Details

sample17.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	9
1	36	9
2	68	9
3	117	9
4	174	9
5	195	9
6	197	9
7	197	9

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: 30.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
4.7b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

4.0ms	(+ (* x x) (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
40.0ms	(- (* x x) (* (* y 4.0) y))
63.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify36.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	234	680
1	1007	622
2	5001	620

prune107.0ms

Filtered

64 candidates to 49 candidates (76.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	5	65

Merged error: 0.1b

Counts

65 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3))
0.0b	(pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3)
4.7b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`cbrt-prod`
30×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 140

Calls

4 calls:

8.0ms	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3))
8.0ms	(pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3)
3.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3))
72.0ms	(pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3)
40.0ms	(- (* x x) (* (* y 4.0) y))
63.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	482	2261
1	2419	2131
2	5002	2116

prune213.0ms

Filtered

152 candidates to 84 candidates (55.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	152	5	157

Merged error: 0.1b

Counts

157 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b	(- (* x x) (* (* y 4.0) y))
28.6b	(sqrt (+ (* x x) (* (* y 4.0) y)))
28.6b	(sqrt (+ (* x x) (* (* y 4.0) y)))
28.7b	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* x x) (* (* y 4.0) y))
3.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
3.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
9.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* x x) (* (* y 4.0) y))
49.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
52.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
98.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

simplify165.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	274	1117
1	1020	1045
2	4854	1032
3	5002	1032

prune236.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	98	5	103

Merged error: 0.1b

Counts

103 → 5

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	3	3
Total	5	5

Merged error: 0.1b

Counts

5 → 5

regimes158.0ms

Accuracy

56.4% (13.8b remaining)

Error of 14.2b against oracle of 0.4b and baseline of 32.0b

bsearch51.0ms

Steps

Iters	Range		Point
3	1.8258022505594032e+219	2.2962424587188664e+219	2.0904248676491008e+219
10	2.716379892692296e+59	2.1905246858573327e+69	2.4050824137629305e+64
3	1.0888580463863271e-113	1.4549328360334433e-113	1.418892650785543e-113
0	0.0	3.95252516673e-323	1.976262583365e-323

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	37
1	36	37

end0.0ms

sample414.0ms

Algorithm

intervals

Results

282.0ms

8000×

body

valid