (+ (fma x x (* y y)) (* y y)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`fma-udef`

Counts

3 → 46

Calls

3 calls:

1.0ms	(fma (sqrt (+ (fma x x (* y y)) (* y y))) (sqrt (+ (fma x x (* y y)) (* y y))) (* y y))
5.0ms	(sqrt (+ (fma x x (* y y)) (* y y)))
3.0ms	(sqrt (+ (fma x x (* y y)) (* y y)))

series283.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(fma (sqrt (+ (fma x x (* y y)) (* y y))) (sqrt (+ (fma x x (* y y)) (* y y))) (* y y))
64.0ms	(sqrt (+ (fma x x (* y y)) (* y y)))
62.0ms	(sqrt (+ (fma x x (* y y)) (* y y)))

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	124	447
1	409	374
2	1303	373
3	5001	363

prune153.0ms

Filtered

55 candidates to 49 candidates (89.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	51	4	55
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	53	8	61

Merged error: 0.0b

Counts

61 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (sqrt 2) y) x)
0.2b	(fma (sqrt (+ (fma x x (* y y)) (* y y))) (* 1 (hypot (* (sqrt 2) y) x)) (* y y))
0.5b	(* (sqrt 2) y)
7.7b	(sqrt (+ (fma x x (* y y)) (* y y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`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×	`sqrt-div` `unswap-sqr`
1×	`rem-sqrt-square` `hypot-udef` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `hypot-def`

Counts

4 → 62

Calls

4 calls:

1.0ms	(hypot (* (sqrt 2) y) x)
1.0ms	(fma (sqrt (+ (fma x x (* y y)) (* y y))) (* 1 (hypot (* (sqrt 2) y) x)) (* y y))
5.0ms	(* (sqrt 2) y)
3.0ms	(sqrt (+ (fma x x (* y y)) (* y y)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(hypot (* (sqrt 2) y) x)
307.0ms	(fma (sqrt (+ (fma x x (* y y)) (* y y))) (* 1 (hypot (* (sqrt 2) y) x)) (* y y))
42.0ms	(* (sqrt 2) y)
62.0ms	(sqrt (+ (fma x x (* y y)) (* y y)))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	214	455
1	812	402
2	5001	401

prune199.0ms

Filtered

74 candidates to 59 candidates (79.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	74	8	82

Merged error: 0.0b

Counts

82 → 8

regimes90.0ms

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	8	6
1	8	6

end0.0ms

sample643.0ms

Algorithm

intervals

Results

414.0ms

14283×

body

valid