Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	195×	body	80	valid
7.0ms	25×	body	2560	valid
3.0ms	12×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	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

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 (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.1b	(- (sqrt (+ (* re re) (* im im))) re)
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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))
13.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
167.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

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

prune215.0ms

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: 7.1b

Counts

101 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (- (hypot re im) re)))
1.1b	(- (hypot re im) re)

rewrite13.0ms

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:

8.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series236.0ms

Counts

2 → 6

Calls

2 calls:

177.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
58.0ms	(- (hypot re im) re)

simplify132.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (127.0ms)

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

prune104.0ms

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: 7.0b

Counts

53 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
14.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

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))

series379.0ms

Counts

2 → 6

Calls

2 calls:

238.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
141.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify52.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	135	250
1	408	217
2	1603	205
3	5001	200

prune87.0ms

Filtered

29 candidates to 25 candidates (86.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	28	6	34

Merged error: 7.0b

Counts

34 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
14.7b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite5.0ms

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:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series455.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (hypot re im))
106.0ms	(cbrt (hypot re im))
106.0ms	(cbrt (hypot re im))
136.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify144.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (133.0ms)

Iter	Nodes	Cost
0	84	329
1	188	287
2	663	279
3	3464	272
4	5001	263

prune175.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	60	7	67

Merged error: 7.0b

Counts

67 → 7

regimes84.0ms

Accuracy

22.4% (4.6b remaining)

Error of 11.7b against oracle of 7.2b and baseline of 13.1b

bsearch81.0ms

Steps

Iters	Range		Point
10	1.7693135749404962e+167	5.630928303641423e+177	6.309087312320916e+170

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

sample893.0ms

Algorithm

intervals

Results

295.0ms	6061×	body	80	valid
192.0ms	707×	body	2560	valid
104.0ms	457×	body	1280	valid
93.0ms	283×	body	5120	valid
48.0ms	278×	body	640	valid
19.0ms	145×	body	320	valid
6.0ms	69×	body	160	valid