Details

sample13.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
1.0ms	79×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 21.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
20.1b	(sqrt (+ (* x x) y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

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

series59.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (* x x) y)
41.0ms	(sqrt (+ (* x x) y))

simplify46.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	141	152
1	475	139
2	1515	138
3	5002	136

prune58.0ms

Filtered

32 candidates to 25 candidates (78.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 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` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

7.0ms

(* 1/2 (/ y x))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(* 1/2 (/ y x))

simplify64.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	164	128
1	727	118
2	2966	118
3	5001	118

prune49.0ms

Filtered

35 candidates to 24 candidates (68.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	35	4	39

Merged error: 0b

Counts

39 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

6.1b	(- (pow x 4) (pow y 2))
20.1b	(sqrt (/ (- (pow x 4) (pow y 2)) (- (* x x) y)))
36.5b	(/ (- (pow x 4) (pow y 2)) (- (* x x) y))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

222×	`add-sqr-sqrt`
153×	`difference-of-squares`
129×	`times-frac`
70×	`unpow-prod-down` `sqrt-prod` `sqr-pow`
66×	`*-un-lft-identity`
46×	`add-cube-cbrt`
30×	`unpow2`
16×	`associate-/l*`
10×	`distribute-lft-out--`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `associate-/r*` `associate-/r/` `flip--`
2×	`rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-sub` `div-exp` `clear-num`

Counts

3 → 208

Calls

3 calls:

10.0ms	(- (pow x 4) (pow y 2))
16.0ms	(sqrt (/ (- (pow x 4) (pow y 2)) (- (* x x) y)))
15.0ms	(/ (- (pow x 4) (pow y 2)) (- (* x x) y))

series170.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(- (pow x 4) (pow y 2))
78.0ms	(sqrt (/ (- (pow x 4) (pow y 2)) (- (* x x) y)))
52.0ms	(/ (- (pow x 4) (pow y 2)) (- (* x x) y))

simplify68.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	735	2622
1	2129	2347
2	5003	2193

prune334.0ms

Filtered

217 candidates to 118 candidates (54.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	217	4	221

Merged error: 0b

Counts

221 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

9.0ms

(* 1/2 (/ y x))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(* 1/2 (/ y x))

simplify65.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	164	128
1	727	118
2	2966	118
3	5001	118

prune41.0ms

Filtered

35 candidates to 24 candidates (68.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

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

Merged error: 0b

Counts

39 → 4

regimes136.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.1b

bsearch64.0ms

Steps

Iters	Range		Point
7	5.777920486632989e+96	1.0360182301372079e+99	8.910291731607776e+98
8	-2.9980302389965735e+156	-3.605266790381871e+152	-1.3322539688256998e+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

sample352.0ms

Algorithm

intervals

Results

141.0ms	8000×	body	80	valid
49.0ms	2694×	body	80	nan