Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
5.0ms	25×	body	2560	valid
3.0ms	16×	body	1280	valid
1.0ms	12×	body	640	valid
1.0ms	6×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 39.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))
0.1b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

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

series328.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))
183.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	328	564
1	1239	485
2	5001	458

prune235.0ms

Filtered

90 candidates to 79 candidates (87.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 7.6b

Counts

91 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2.0 (+ (hypot re im) re))
0.1b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.7b	(+ (hypot re im) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

6.0ms	(* 2.0 (+ (hypot re im) re))
5.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series327.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* 2.0 (+ (hypot re im) re))
197.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
61.0ms	(+ (hypot re im) re)

simplify102.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	247	292
1	928	261
2	4404	255
3	5001	254

prune145.0ms

Filtered

66 candidates to 55 candidates (83.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Merged error: 7.5b

Counts

72 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

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

series501.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
55.0ms	(+ (hypot re im) re)
62.0ms	(+ (hypot re im) re)
61.0ms	(+ (hypot re im) re)

simplify68.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	228	369
1	642	340
2	2531	337
3	5001	333

prune288.0ms

Filtered

79 candidates to 72 candidates (91.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	78	7	85

Merged error: 7.5b

Counts

85 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
0.1b	(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)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

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

series565.0ms

Counts

3 → 9

Calls

3 calls:

164.0ms	(* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
250.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
151.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify80.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	193	429
1	702	357
2	3174	327
3	5002	323

prune254.0ms

Filtered

54 candidates to 44 candidates (81.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	52	9	61

Merged error: 7.5b

Counts

61 → 9

regimes136.0ms

Accuracy

25.9% (4.3b remaining)

Error of 11.7b against oracle of 7.5b and baseline of 13.2b

bsearch50.0ms

Steps

Iters	Range		Point
9	-1.1628533187808574e-30	-7.903618875538946e-36	-9.38108909832793e-31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	28	13
2	28	13

end0.0ms

sample680.0ms

Algorithm

intervals

Results

208.0ms	6040×	body	80	valid
142.0ms	717×	body	2560	valid
79.0ms	487×	body	1280	valid
65.0ms	268×	body	5120	valid
33.0ms	266×	body	640	valid
14.0ms	153×	body	320	valid
4.0ms	69×	body	160	valid