Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	14	6
1	25	6
2	31	6
3	32	6
4	32	6

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 38.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
35.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
50×	`distribute-lft-out`
37×	`associate-l`
23×	`add-sqr-sqrt` `fma-def`
14×	`swap-sqr` `sqrt-prod`
10×	`add-cube-cbrt` `add-log-exp`
5×	`hypot-def`
4×	`pow1` `sum-log`
3×	`add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `associate-r` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+` `sqrt-div` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 101

Calls

3 calls:

18.0ms	(+ (* x x) (* y y))
28.0ms	(+ (+ (* x x) (* y y)) (* z z))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
45.0ms	(+ (+ (* x x) (* y y)) (* z z))
126.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify154.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	222	476
1	1007	434
2	3537	423
3	5001	419

prune186.0ms

Filtered

110 candidates to 67 candidates (60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	6	111

Merged error: 13.9b

Counts

111 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
29.7b	(sqrt (+ (* x x) (* y y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
26×	`hypot-def`
17×	`swap-sqr`
15×	`fma-def`
11×	`associate-l` `*-commutative` `unswap-sqr`
10×	`distribute-lft-out`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
5×	`add-log-exp`
4×	`pow1`
3×	`add-exp-log` `expm1-log1p-u` `associate-r` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `flip3-+` `sqrt-div` `flip-+`
1×	`rem-sqrt-square` `hypot-udef` `sqrt-pow1` `pow1/2` `sum-log`

Counts

3 → 91

Calls

3 calls:

22.0ms	(+ (* x x) (* y y))
1.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
19.0ms	(sqrt (+ (* x x) (* y y)))

series274.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* x x) (* y y))
195.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
44.0ms	(sqrt (+ (* x x) (* y y)))

simplify100.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	149	268
1	587	243
2	1730	238
3	5001	236

prune158.0ms

Filtered

100 candidates to 64 candidates (64.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	104	2	106

Merged error: 0.0b

Counts

106 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot y x)
0.0b	(hypot (hypot y x) z)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(hypot y x)
1.0ms	(hypot (hypot y x) z)

series279.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(hypot y x)
222.0ms	(hypot (hypot y x) z)

simplify192.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	38	68
1	43	60
2	49	60
3	57	60
4	85	60
5	159	60
6	660	60
7	2202	60
8	5001	60

prune55.0ms

Filtered

26 candidates to 26 candidates (100.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.0b

Counts

28 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(fma z z (fma x x (* y y)))
35.5b	(sqrt (fma z z (fma x x (* y y))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 35

Calls

3 calls:

1.0ms	(fma x x (* y y))
1.0ms	(fma z z (fma x x (* y y)))
2.0ms	(sqrt (fma z z (fma x x (* y y))))

series233.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma x x (* y y))
58.0ms	(fma z z (fma x x (* y y)))
133.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify160.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	71	187
1	178	162
2	626	162
3	3160	161
4	5001	161

prune90.0ms

Filtered

44 candidates to 35 candidates (79.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	44	2	46

Merged error: 0.0b

Counts

46 → 2

regimes61.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	2

end0.0ms

sample423.0ms

Algorithm

intervals

Results

253.0ms

8000×

body

valid