Details

sample16.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	88×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

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: 25.1b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

23.4b

(sqrt (+ (* x x) y))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

4.0ms

(sqrt (+ (* x x) y))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(sqrt (+ (* x x) y))

simplify140.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	116	95
1	334	90
2	997	89
3	3969	87
4	5002	87

prune38.0ms

Filtered

18 candidates to 15 candidates (83.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Merged error: 0b

Counts

19 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (+ (* x x) y)) 3)
23.4b	(sqrt (+ (* x x) y))
36.4b	(cbrt (pow (sqrt (+ (* x x) y)) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
15×	`add-sqr-sqrt` `sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `cube-div` `add-cbrt-cube`
3×	`pow-unpow` `pow-pow` `flip3-+` `flip-+` `add-log-exp`
2×	`cube-mult` `cbrt-div` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 78

Calls

3 calls:

6.0ms	(pow (sqrt (+ (* x x) y)) 3)
4.0ms	(sqrt (+ (* x x) y))
6.0ms	(cbrt (pow (sqrt (+ (* x x) y)) 3))

series136.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(pow (sqrt (+ (* x x) y)) 3)
43.0ms	(sqrt (+ (* x x) y))
51.0ms	(cbrt (pow (sqrt (+ (* x x) y)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	276	487
1	952	459
2	5001	446

prune122.0ms

Filtered

87 candidates to 48 candidates (55.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0b

Counts

91 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))
0.0b	(* 1/2 (/ y x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

3.0ms	(+ x (* 1/2 (/ y x)))
9.0ms	(* 1/2 (/ y x))

series40.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ x (* 1/2 (/ y x)))
17.0ms	(* 1/2 (/ y x))

simplify115.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	223	199
1	960	187
2	4238	187
3	5001	187

prune64.0ms

Filtered

49 candidates to 34 candidates (69.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	49	4	53

Merged error: 0b

Counts

53 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))
0.0b	(* 1/2 (/ y x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

3.0ms	(+ x (* 1/2 (/ y x)))
7.0ms	(* 1/2 (/ y x))

series45.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ x (* 1/2 (/ y x)))
18.0ms	(* 1/2 (/ y x))

simplify107.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	223	199
1	960	187
2	4238	187
3	5001	187

prune71.0ms

Filtered

49 candidates to 34 candidates (69.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	49	4	53

Merged error: 0b

Counts

53 → 4

regimes177.0ms

Accuracy

98.1% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.1b

bsearch50.0ms

Steps

Iters	Range		Point
6	1.8621764492367103e+67	9.629142787391428e+67	9.527858290068734e+67
9	-1.6711135734881002e+155	-6.126904703272576e+149	-1.3580393227713455e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	10
1	29	10
2	31	10
3	31	10

end0.0ms

sample433.0ms

Algorithm

intervals

Results

200.0ms	8000×	body	80	valid
63.0ms	2618×	body	80	nan