Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-/r` `sum-log` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

3 → 67

Calls

3 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series253.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
166.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify114.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	259	758
1	1001	695
2	4269	689
3	5002	687

prune180.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Merged error: 19.3b

Counts

77 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.9b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

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

series250.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
52.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
163.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify40.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	244	469
1	1256	426
2	5002	424

prune141.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 19.3b

Counts

63 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

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

series353.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (+ (* x x) (* y y)) (* z z))
215.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify113.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	264	1246
1	989	1175
2	4707	1148
3	5002	1148

prune184.0ms

Filtered

100 candidates to 62 candidates (62.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	96	10	106

Merged error: 19.2b

Counts

106 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)
0.3b	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
28×	`cbrt-prod`
25×	`associate-r` `sqrt-prod`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`pow1` `cbrt-div` `associate-/l*`
4×	`add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l` `associate-/r*` `flip-+`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-div` `associate-r/` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)
12.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)
209.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
107.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	465	1855
1	1778	1748
2	5002	1729

prune379.0ms

Filtered

123 candidates to 109 candidates (88.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	123	10	133

Merged error: 19.2b

Counts

133 → 10

regimes436.0ms

Accuracy

64.5% (7.0b remaining)

Error of 25.3b against oracle of 18.3b and baseline of 38.0b

bsearch95.0ms

Steps

Iters	Range		Point
10	8.565423343579683e+117	8.152131796852354e+127	6.706873256878666e+122
11	-1.4185660712987705e+171	-7.633398144368219e+146	-9.469007215145339e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	13
1	31	13
2	31	13

end0.0ms

sample511.0ms

Algorithm

intervals

Results

346.0ms

8000×

body

valid