Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	198×	body	80	valid
3.0ms	17×	body	2560	valid
2.0ms	15×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	10×	body	640	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sqrt (+ (* re re) (* im im))) re)
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 59

Calls

2 calls:

49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series80.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	211	590
1	687	366
2	3279	321
3	5001	295

prune140.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.1b

localize9.0ms

Local error

Found 1 expressions with local error:

1.1b	(- (hypot re im) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

9.0ms

(- (hypot re im) re)

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(- (hypot re im) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	119	199
1	333	125
2	1490	116
3	5001	85

prune72.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.9b

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)))
1.1b	(- (hypot re im) re)
1.1b	(- (hypot re im) re)

rewrite67.0ms

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:

9.0ms	(sqrt (- (hypot re im) re))
40.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
6.0ms	(- (hypot re im) re)
6.0ms	(- (hypot re im) re)

series278.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (- (hypot re im) re))
55.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
55.0ms	(- (hypot re im) re)
52.0ms	(- (hypot re im) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (36.0ms)

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

prune339.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.9b

localize12.0ms

Local error

Found 1 expressions with local error:

14.4b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series132.0ms

Counts

1 → 3

Calls

1 calls:

132.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify52.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	48	100
1	133	85
2	439	82
3	1931	78
4	5001	78

prune40.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.9b

regimes162.0ms

Accuracy

18.7% (4.9b remaining)

Error of 12.1b against oracle of 7.2b and baseline of 13.2b

bsearch129.0ms

Steps

Iters	Range		Point
8	3.304685596646942e+248	2.4340545909919966e+252	3.360843720164908e+248
6	1.6488320848514274e+131	1.765052389435011e+132	9.353483842517877e+131
7	7732.291311132395	674633.4983844218	122037.34724714007

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	35	26
1	40	13
2	43	13
3	43	13

end0.0ms

sample694.0ms

Algorithm

intervals

Results

199.0ms	6017×	body	80	valid
128.0ms	680×	body	2560	valid
74.0ms	506×	body	1280	valid
63.0ms	285×	body	5120	valid
31.0ms	266×	body	640	valid
13.0ms	150×	body	320	valid
6.0ms	96×	body	160	valid