Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

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

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 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.3b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite21.0ms

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))

series246.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
52.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
159.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (116.0ms)

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

prune191.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	7	77

Merged error: 17.3b

Counts

77 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
37.3b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite23.0ms

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))
8.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
7.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series281.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
190.0ms	(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

prune113.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	57	7	64

Merged error: 17.3b

Counts

64 → 7

localize18.0ms

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)))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
122×	`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×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

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)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
166.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
98.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify68.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	391	2965
1	1318	2831
2	5002	2779

prune395.0ms

Filtered

168 candidates to 108 candidates (64.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	168	7	175

Merged error: 17.3b

Counts

175 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
0.4b	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
38.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
38.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
72×	`times-frac`
62×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`associate-/r` `associate-/l`
8×	`add-exp-log` `cbrt-div`
4×	`pow1` `flip3-+` `add-cbrt-cube` `flip-+` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `pow1/3` `div-exp` `clear-num` `div-inv`

Counts

4 → 150

Calls

4 calls:

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

series650.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
223.0ms	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
109.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify79.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	295	2354
1	1094	2290
2	5001	2276

prune628.0ms

Filtered

162 candidates to 148 candidates (91.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	162	7	169

Merged error: 17.3b

Counts

169 → 7

regimes467.0ms

Accuracy

54.1% (9.0b remaining)

Error of 26.9b against oracle of 17.9b and baseline of 37.5b

bsearch110.0ms

Steps

Iters	Range		Point
9	3.49360888869625e+131	3.351355619502645e+138	4.9296672245653324e+135
7	-5.530494810296786e-229	-3.8841983415636587e-231	-4.6992675325234154e-229
6	-2.612645209590514e-104	-5.091613400763011e-105	-5.1573652837714696e-105
4	-2.515916130415698e+129	-1.8012913134826672e+129	-2.0469435943033968e+129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	41	21
2	41	21

end0.0ms

sample429.0ms

Algorithm

intervals

Results

264.0ms

8000×

body

valid