Details

sample35.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
5.0ms	18×	body	2560	valid
4.0ms	19×	body	1280	valid
4.0ms	12×	body	5120	valid
2.0ms	9×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	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: 37.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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:

12.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series282.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
54.0ms	(+ (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	375
1	830	337
2	2660	322
3	5002	320

prune168.0ms

Filtered

62 candidates to 56 candidates (90.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	4	63

Merged error: 7.6b

Counts

63 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot re im) re)))
0.0b	(hypot re im)
0.8b	(+ (hypot re im) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

4.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
1.0ms	(hypot re im)
3.0ms	(+ (hypot re im) re)

series321.0ms

Counts

3 → 9

Calls

3 calls:

204.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
54.0ms	(hypot re im)
63.0ms	(+ (hypot re im) re)

simplify55.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	196	197
1	536	180
2	1779	174
3	5002	172

prune135.0ms

Filtered

51 candidates to 47 candidates (92.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	48	7	55

Merged error: 7.5b

Counts

55 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.0b	(hypot re im)
0.4b	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
0.8b	(+ (hypot re im) re)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(sqrt (+ (hypot re im) re))
1.0ms	(hypot re im)
8.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series457.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (+ (hypot re im) re))
55.0ms	(hypot re im)
205.0ms	(* (sqrt 2.0) (sqrt (+ (hypot re im) re)))
64.0ms	(+ (hypot re im) re)

simplify118.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	300	457
1	1015	427
2	4386	412
3	5001	411

prune215.0ms

Filtered

93 candidates to 74 candidates (79.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	94	6	100

Merged error: 7.5b

Counts

100 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
15.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`hypot-udef` `fma-udef`

Counts

4 → 50

Calls

4 calls:

1.0ms	(hypot re im)
8.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (hypot re im))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series386.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot re im)
92.0ms	(sqrt (hypot re im))
91.0ms	(sqrt (hypot re im))
150.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	128	269
1	344	231
2	1419	217
3	5002	210

prune164.0ms

Filtered

62 candidates to 52 candidates (83.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	59	9	68

Merged error: 7.5b

Counts

68 → 9

regimes99.0ms

Accuracy

24.4% (4.4b remaining)

Error of 11.8b against oracle of 7.4b and baseline of 13.2b

bsearch194.0ms

Steps

Iters	Range	Point
8	-6.167970123584788e-43	-2.0214988117747877e-45	-1.4654363927656778e-43
9	-1.6263070950360542e+97	-9.316421477354923e+91	-2.0110444043841323e+96
10	-1.0269636514224566e+167	-2.3864984321674706e+156	-1.1576207092487859e+157

Iters

Range

Point

-6.167970123584788e-43

-2.0214988117747877e-45

-1.4654363927656778e-43

-1.6263070950360542e+97

-9.316421477354923e+91

-2.0110444043841323e+96

-1.0269636514224566e+167

-2.3864984321674706e+156

-1.1576207092487859e+157

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	32	24
1	35	12
2	38	12
3	38	12

end0.0ms

sample915.0ms

Algorithm

intervals

Results

296.0ms	6051×	body	80	valid
195.0ms	681×	body	2560	valid
112.0ms	486×	body	1280	valid
89.0ms	260×	body	5120	valid
51.0ms	278×	body	640	valid
22.0ms	159×	body	320	valid
8.0ms	85×	body	160	valid