Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	192×	body	80	valid
4.0ms	21×	body	2560	valid
4.0ms	8×	body	640	valid
3.0ms	18×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	7×	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: 41.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

14.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series253.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

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

prune208.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 8.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
0.6b	(- (* 1 (hypot re im)) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
4.0ms	(- (* 1 (hypot re im)) re)

series242.0ms

Counts

2 → 6

Calls

2 calls:

183.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
59.0ms	(- (* 1 (hypot re im)) re)

simplify142.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	219	241
1	758	199
2	4930	190
3	5001	190

prune113.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 2.0 (fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))))
15.7b	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
31.6b	(sqrt (+ (* re re) (* im im)))
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

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` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `hypot-def`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 59

Calls

4 calls:

3.0ms	(sqrt (* 2.0 (fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))))
1.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (* 2.0 (fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))))
95.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	212	588
1	740	514
2	2506	503
3	5001	501

prune286.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 8.4b

localize23.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (* re re) (* im im)))
31.6b	(sqrt (+ (* re re) (* im im)))
31.6b	(sqrt (+ (* re re) (* im im)))
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `hypot-def` `log1p-expm1-u` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	412
1	254	392
2	619	392
3	1573	392
4	5001	392

prune511.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.4b

regimes98.0ms

Accuracy

13% (5.0b remaining)

Error of 12.8b against oracle of 7.8b and baseline of 13.5b

bsearch105.0ms

Steps

Iters	Range		Point
6	1.4438967309753967e+154	1.0661150064925747e+155	4.9019714476158837e+154
10	5.610934862378552e-46	2.6486499677985105e-30	1.4512261620833975e-30

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	14
1	43	14
2	43	14

end0.0ms

sample694.0ms

Algorithm

intervals

Results

203.0ms	5986×	body	80	valid
147.0ms	731×	body	2560	valid
78.0ms	466×	body	1280	valid
76.0ms	301×	body	5120	valid
38.0ms	282×	body	640	valid
14.0ms	150×	body	320	valid
5.0ms	84×	body	160	valid