Details

sample20.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
3.0ms	100×	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: 18.3b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
17.1b	(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:

18.0ms	(+ (* x x) y)
45.0ms	(sqrt (+ (* x x) y))

simplify55.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (52.0ms)

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

prune99.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

17.1b	(sqrt (* (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y))))
17.9b	(cbrt (+ (* x x) y))
17.9b	(cbrt (+ (* x x) y))
17.9b	(cbrt (+ (* x x) y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

36.0ms	(sqrt (* (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y))))
2.0ms	(cbrt (+ (* x x) y))
2.0ms	(cbrt (+ (* x x) y))
3.0ms	(cbrt (+ (* x x) y))

series285.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (* (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y))))
79.0ms	(cbrt (+ (* x x) y))
80.0ms	(cbrt (+ (* x x) y))
80.0ms	(cbrt (+ (* x x) y))

simplify145.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	318	1273
1	738	1232
2	3000	1213
3	5001	1146

prune244.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune5.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

9.4b	(* (* x x) y)
10.6b	(hypot (pow y 3/2) (pow x 3))
17.2b	(/ (hypot (pow y 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y)))))
20.1b	(sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`associate-/r*`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`hypot-udef` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `associate-l` `clear-num` `*-commutative` `hypot-def` `div-inv` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

7.0ms	(* (* x x) y)
0.0ms	(hypot (pow y 3/2) (pow x 3))
36.0ms	(/ (hypot (pow y 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y)))))
31.0ms	(sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y))))

series1.6s

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* x x) y)
306.0ms	(hypot (pow y 3/2) (pow x 3))
1.3s	(/ (hypot (pow y 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y)))))
61.0ms	(sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y))))

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	419	1377
1	1813	1277
2	5002	1261

prune323.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes169.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.8b

bsearch26.0ms

Steps

Iters	Range		Point
0	5.935778912611107e+140	5.966704354637365e+140	5.951241633624236e+140
7	-1.5931363873182533e+155	-1.016503209116054e+153	-1.3348711429761005e+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

sample538.0ms

Algorithm

intervals

Results

276.0ms	8000×	body	80	valid
90.0ms	2700×	body	80	nan