Metrics for _multiplyComplex, real part

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
100%	99.8%	0%	0.2%	0%	0%	0%	1

Compiler

Compiled 12 to 8 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-sub: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.1s (43.4%)

Results

774.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 217.0ms

ival-mult: 165.0ms (76.1% of total)

ival-sub: 41.0ms (18.9% of total)

const: 8.0ms (3.7% of total)

backward-pass: 3.0ms (1.4% of total)

Bogosity

preprocess85.0ms (3.3%)

Algorithm

2×	egg-herbie

Rules

778×	`fnmadd-define`
650×	`fmsub-define`
640×	`fnmsub-define`
576×	`sum4-define`
560×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	98
1	131	90
2	243	90
3	522	90
4	1392	90
5	2590	90
6	2906	90
7	2930	90
0	7	6
1	16	6
2	32	6
3	51	6
4	81	6
5	156	6
6	296	6
7	518	6
8	835	6
9	1198	6
10	1372	6
11	1394	6
0	1394	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (* x.re y.re) (* x.im y.im))

Outputs
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Call 2

Inputs
(- (* x.re y.re) (* x.im y.im))
(- (* (neg x.re) y.re) (* x.im y.im))
(- (* x.re y.re) (* (neg x.im) y.im))
(- (* x.re (neg y.re)) (* x.im y.im))
(- (* x.re y.re) (* x.im (neg y.im)))
(neg (- (* (neg x.re) y.re) (* x.im y.im)))
(neg (- (* x.re y.re) (* (neg x.im) y.im)))
(neg (- (* x.re (neg y.re)) (* x.im y.im)))
(neg (- (* x.re y.re) (* x.im (neg y.im))))
(- (* x.im y.re) (* x.re y.im))
(- (* y.re x.re) (* x.im y.im))
(- (* y.im y.re) (* x.im x.re))
(- (* x.re x.im) (* y.re y.im))
(- (* x.re y.re) (* y.im x.im))
(- (* x.re y.im) (* x.im y.re))

Outputs
(- (* x.re y.re) (* x.im y.im))
(fmsub x.re y.re (* x.im y.im))
(- (* (neg x.re) y.re) (* x.im y.im))
(fnmsub x.re y.re (* x.im y.im))
(- (* x.re y.re) (* (neg x.im) y.im))
(fma x.re y.re (* x.im y.im))
(- (* x.re (neg y.re)) (* x.im y.im))
(fnmsub x.re y.re (* x.im y.im))
(- (* x.re y.re) (* x.im (neg y.im)))
(fma x.re y.re (* x.im y.im))
(neg (- (* (neg x.re) y.re) (* x.im y.im)))
(fma x.re y.re (* x.im y.im))
(neg (- (* x.re y.re) (* (neg x.im) y.im)))
(fnmsub x.re y.re (* x.im y.im))
(neg (- (* x.re (neg y.re)) (* x.im y.im)))
(fma x.re y.re (* x.im y.im))
(neg (- (* x.re y.re) (* x.im (neg y.im))))
(fnmsub x.re y.re (* x.im y.im))
(- (* x.im y.re) (* x.re y.im))
(fmsub y.re x.im (* x.re y.im))
(- (* y.re x.re) (* x.im y.im))
(fmsub x.re y.re (* x.im y.im))
(- (* y.im y.re) (* x.im x.re))
(fmsub y.re y.im (* x.re x.im))
(- (* x.re x.im) (* y.re y.im))
(fmsub x.re x.im (* y.re y.im))
(- (* x.re y.re) (* y.im x.im))
(fmsub x.re y.re (* x.im y.im))
(- (* x.re y.im) (* x.im y.re))
(fmsub x.re y.im (* y.re x.im))

Symmetry

(sort x.re y.re)

(sort x.im y.im)

explain89.0ms (3.5%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))`
0	-	-	`x.im`
0	-	-	`(*.f64 x.re y.re)`
0	-	-	`(*.f64 x.im y.im)`
0	-	-	`y.im`
0	-	-	`y.re`
0	-	-	`x.re`

Results

62.0ms

512×

valid

Compiler

Compiled 55 to 23 computations (58.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sub: 9.0ms (51.4% of total)

ival-mult: 8.0ms (45.7% of total)

const: 1.0ms (5.7% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x.im y.im)
✓	cost-diff	(*.f64 x.re y.re)
✓	cost-diff	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Rules

420×	`fnmadd-define`
342×	`fma-define`
294×	`sum3-define`
240×	`sum4-define`
232×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	16	16
2	32	16
3	51	16
4	81	16
5	156	16
6	296	16
7	518	16
8	835	16
9	1198	16
10	1372	16
11	1394	16
0	1394	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (* x.re y.re) (* x.im y.im))
(* x.re y.re)
x.re
y.re
(* x.im y.im)
x.im
y.im

