Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune2.0ms

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: 40.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 90

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
12.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series289.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
171.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	345	852
1	1445	759
2	5001	739

prune269.0ms

Filtered

102 candidates to 84 candidates (82.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 17.3b

Counts

103 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
124×	`add-sqr-sqrt`
84×	`times-frac`
55×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
11×	`pow1`
9×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+` `hypot-def`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 166

Calls

4 calls:

7.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
26.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
167.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
105.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	403	3047
1	1364	2901
2	5001	2851

prune448.0ms

Filtered

178 candidates to 118 candidates (66.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	178	6	184

Merged error: 17.3b

Counts

184 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sum-log` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 115

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
33.0ms	(+ (* x x) (* y y))
226.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	348	1348
1	1426	1262
2	5002	1230

prune274.0ms

Filtered

127 candidates to 85 candidates (66.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	124	9	133

Merged error: 12.7b

Counts

133 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
29.7b	(sqrt (+ (* x x) (* y y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `hypot-udef` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
8.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
4.0ms	(sqrt (+ (* x x) (* y y)))

series358.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* x x) (* y y))
289.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
36.0ms	(sqrt (+ (* x x) (* y y)))

simplify81.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	249	729
1	912	678
2	3040	660
3	5002	659

prune207.0ms

Filtered

83 candidates to 62 candidates (74.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	3	3	6
Picked	1	0	1
Done	0	2	2
Total	83	9	92

Merged error: 0.1b

Counts

92 → 9

regimes647.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4

end0.0ms

sample529.0ms

Algorithm

intervals

Results

356.0ms

8000×

body

valid

Details

sample20.0ms

simplify8.0ms

prune2.0ms

localize9.0ms

rewrite30.0ms

series289.0ms

simplify41.0ms

prune269.0ms

localize18.0ms

rewrite52.0ms

series530.0ms

simplify72.0ms

prune448.0ms

localize10.0ms

rewrite32.0ms

series398.0ms

simplify44.0ms

prune274.0ms

localize9.0ms

rewrite18.0ms

series358.0ms

simplify81.0ms

prune207.0ms

regimes647.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample529.0ms

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