Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	192×	body	80	valid
5.0ms	25×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	9×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	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: 39.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
31.4b	(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))
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)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* re re) (* im im))
179.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
41.0ms	(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

prune241.0ms

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: 8.6b

Counts

101 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (- (hypot re im) re)))
0.7b	(- (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)

series251.0ms

Counts

2 → 6

Calls

2 calls:

189.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
62.0ms	(- (hypot re im) re)

simplify132.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (126.0ms)

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

prune122.0ms

Filtered

49 candidates to 36 candidates (73.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	47	6	53

Merged error: 8.3b

Counts

53 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.3b	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
0.7b	(- (hypot re im) re)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `associate-r`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 83

Calls

3 calls:

4.0ms	(sqrt (- (hypot re im) re))
9.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series385.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(sqrt (- (hypot re im) re))
193.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
61.0ms	(- (hypot re im) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	338	590
1	1250	494
2	5002	482

prune218.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Merged error: 8.3b

Counts

98 → 5

localize15.0ms

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))
12.0b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
9.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series408.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
118.0ms	(cbrt (hypot re im))
61.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify95.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	167	446
1	570	322
2	2968	294
3	5001	292

prune255.0ms

Filtered

69 candidates to 59 candidates (85.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	66	8	74

Merged error: 8.3b

Counts

74 → 8

regimes101.0ms

Accuracy

20.7% (4.7b remaining)

Error of 12.0b against oracle of 7.3b and baseline of 13.2b

bsearch165.0ms

Steps

Iters	Range		Point
9	5.72039747560308e+146	1.3412804874082685e+153	2.2835215283316402e+148
7	3.846365557906961e+79	1.182396247124819e+81	2.518487263438123e+80
8	1.7517637380581486e+18	3.775313734612271e+22	5.662390610560372e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	36	26
1	41	13
2	44	13
3	44	13

end0.0ms

sample694.0ms

Algorithm

intervals

Results

207.0ms	6020×	body	80	valid
146.0ms	728×	body	2560	valid
79.0ms	475×	body	1280	valid
69.0ms	274×	body	5120	valid
40.0ms	287×	body	640	valid
14.0ms	130×	body	320	valid
5.0ms	86×	body	160	valid