Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
7.0ms	27×	body	2560	valid
3.0ms	10×	body	5120	valid
3.0ms	13×	body	1280	valid
1.0ms	5×	body	640	valid
0.0ms	1×	body	320	valid

simplify10.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(- (sqrt (+ (* re re) (* im im))) re)
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

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:

4.0ms	(+ (* re re) (* im im))
11.0ms	(- (sqrt (+ (* re re) (* im im))) re)
14.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
170.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5002	533

prune213.0ms

Filtered

100 candidates to 72 candidates (72.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 6.8b

Counts

101 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (- (hypot re im) re)))
0.0b	(- (hypot re im) re)

rewrite16.0ms

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` `flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

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

series235.0ms

Counts

2 → 6

Calls

2 calls:

180.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
55.0ms	(- (hypot re im) re)

simplify139.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	221	312
1	728	227
2	4440	212
3	5001	202

prune105.0ms

Filtered

49 candidates to 37 candidates (75.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	48	5	53

Merged error: 6.8b

Counts

53 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3)) (- re re))))
0.5b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
8.1b	(fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
8×	`pow1`
6×	`unpow-prod-down` `cube-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `sqrt-pow1` `pow1/3` `sqrt-div` `associate-*r/`
1×	`cube-mult` `pow-to-exp` `flip3-+` `pow1/2` `unpow3` `pow-prod-down` `pow-exp` `sqrt-prod` `flip-+` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

8.0ms	(sqrt (* 2.0 (+ (fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3)) (- re re))))
1.0ms	(cbrt (hypot re im))
3.0ms	(pow (cbrt (hypot re im)) 3)
1.0ms	(fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3))

series458.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (* 2.0 (+ (fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3)) (- re re))))
113.0ms	(cbrt (hypot re im))
83.0ms	(pow (cbrt (hypot re im)) 3)
93.0ms	(fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	327	502
1	1223	454
2	5003	418

prune229.0ms

Filtered

82 candidates to 60 candidates (73.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	80	7	87

Merged error: 6.8b

Counts

87 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
13.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite7.0ms

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

Counts

4 → 53

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series568.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (hypot re im))
87.0ms	(sqrt (hypot re im))
247.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
145.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify93.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	200	404
1	587	351
2	2835	329
3	5001	327

prune168.0ms

Filtered

65 candidates to 53 candidates (81.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	64	8	72

Merged error: 6.8b

Counts

72 → 8

regimes93.0ms

Accuracy

22.2% (4.5b remaining)

Error of 11.7b against oracle of 7.2b and baseline of 12.9b

bsearch68.0ms

Steps

Iters	Range		Point
8	6.833758105093816e+192	4.345875884008889e+195	4.848051965026175e+194

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample895.0ms

Algorithm

intervals

Results

295.0ms	6077×	body	80	valid
186.0ms	692×	body	2560	valid
109.0ms	487×	body	1280	valid
92.0ms	272×	body	5120	valid
43.0ms	248×	body	640	valid
18.0ms	139×	body	320	valid
9.0ms	85×	body	160	valid