Details

sample18.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
3.0ms	281×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

prune2.0ms

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: 0.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (+ x y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `sqrt-div`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `hypot-def` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 19

Calls

1 calls:

4.0ms

(sqrt (+ x y))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(sqrt (+ x y))

simplify73.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	120	95
1	299	86
2	963	83
3	2862	78
4	5001	78

prune32.0ms

Filtered

22 candidates to 17 candidates (22.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Merged error: 0b

Counts

23 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ x y)))
0.4b	(* (fabs (cbrt (+ x y))) (sqrt (cbrt (+ x y))))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`cbrt-prod`
16×	`sqrt-prod`
12×	`add-cube-cbrt`
10×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

4.0ms	(sqrt (cbrt (+ x y)))
8.0ms	(* (fabs (cbrt (+ x y))) (sqrt (cbrt (+ x y))))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))

series599.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt (cbrt (+ x y)))
191.0ms	(* (fabs (cbrt (+ x y))) (sqrt (cbrt (+ x y))))
131.0ms	(cbrt (+ x y))
126.0ms	(cbrt (+ x y))

simplify119.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	323	657
1	1088	622
2	4431	614
3	5001	614

prune202.0ms

Filtered

98 candidates to 81 candidates (17.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* y y) (* x y))
6.2b	(hypot (pow y 3/2) (pow x 3/2))
10.5b	(/ (hypot (pow y 3/2) (pow x 3/2)) (sqrt (+ (* x x) (- (* y y) (* x y)))))
27.6b	(sqrt (+ (* x x) (- (* y y) (* x y))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

293×	`*-un-lft-identity`
234×	`add-sqr-sqrt`
180×	`prod-diff`
153×	`associate-l`
142×	`add-cube-cbrt`
93×	`associate-r`
65×	`sqrt-prod`
50×	`distribute-lft-out`
48×	`times-frac`
46×	`distribute-lft-out--`
42×	`swap-sqr`
36×	`*-commutative` `unswap-sqr`
16×	`associate-/r*`
15×	`fma-neg`
10×	`difference-of-squares`
8×	`distribute-rgt-out--`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `hypot-def`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`associate-/l*`
2×	`hypot-udef` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 359

Calls

4 calls:

20.0ms	(- (* y y) (* x y))
1.0ms	(hypot (pow y 3/2) (pow x 3/2))
41.0ms	(/ (hypot (pow y 3/2) (pow x 3/2)) (sqrt (+ (* x x) (- (* y y) (* x y)))))
56.0ms	(sqrt (+ (* x x) (- (* y y) (* x y))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* y y) (* x y))
207.0ms	(hypot (pow y 3/2) (pow x 3/2))
287.0ms	(/ (hypot (pow y 3/2) (pow x 3/2)) (sqrt (+ (* x x) (- (* y y) (* x y)))))
67.0ms	(sqrt (+ (* x x) (- (* y y) (* x y))))

simplify119.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	971	4761
1	3208	3185
2	5001	2907

prune333.0ms

Filtered

371 candidates to 103 candidates (72.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	371	0	371
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	371	3	374

Merged error: 0b

Counts

374 → 3

regimes70.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

end0.0ms

sample452.0ms

Algorithm

intervals

Results

118.0ms	8000×	body	80	valid
99.0ms	7997×	body	80	nan