Outputs
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re y.re)
(*.f64 x.re y.re)
x.re
y.re
(* x.im y.im)
(*.f64 x.im y.im)
x.im
y.im

localize39.0ms (1.5%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x.re y.re)
✓	accuracy	100.0%	(*.f64 x.im y.im)
✓	accuracy	99.3%	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Results

31.0ms

256×

valid

Compiler

Compiled 22 to 8 computations (63.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 9.0ms (79.8% of total)

ival-sub: 1.0ms (8.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series6.0ms (0.2%)

Counts

3 → 96

Calls

Call 1

Inputs
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (* x.re y.re)>
#<alt (* x.im y.im)>

Outputs
#<alt (* -1 (* x.im y.im))>
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (* x.re y.re)>
#<alt (* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))>
#<alt (* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))>
#<alt (* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))>
#<alt (* x.re y.re)>
#<alt (* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))>
#<alt (* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))>
#<alt (* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))>
#<alt (* -1 (* x.im y.im))>
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (- (* x.re y.re) (* x.im y.im))>
#<alt (* x.re y.re)>
#<alt (* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))>
#<alt (* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))>
#<alt (* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))>
#<alt (* x.re y.re)>
#<alt (* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))>
#<alt (* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))>
#<alt (* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))>
#<alt (* x.re y.re)>
#<alt (+ (* -1 (* x.im y.im)) (* x.re y.re))>
#<alt (+ (* -1 (* x.im y.im)) (* x.re y.re))>
#<alt (+ (* -1 (* x.im y.im)) (* x.re y.re))>
#<alt (* -1 (* x.im y.im))>
#<alt (* x.im (- (/ (* x.re y.re) x.im) y.im))>
#<alt (* x.im (- (/ (* x.re y.re) x.im) y.im))>
#<alt (* x.im (- (/ (* x.re y.re) x.im) y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))>
#<alt (* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))>
#<alt (* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))>
#<alt (* x.re y.re)>
#<alt (+ (* -1 (* x.im y.im)) (* x.re y.re))>
#<alt (+ (* -1 (* x.im y.im)) (* x.re y.re))>
#<alt (+ (* -1 (* x.im y.im)) (* x.re y.re))>
#<alt (* -1 (* x.im y.im))>
#<alt (* y.im (- (/ (* x.re y.re) y.im) x.im))>
#<alt (* y.im (- (/ (* x.re y.re) y.im) x.im))>
#<alt (* y.im (- (/ (* x.re y.re) y.im) x.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))>
#<alt (* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))>
#<alt (* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	y.re	@	-inf	(* x.re y.re)
0.0ms	x.im	@	0	(- (* x.re y.re) (* x.im y.im))
0.0ms	x.re	@	0	(- (* x.re y.re) (* x.im y.im))
0.0ms	x.re	@	-inf	(- (* x.re y.re) (* x.im y.im))
0.0ms	y.im	@	inf	(- (* x.re y.re) (* x.im y.im))

rewrite182.0ms (7.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2398×	`sum4-define`
1706×	`+-lowering-+.f64`
1706×	`+-lowering-+.f32`
1194×	`fma-define`
1048×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	22	12
2	55	12
3	262	12
4	1312	12
5	4095	12
6	7821	12
0	8148	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 296

Calls

Call 1

Inputs
(- (* x.re y.re) (* x.im y.im))
(* x.re y.re)
(* x.im y.im)

