Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	181×	body	80	valid
10.0ms	30×	body	2560	valid
5.0ms	18×	body	1280	valid
3.0ms	7×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune175.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.8b	(+ (hypot re im) re)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

4.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series242.0ms

Counts

2 → 6

Calls

2 calls:

185.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
57.0ms	(+ (hypot re im) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	183	173
1	519	156
2	1741	150
3	5001	148

prune101.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.3b	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
0.8b	(+ (hypot re im) re)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ (hypot re im) re))
15.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series371.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(sqrt (+ (hypot re im) re))
194.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
54.0ms	(+ (hypot re im) re)

simplify107.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	287	433
1	995	403
2	4338	388
3	5001	387

prune194.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.2b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series556.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (hypot re im))
88.0ms	(sqrt (hypot re im))
243.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
137.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify78.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	194	379
1	555	327
2	2601	302
3	5001	300

prune174.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.9b

regimes69.0ms

Accuracy

24.2% (4.2b remaining)

Error of 11.6b against oracle of 7.5b and baseline of 13.0b

bsearch48.0ms

Steps

Iters	Range		Point
7	-2.1585595910751272e-09	-8.027944005163871e-11	-5.059081741722492e-10

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

410.0ms	6082×	body	80	valid
233.0ms	683×	body	2560	valid
134.0ms	479×	body	1280	valid
106.0ms	261×	body	5120	valid
55.0ms	255×	body	640	valid
28.0ms	162×	body	320	valid
9.0ms	78×	body	160	valid