Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

264×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 27.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
27.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

198×	`*-un-lft-identity`
80×	`distribute-lft-out`
75×	`associate-l`
56×	`times-frac`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
16×	`swap-sqr`
12×	`fma-def`
8×	`associate-/r*`
7×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `*-commutative` `div-inv` `unswap-sqr`

Counts

2 → 118

Calls

2 calls:

14.0ms	(+ (* x.re y.re) (* x.im y.im))
37.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
84.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	243	976
1	848	880
2	3077	858
3	5001	858

prune149.0ms

Filtered

124 candidates to 55 candidates (55.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 17.8b

Counts

125 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
0.3b	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
17.4b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

571×	`add-sqr-sqrt`
552×	`associate-/r*`
463×	`times-frac`
431×	`*-un-lft-identity`
374×	`add-cube-cbrt`
361×	`frac-times`
170×	`add-exp-log`
138×	`associate-/l*`
133×	`associate-l`
124×	`associate-r`
102×	`unswap-sqr`
93×	`div-exp`
62×	`prod-exp`
50×	`add-cbrt-cube`
46×	`clear-num`
44×	`frac-2neg`
41×	`1-exp`
31×	`div-inv`
28×	`*-commutative`
22×	`associate-/r/`
20×	`cbrt-undiv`
19×	`associate-r/` `associate-l/`
15×	`rec-exp`
13×	`cbrt-unprod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`un-div-inv` `remove-double-div`
1×	`pow-flip` `pow-prod-down` `fma-udef` `inv-pow`

Counts

4 → 761

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot y.re y.im) 1))
1.0ms	(fma x.re y.re (* x.im y.im))
68.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series586.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (/ (hypot y.re y.im) 1))
41.0ms	(fma x.re y.re (* x.im y.im))
187.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
305.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify146.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	3091	8405
1	5001	7374

prune742.0ms

Filtered

773 candidates to 281 candidates (63.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	764	9	773
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	774	9	783

Merged error: 5.9b

Counts

783 → 9

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b	(fma x.re y.re (* x.im y.im))
17.4b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `associate-/l/`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

3 → 119

Calls

3 calls:

7.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
1.0ms	(fma x.re y.re (* x.im y.im))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series273.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
41.0ms	(fma x.re y.re (* x.im y.im))
115.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify86.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	338	1212
1	1120	1125
2	4123	1108
3	5001	1103

prune313.0ms

Filtered

128 candidates to 98 candidates (23.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	129	8	137

Merged error: 5.8b

Counts

137 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))))
0.3b	(/ 1 (sqrt (hypot y.re y.im)))
7.6b	(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
10.1b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

6250×	`times-frac`
2703×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1512×	`sqrt-prod`
316×	`associate-/r/`
288×	`associate-/r*`
184×	`div-inv`
109×	`associate-/l*`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
30×	`frac-2neg` `clear-num`
20×	`cbrt-undiv`
12×	`associate-/l/`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 2185

Calls

4 calls:

71.0ms	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))))
5.0ms	(/ 1 (sqrt (hypot y.re y.im)))
10.0ms	(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))))
87.0ms	(/ 1 (sqrt (hypot y.re y.im)))
167.0ms	(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
212.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

simplify544.0ms

Algorithm

egg-herbie

Counts

2197 → 2197

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	55153

prune6.4s

Filtered

2197 candidates to 1418 candidates (35.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	2195	2	2197
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	2195	10	2205

Merged error: 5.1b

Counts

2205 → 10

regimes200.0ms

Accuracy

33.9% (7.7b remaining)

Error of 13.3b against oracle of 5.6b and baseline of 17.3b

bsearch62.0ms

Steps

Iters	Range		Point
7	1.967467882740907e+106	7.856463001522747e+107	1.2363859313436468e+107
6	-6.52330204454965e+152	-1.537752741313912e+152	-1.999293010764536e+152

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	35	20
2	36	20
3	39	20
4	40	20
5	42	20
6	42	20

end0.0ms

sample541.0ms

Algorithm

intervals

Results

315.0ms

8440×

body

valid