Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
4.0ms	21×	body	2560	valid
3.0ms	18×	body	1280	valid
2.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	6×	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: 40.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
28.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
25.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
166.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune234.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
1.5b	(- (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)))
3.0ms	(- (hypot re im) re)

series237.0ms

Counts

2 → 6

Calls

2 calls:

179.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
57.0ms	(- (hypot re im) re)

simplify44.0ms

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

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

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)))
1.5b	(- (hypot re im) re)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `associate-r`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 83

Calls

3 calls:

7.0ms	(sqrt (- (hypot re im) re))
13.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
3.0ms	(- (hypot re im) re)

series353.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(sqrt (- (hypot re im) re))
178.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
54.0ms	(- (hypot re im) re)

simplify44.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	590
1	1250	494
2	5002	482

prune217.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))
0.3b	(* (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))) (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
1.5b	(- (hypot re im) re)
1.5b	(- (hypot re im) re)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

11.0ms	(sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))
82.0ms	(* (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))) (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)

series529.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))
183.0ms	(* (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))) (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
57.0ms	(- (hypot re im) re)
55.0ms	(- (hypot re im) re)

simplify89.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	486	1300
1	2225	1060
2	5001	1032

prune376.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.2b

regimes80.0ms

Accuracy

29% (4.3b remaining)

Error of 11.5b against oracle of 7.3b and baseline of 13.3b

bsearch72.0ms

Steps

Iters	Range		Point
10	9.764437526151242e+129	2.993516045954254e+140	3.126606582428133e+130

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

sample683.0ms

Algorithm

intervals

Results

208.0ms	6029×	body	80	valid
143.0ms	701×	body	2560	valid
76.0ms	471×	body	1280	valid
70.0ms	290×	body	5120	valid
39.0ms	268×	body	640	valid
15.0ms	158×	body	320	valid
5.0ms	83×	body	160	valid