Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	81×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	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: 19.8b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
18.4b	(sqrt (+ (* x x) y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

4.0ms	(+ (* x x) y)
4.0ms	(sqrt (+ (* x x) y))

series63.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* x x) y)
44.0ms	(sqrt (+ (* x x) y))

simplify53.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	153	160
1	518	146
2	1716	138
3	5002	136

prune75.0ms

Filtered

38 candidates to 32 candidates (84.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Merged error: 0b

Counts

39 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (+ (* x x) y))) (cbrt (sqrt (+ (* x x) y))))
18.4b	(sqrt (+ (* x x) y))
18.4b	(sqrt (+ (* x x) y))
18.4b	(sqrt (+ (* x x) y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`cbrt-prod`
29×	`sqrt-prod`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`sqrt-div`
14×	`pow1`
12×	`cbrt-div`
11×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `flip-+` `unswap-sqr`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

14.0ms	(* (cbrt (sqrt (+ (* x x) y))) (cbrt (sqrt (+ (* x x) y))))
4.0ms	(sqrt (+ (* x x) y))
4.0ms	(sqrt (+ (* x x) y))
4.0ms	(sqrt (+ (* x x) y))

series209.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cbrt (sqrt (+ (* x x) y))) (cbrt (sqrt (+ (* x x) y))))
45.0ms	(sqrt (+ (* x x) y))
40.0ms	(sqrt (+ (* x x) y))
44.0ms	(sqrt (+ (* x x) y))

simplify113.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	247	1192
1	837	1127
2	3497	1049
3	5001	1005

prune290.0ms

Filtered

132 candidates to 96 candidates (72.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0b

Counts

136 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

7.0ms

(* 1/2 (/ y x))

series21.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(* 1/2 (/ y x))

simplify67.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	166	139
1	729	124
2	2968	124
3	5001	124

prune50.0ms

Filtered

37 candidates to 26 candidates (70.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	37	4	41

Merged error: 0b

Counts

41 → 4

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify6.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Merged error: 0b

Counts

4 → 4

regimes172.0ms

Accuracy

94.5% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 21.3b

bsearch43.0ms

Steps

Iters	Range		Point
6	0.045458023638768046	0.475758948552502	0.46902383324435853
8	-1.588426443043857e+156	-5.982939677522135e+153	-1.3183108293052407e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	30	9
2	32	9
3	32	9

end0.0ms

sample352.0ms

Algorithm

intervals

Results

150.0ms	8000×	body	80	valid
40.0ms	2540×	body	80	nan