Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

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: 38.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite31.0ms

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:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
11.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series339.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (+ (* x x) (* y y)) (* z z))
37.0ms	(+ (* x x) (* y y))
59.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
198.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

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

prune326.0ms

Filtered

102 candidates to 84 candidates (82.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 20.1b

Counts

103 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (fma y y (* z z)))
0.0b	(fma y y (* z z))
0.1b	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
36.3b	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

1.0ms	(fma x x (fma y y (* z z)))
1.0ms	(fma y y (* z z))
4.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
3.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma x x (fma y y (* z z)))
41.0ms	(fma y y (* z z))
77.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
219.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	144	330
1	630	286
2	3536	286
3	5001	286

prune168.0ms

Filtered

67 candidates to 47 candidates (70.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Merged error: 20.1b

Counts

73 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite61.0ms

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:

8.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
29.0ms	(* (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)))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
206.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
122.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
123.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify88.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (51.0ms)

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

prune517.0ms

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: 20.1b

Counts

184 → 6

localize12.0ms

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))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite37.0ms

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:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
16.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (+ (* x x) (* y y)) (* z z))
41.0ms	(+ (* x x) (* y y))
271.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
125.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	348	1349
1	1426	1262
2	5002	1230

prune307.0ms

Filtered

127 candidates to 86 candidates (67.7%)

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: 15.0b

Counts

133 → 9

regimes393.0ms

Accuracy

83.8% (2.4b remaining)

Error of 16.4b against oracle of 14.0b and baseline of 29.2b

bsearch92.0ms

Steps

Iters	Range		Point
9	1.5417294436712868e+153	3.1879290791134477e+158	1.3321670395294099e+154
8	-7.510165108443872e+153	-5.683355409305291e+150	-7.374201052106234e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	29	12
2	29	12

end0.0ms

sample459.0ms

Algorithm

intervals

Results

279.0ms

8000×

body

valid

Details

sample19.0ms

simplify19.0ms

prune3.0ms

localize10.0ms

rewrite31.0ms

series339.0ms

simplify56.0ms

prune326.0ms

localize10.0ms

rewrite10.0ms

series390.0ms

simplify121.0ms

prune168.0ms

localize15.0ms

rewrite61.0ms

series632.0ms

simplify88.0ms

prune517.0ms

localize12.0ms

rewrite37.0ms

series482.0ms

simplify60.0ms

prune307.0ms

regimes393.0ms

bsearch92.0ms

simplify3.0ms

end0.0ms

sample459.0ms

Profiling