Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	208×	body	80	valid
5.0ms	14×	body	5120	valid
4.0ms	14×	body	2560	valid
3.0ms	12×	body	1280	valid
1.0ms	3×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	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: 35.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt` `sqrt-prod`
6×	`add-cube-cbrt` `fma-def`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out`

Counts

3 → 53

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune170.0ms

Filtered

62 candidates to 56 candidates (90.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	57	5	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	5	63

Merged error: 5.0b

Counts

63 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.7b	(+ (hypot re im) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series245.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
59.0ms	(+ (hypot re im) re)

simplify53.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	183	173
1	519	156
2	1741	150
3	5001	148

prune98.0ms

Filtered

38 candidates to 34 candidates (89.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	37	6	43

Merged error: 5.0b

Counts

43 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.4b	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
0.7b	(+ (hypot re im) re)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
9×	`add-cube-cbrt`
8×	`pow1`
7×	`associate-r`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

3 → 71

Calls

3 calls:

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

series367.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(sqrt (+ (hypot re im) re))
186.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
59.0ms	(+ (hypot re im) re)

simplify110.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	287	433
1	995	403
2	4338	388
3	5001	387

prune168.0ms

Filtered

80 candidates to 61 candidates (76.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	80	6	86

Merged error: 5.0b

Counts

86 → 6

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
11.7b	(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)

series371.0ms

Counts

2 → 6

Calls

2 calls:

230.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
140.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	129	225
1	378	193
2	1445	178
3	5002	174

prune69.0ms

Filtered

29 candidates to 24 candidates (82.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	29	6	35

Merged error: 5.0b

Counts

35 → 6

regimes95.0ms

Accuracy

22.8% (4.7b remaining)

Error of 11.8b against oracle of 7.1b and baseline of 13.2b

bsearch54.0ms

Steps

Iters	Range		Point
7	-2.614450835621939e+149	-7.000880430181569e+147	-5.478528329622074e+148

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample870.0ms

Algorithm

intervals

Results

281.0ms	6071×	body	80	valid
188.0ms	686×	body	2560	valid
101.0ms	475×	body	1280	valid
85.0ms	265×	body	5120	valid
46.0ms	273×	body	640	valid
22.0ms	152×	body	320	valid
7.0ms	78×	body	160	valid