Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	207×	body	80	valid
3.0ms	18×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	5×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	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: 37.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

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:

28.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

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

prune187.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.3b	(- (hypot re im) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

0.0ms	(hypot re im)
10.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
3.0ms	(- (hypot re im) re)

series281.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(hypot re im)
177.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
57.0ms	(- (hypot re im) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	283	345
1	1118	247
2	5001	236

prune153.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
12.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

4 → 45

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
4.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

series459.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot re im)
46.0ms	(hypot re im)
233.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re)) 0)))
135.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

simplify38.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	207	358
1	759	315
2	5001	299

prune222.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
12.1b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (* -1 re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (* -1 re))

series476.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (hypot re im))
109.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
142.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (* -1 re))

simplify157.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	105	393
1	266	348
2	917	340
3	4671	322
4	5001	322

prune275.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.0b

regimes73.0ms

Accuracy

26.8% (4.1b remaining)

Error of 11.2b against oracle of 7.1b and baseline of 12.7b

bsearch52.0ms

Steps

Iters	Range		Point
8	1.9386486951852963e+68	6.310868864655015e+71	7.848622788519904e+68

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample653.0ms

Algorithm

intervals

Results

202.0ms	6096×	body	80	valid
121.0ms	637×	body	2560	valid
72.0ms	296×	body	5120	valid
70.0ms	443×	body	1280	valid
36.0ms	303×	body	640	valid
13.0ms	146×	body	320	valid
5.0ms	79×	body	160	valid