Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

478×

body

valid

simplify277.0ms

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 3 expressions with local error:

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

rewrite22.0ms

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:

4.0ms	(+ (* x x) (* y y))
9.0ms	(+ (+ (* x x) (* y y)) (* y y))
8.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series100.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* y y))
36.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify139.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (133.0ms)

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

prune114.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	55	7	62

Merged error: 0.0b

Counts

62 → 7

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:

1.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

(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

prune34.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	13	7	20

Merged error: 0.0b

Counts

20 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
6.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series258.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (+ (* x x) (* y y)) (* y y))
126.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
47.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
51.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify88.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	175	647
1	742	534
2	3044	495
3	5001	493

prune181.0ms

Filtered

76 candidates to 66 candidates (86.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	77	6	83

Merged error: 0.0b

Counts

83 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* (sqrt 1) (hypot x (* (sqrt 2) y))) (* y y))
0.4b	(* (sqrt 2) y)
6.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* y y))
1.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* (sqrt 1) (hypot x (* (sqrt 2) y))) (* y y))
5.0ms	(* (sqrt 2) y)
7.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* y y))
275.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* (sqrt 1) (hypot x (* (sqrt 2) y))) (* y y))
40.0ms	(* (sqrt 2) y)
48.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	244	579
1	1076	487
2	5001	463

prune225.0ms

Filtered

82 candidates to 64 candidates (78.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	3	3
Picked	0	1	1
Done	1	1	2
Total	82	6	88

Merged error: 0.0b

Counts

88 → 6

regimes139.0ms

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	10	7
1	10	7

end0.0ms

sample530.0ms

Algorithm

intervals

Results

315.0ms

14068×

body

valid