Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	192×	body	80	valid
5.0ms	21×	body	2560	valid
3.0ms	10×	body	5120	valid
3.0ms	13×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	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: 38.9b

Counts

2 → 1

localize14.0ms

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)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
9.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
181.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune211.0ms

Filtered

79 candidates to 69 candidates (87.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 7.8b

Counts

80 → 6

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (hypot re im) re)
0.2b	(sqrt (* 2.0 (+ (hypot re im) re)))

rewrite13.0ms

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:

3.0ms	(+ (hypot re im) re)
9.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))

series242.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(+ (hypot re im) re)
188.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (50.0ms)

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

prune95.0ms

Filtered

38 candidates to 34 candidates (89.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Merged error: 7.6b

Counts

44 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.2b	(+ (hypot re im) re)
0.3b	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))

rewrite17.0ms

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:

3.0ms	(sqrt (+ (hypot re im) re))
3.0ms	(+ (hypot re im) re)
8.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))

series376.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(sqrt (+ (hypot re im) re))
61.0ms	(+ (hypot re im) re)
187.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))

simplify108.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (102.0ms)

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

prune170.0ms

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: 7.6b

Counts

86 → 6

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
15.6b	(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)

series389.0ms

Counts

2 → 6

Calls

2 calls:

245.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
143.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify46.0ms

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

prune70.0ms

Filtered

29 candidates to 24 candidates (82.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	26	9	35

Merged error: 7.6b

Counts

35 → 9

regimes139.0ms

Accuracy

-1.6% (6.1b remaining)

Error of 13.4b against oracle of 7.3b and baseline of 13.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	21
1	39	21
2	39	21

end0.0ms

sample900.0ms

Algorithm

intervals

Results

284.0ms	6010×	body	80	valid
190.0ms	701×	body	2560	valid
107.0ms	490×	body	1280	valid
94.0ms	289×	body	5120	valid
49.0ms	272×	body	640	valid
19.0ms	150×	body	320	valid
8.0ms	88×	body	160	valid