Details

sample19.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	69×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.4b	(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:

3.0ms	(+ (* x x) y)
5.0ms	(sqrt (+ (* x x) y))

series63.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (48.0ms)

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

prune92.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(hypot x (pow y 1/2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `hypot-udef` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot x (pow y 1/2))

series86.0ms

Counts

1 → 3

Calls

1 calls:

86.0ms

(hypot x (pow y 1/2))

simplify125.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	67	50
1	162	41
2	598	40
3	2964	39
4	5001	39

prune36.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (cbrt (+ (* x x) y)))
0.3b	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
20.2b	(cbrt (+ (* x x) y))
20.2b	(cbrt (+ (* x x) y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`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` `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 → 82

Calls

4 calls:

5.0ms	(sqrt (cbrt (+ (* x x) y)))
14.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
7.0ms	(cbrt (+ (* x x) y))
3.0ms	(cbrt (+ (* x x) y))

series328.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (cbrt (+ (* x x) y)))
95.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
79.0ms	(cbrt (+ (* x x) y))
80.0ms	(cbrt (+ (* x x) y))

simplify96.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	269	751
1	945	703
2	3606	694
3	5001	687

prune267.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize4.0ms

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 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

94.5% (1.2b remaining)

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

bsearch59.0ms

Steps

Iters	Range		Point
7	1.1608947055862536e+73	1.608126041204279e+75	1.381207891657496e+75
9	-1.0613399251863006e+82	-6.9458542767114855e+72	-9.936810330166151e+81

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	15
1	34	15
2	36	15
3	36	15

end0.0ms

sample540.0ms

Algorithm

intervals

Results

283.0ms	8000×	body	80	valid
86.0ms	2539×	body	80	nan