Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

441×

body

valid

simplify330.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (10.0ms)

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	434	3
10	786	3
11	3475	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))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

190×	`*-un-lft-identity`
111×	`distribute-lft-out`
74×	`associate-l`
37×	`fma-def`
19×	`add-log-exp`
17×	`swap-sqr`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `sum-log`
8×	`associate-+l+`
6×	`+-commutative`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `associate-r` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`*-commutative` `unswap-sqr`

Counts

3 → 124

Calls

3 calls:

16.0ms	(+ (* x x) (* y y))
26.0ms	(+ (+ (* x x) (* y y)) (* y y))
42.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series108.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
36.0ms	(+ (+ (* x x) (* y y)) (* y y))
40.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify158.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	233	556
1	1115	435
2	4583	409
3	5001	407

prune146.0ms

Filtered

133 candidates to 69 candidates (51.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Merged error: 0.0b

Counts

135 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
20×	`fma-def`
14×	`distribute-lft-out`
11×	`add-sqr-sqrt`
10×	`associate-l` `add-log-exp`
9×	`add-cube-cbrt`
4×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `associate-+l+` `swap-sqr` `associate-r` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`associate-+r+` `flip3-+` `flip-+`
1×	`*-commutative` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

1.0ms	(fma y y (* y y))
9.0ms	(+ (* x x) (fma y y (* y y)))
16.0ms	(+ (+ (* x x) (fma y y (* y y))) (* y y))

series146.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(fma y y (* y y))
43.0ms	(+ (* x x) (fma y y (* y y)))
50.0ms	(+ (+ (* x x) (fma y y (* y y))) (* y y))

simplify151.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	185	330
1	903	286
2	4192	273
3	5001	268

prune133.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Merged error: 0.0b

Counts

86 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot y y)
0.1b	(hypot y y)
0.1b	(+ (+ (* x x) (* (hypot y y) (hypot y y))) (* y y))
0.4b	(* (hypot y y) (hypot y y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
25×	`distribute-lft-out`
20×	`associate-l`
11×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
8×	`fma-def` `swap-sqr`
6×	`add-exp-log` `hypot-udef` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `sum-log`
2×	`+-commutative` `associate-+l+`
1×	`pow2` `flip3-+` `pow-plus` `sqrt-unprod` `pow-prod-down` `prod-exp` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

1.0ms	(hypot y y)
1.0ms	(hypot y y)
28.0ms	(+ (+ (* x x) (* (hypot y y) (hypot y y))) (* y y))
4.0ms	(* (hypot y y) (hypot y y))

series413.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(hypot y y)
94.0ms	(hypot y y)
113.0ms	(+ (+ (* x x) (* (hypot y y) (hypot y y))) (* y y))
111.0ms	(* (hypot y y) (hypot y y))

simplify163.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	200	444
1	864	369
2	3953	345
3	5001	343

prune359.0ms

Filtered

96 candidates to 63 candidates (65.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (fma (hypot y y) (hypot y y) (* y y)))
0.1b	(hypot y y)
0.1b	(hypot y y)
0.3b	(fma (hypot y y) (hypot y y) (* y y))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `fma-udef`

Counts

4 → 40

Calls

4 calls:

1.0ms	(fma x x (fma (hypot y y) (hypot y y) (* y y)))
1.0ms	(hypot y y)
1.0ms	(hypot y y)
1.0ms	(fma (hypot y y) (hypot y y) (* y y))

series567.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(fma x x (fma (hypot y y) (hypot y y) (* y y)))
93.0ms	(hypot y y)
92.0ms	(hypot y y)
231.0ms	(fma (hypot y y) (hypot y y) (* y y))

simplify53.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	84	238
1	247	197
2	863	191
3	5002	188

prune116.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	54	6	60

Merged error: 0b

Counts

60 → 6

regimes68.0ms

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	9	6
1	9	6

end0.0ms

sample532.0ms

Algorithm

intervals

Results

318.0ms

14005×

body

valid