Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

prune3.0ms

Filtered

1 candidates to 0 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: 38.7b

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))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
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 → 78

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* 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))

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
12.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
28.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune146.0ms

Filtered

90 candidates to 71 candidates (21.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 22.4b

Counts

91 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.7b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3-+` `associate-*r/` `sum-log` `flip-+`
3×	`associate-r` `associate-l`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

5.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
7.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
12.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
26.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify42.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	310	539
1	1615	492
2	5001	492

prune91.0ms

Filtered

71 candidates to 50 candidates (29.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 22.4b

Counts

77 → 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))
35.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

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))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
29.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	330	1316
1	1338	1241
2	5002	1218

prune137.0ms

Filtered

114 candidates to 73 candidates (36.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 22.3b

Counts

120 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0b	(exp (log (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
35.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

81×	`sqrt-prod`
72×	`times-frac`
60×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
40×	`log-prod` `exp-sum`
6×	`pow1` `add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`exp-prod` `sqrt-div`
3×	`flip3-+` `flip-+`
2×	`div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `log-div` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `exp-diff` `div-exp` `clear-num` `sum-log` `log-pow` `rem-exp-log`

Counts

4 → 142

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
10.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
10.0ms	(exp (log (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
29.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
32.0ms	(exp (log (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	461	2082
1	1549	1970
2	5001	1901

prune171.0ms

Filtered

154 candidates to 89 candidates (42.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	151	12	163

Merged error: 22.3b

Counts

163 → 12

regimes1.1s

Accuracy

62.9% (7.3b remaining)

Error of 25.7b against oracle of 18.5b and baseline of 38.0b

bsearch33.0ms

Steps

Iters	Range		Point
7	4.5942725875421524e+67	4.2361412570822106e+69	4.1482053798994166e+69
9	-8.861200960569297e+116	-1.4734112449091008e+108	-3.8835198140411694e+114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	33	12
2	33	12

end0.0ms

sample669.0ms

Algorithm

intervals

Results

379.0ms

8000×

body

valid

Details

sample23.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite25.0ms

series55.0ms

simplify37.0ms

prune146.0ms

localize9.0ms

rewrite23.0ms

series54.0ms

simplify42.0ms

prune91.0ms

localize10.0ms

rewrite30.0ms

series63.0ms

simplify45.0ms

prune137.0ms

localize14.0ms

rewrite34.0ms

series85.0ms

simplify51.0ms

prune171.0ms

regimes1.1s

bsearch33.0ms

simplify2.0ms

end0.0ms

sample669.0ms

Profiling