Details

sample21.0ms

Algorithm

intervals

Results

12.0ms

445×

body

valid

simplify279.0ms

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))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(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

prune29.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Merged error: 0.1b

Counts

15 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* y y))
4.0ms	(+ (* x x) (* y y))
8.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series96.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (+ (* x x) (* y y)) (* y y))
29.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify133.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	237	373
1	1141	313
2	4748	287
3	5001	286

prune109.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	2	2
Picked	0	1	1
Done	1	0	1
Total	58	6	64

Merged error: 0.0b

Counts

64 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
6.5b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.5b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
1.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
125.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
50.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
52.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify82.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	200	583
1	838	494
2	2618	468
3	5001	441

prune177.0ms

Filtered

72 candidates to 62 candidates (86.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	70	8	78

Merged error: 0.0b

Counts

78 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* 1 (hypot x (* (sqrt 2) y))) (* y y))
0.4b	(* (sqrt 2) y)
6.5b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite18.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r`
2×	`flip3-+` `sqrt-div` `flip-+` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `fma-udef` `hypot-def`

Counts

4 → 66

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
1.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* 1 (hypot x (* (sqrt 2) y))) (* y y))
7.0ms	(* (sqrt 2) y)
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
266.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* 1 (hypot x (* (sqrt 2) y))) (* y y))
39.0ms	(* (sqrt 2) y)
47.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	272	502
1	1178	449
2	5001	430

prune187.0ms

Filtered

78 candidates to 60 candidates (76.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	3	2	5
Picked	0	1	1
Done	1	1	2
Total	79	7	86

Merged error: 0b

Counts

86 → 7

regimes129.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	22	12
2	22	12

end0.0ms

sample515.0ms

Algorithm

intervals

Results

304.0ms

14063×

body

valid