Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	202×	body	80	valid
6.0ms	26×	body	2560	valid
1.0ms	9×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
17×	`sqrt-prod`
7×	`pow1`
6×	`fma-neg`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

3 → 74

Calls

3 calls:

30.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
26.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.6b	(- (hypot re im) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

10.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
4.0ms	(- (hypot re im) re)

series241.0ms

Counts

2 → 6

Calls

2 calls:

185.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
56.0ms	(- (hypot re im) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	273	321
1	1082	232
2	5001	228

prune121.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`sqrt-prod`
27×	`add-cube-cbrt`
20×	`pow1`
18×	`prod-diff`
14×	`sqrt-div`
12×	`swap-sqr`
9×	`flip3--` `sqrt-pow1` `pow1/2` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l` `add-log-exp`
7×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

8.0ms	(sqrt (- (hypot re im) re))
22.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)

series291.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (- (hypot re im) re))
58.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
58.0ms	(- (hypot re im) re)
55.0ms	(- (hypot re im) re)

simplify49.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	286	899
1	1123	706
2	5001	691

prune358.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)
0.7b	(pow (cbrt (sqrt (- (hypot re im) re))) 4)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`prod-diff`
11×	`unpow-prod-down`
10×	`add-log-exp`
9×	`fma-neg`
8×	`cbrt-prod`
5×	`pow1` `add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `flip3--` `diff-log` `flip--`
2×	`pow-pow`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)
6.0ms	(pow (cbrt (sqrt (- (hypot re im) re))) 4)

series366.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (hypot re im) re)
58.0ms	(- (hypot re im) re)
59.0ms	(- (hypot re im) re)
193.0ms	(pow (cbrt (sqrt (- (hypot re im) re))) 4)

simplify43.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	308	863
1	1038	626
2	5002	618

prune423.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.8b

regimes116.0ms

Accuracy

29.8% (4.1b remaining)

Error of 12.1b against oracle of 8.0b and baseline of 13.8b

bsearch19.0ms

Steps

Iters	Range		Point
3	4.605582192120401e-79	5.65622905522155e-79	5.541062179101876e-79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	33	14

end0.0ms

sample764.0ms

Algorithm

intervals

Results

226.0ms	5949×	body	80	valid
165.0ms	736×	body	2560	valid
86.0ms	489×	body	1280	valid
83.0ms	301×	body	5120	valid
43.0ms	291×	body	640	valid
20.0ms	163×	body	320	valid
5.0ms	71×	body	160	valid