Details

sample54.0ms

Algorithm

intervals

Results

45.0ms

256×

body

valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 38.9b

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

rewrite26.0ms

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))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series274.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
25.0ms	(+ (* x x) (* y y))
53.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
160.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (35.0ms)

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

prune306.0ms

Filtered

102 candidates to 84 candidates (82.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 18.4b

Counts

103 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
24×	`sqrt-prod`
22×	`times-frac` `associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
17×	`sqrt-div`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod` `hypot-def`
1×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`

Counts

4 → 108

Calls

4 calls:

17.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
16.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
165.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	1625
1	1505	1406
2	5001	1336

prune334.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	122	5	127

Merged error: 18.4b

Counts

127 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(fma z z (fma x x (* y y)))
0.1b	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
36.2b	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

rewrite9.0ms

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

series313.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma x x (* y y))
47.0ms	(fma z z (fma x x (* y y)))
55.0ms	(* 0.3333333333333333 (fma z z (fma x x (* y y))))
178.0ms	(sqrt (* 0.3333333333333333 (fma z z (fma x x (* y y)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	145	338
1	563	286
2	3080	286
3	5003	286

prune166.0ms

Filtered

67 candidates to 52 candidates (77.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Merged error: 8.3b

Counts

72 → 7

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))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite30.0ms

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))
8.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
29.0ms	(+ (* x x) (* y y))
228.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (38.0ms)

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

prune285.0ms

Filtered

127 candidates to 86 candidates (67.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	124	10	134

Merged error: 8.2b

Counts

134 → 10

regimes307.0ms

Accuracy

55.8% (10.3b remaining)

Error of 16.5b against oracle of 6.2b and baseline of 29.5b

bsearch76.0ms

Steps

Iters	Range		Point
10	1.0052274525735014e+135	5.72039747560308e+146	5.644210078755395e+146
9	-6.311616513999659e+143	-9.938214279124584e+135	-6.015427973878576e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample434.0ms

Algorithm

intervals

Results

269.0ms

8000×

body

valid