Outputs
(+.f64 (.f64 x.re y.re) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(+.f64 (.f64 x.re y.re) (neg.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 x.re y.re)) (.f64 x.im y.im))))
(+.f64 (.f64 x.re y.re) (+.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 #s(literal 0 binary64) (.f64 x.re y.re))))
(+.f64 (.f64 x.re y.re) (neg.f64 (+.f64 (.f64 x.im y.im) (.f64 #s(literal 0 binary64) (.f64 x.re y.re)))))
(+.f64 x.im (+.f64 (.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im))) (.f64 x.re y.re)))
(+.f64 y.im (+.f64 (.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im))) (.f64 x.re y.re)))
(+.f64 (.f64 x.im y.im) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))))
(+.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) #s(literal 0 binary64))
(+.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 #s(literal 0 binary64) (.f64 x.re y.re)))
(+.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 (.f64 #s(literal 0 binary64) (*.f64 x.re y.re)) #s(literal -1 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) y.im) (+.f64 (-.f64 y.im (.f64 x.im y.im)) (.f64 x.re y.re)))
(+.f64 #s(literal 0 binary64) (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(+.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 x.re y.re))
(+.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x.re y.re)) #s(literal -1 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) x.im) (+.f64 (-.f64 x.im (.f64 x.im y.im)) (.f64 x.re y.re)))
(+.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(+.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im))) #s(literal -1 binary64)))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) (.f64 x.im y.im))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) (+.f64 (.f64 x.im y.im) (.f64 #s(literal 0 binary64) (.f64 x.re y.re))))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) (neg.f64 (+.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 #s(literal 0 binary64) (.f64 x.re y.re)))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 x.re y.re)) (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (+.f64 (.f64 x.re y.re) (.f64 (*.f64 x.im y.im) #s(literal -3 binary64))))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 x.im (.f64 y.im #s(literal -2 binary64))))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (.f64 #s(literal 0 binary64) (.f64 x.re y.re))))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (neg.f64 (+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (.f64 #s(literal 0 binary64) (.f64 x.re y.re)))))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))) (.f64 (*.f64 x.im y.im) #s(literal -3 binary64)))
(+.f64 (+.f64 (.f64 x.re y.re) (.f64 (.f64 x.im y.im) #s(literal -3 binary64))) (.f64 x.im (*.f64 y.im #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 x.im y.im) #s(literal -3 binary64)) (+.f64 (.f64 x.re y.re) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 x.im y.im) #s(literal 3 binary64)) (+.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (+.f64 (.f64 x.re y.re) (.f64 x.im (*.f64 y.im #s(literal -2 binary64))))))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x.re y.re)) #s(literal -1 binary64)) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(+.f64 (.f64 (.f64 #s(literal 0 binary64) (.f64 x.re y.re)) #s(literal -1 binary64)) (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))
(+.f64 (+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))) (.f64 (.f64 x.im y.im) #s(literal -4 binary64)))
(+.f64 (-.f64 (.f64 x.re y.re) x.im) (-.f64 x.im (.f64 x.im y.im)))
(+.f64 (-.f64 (.f64 x.re y.re) y.im) (-.f64 y.im (.f64 x.im y.im)))
(+.f64 (+.f64 (.f64 x.re y.re) y.im) (.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im))))
(+.f64 (+.f64 (.f64 x.re y.re) x.im) (.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im))))
(+.f64 (+.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 x.re y.re)) (-.f64 #s(literal 0 binary64) (.f64 x.re y.re)))
(+.f64 (-.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) x.im) (neg.f64 (.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im)))))
(+.f64 (-.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) y.im) (neg.f64 (.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im)))))
(+.f64 (+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) y.im) (neg.f64 (-.f64 y.im (.f64 x.im y.im))))
(+.f64 (+.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))) x.im) (neg.f64 (-.f64 x.im (.f64 x.im y.im))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(-.f64 (.f64 x.re y.re) (+.f64 (.f64 #s(literal 0 binary64) (.f64 x.re y.re)) (.f64 x.im y.im)))
(-.f64 (.f64 x.re y.re) (+.f64 (.f64 x.im y.im) (.f64 #s(literal 0 binary64) (.f64 x.re y.re))))
(-.f64 (.f64 x.im y.im) (-.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (.f64 x.re y.re)))
(-.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) #s(literal 0 binary64))
(-.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 #s(literal 0 binary64) (.f64 x.re y.re)))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 x.im y.im) (.f64 x.re y.re)))
(-.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (-.f64 #s(literal 0 binary64) (.f64 x.re y.re)))
(-.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
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(fma.f64 (-.f64 #s(literal 0 binary64) y.im) x.im (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(fma.f64 (-.f64 #s(literal 0 binary64) y.im) (-.f64 #s(literal 0 binary64) x.im) (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(fma.f64 (-.f64 #s(literal 0 binary64) y.im) (.f64 x.im #s(literal 2 binary64)) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 #s(literal 0 binary64) (.f64 x.im y.im) (.f64 x.re y.re))
(fma.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal -1 binary64) (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))
(fma.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal 2 binary64) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) y.im (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) (-.f64 #s(literal 0 binary64) y.im) (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) (.f64 y.im #s(literal 2 binary64)) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 #s(literal -1 binary64) (.f64 x.im y.im) (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))
(fma.f64 #s(literal -1 binary64) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))
(fma.f64 #s(literal -1 binary64) (-.f64 (.f64 x.im y.im) (.f64 x.re y.re)) (*.f64 x.im y.im))
(fma.f64 #s(literal -1 binary64) (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (+.f64 (.f64 x.re y.re) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x.im y.im) (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))
(fma.f64 #s(literal 1 binary64) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))
(fma.f64 #s(literal 2 binary64) (.f64 x.im y.im) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))))
(fma.f64 #s(literal 2 binary64) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) #s(literal -1 binary64) (+.f64 (.f64 x.re y.re) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(fma.f64 #s(literal -2 binary64) (.f64 x.im y.im) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 (.f64 y.im #s(literal -2 binary64)) x.im (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 (.f64 x.im #s(literal -2 binary64)) y.im (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 (.f64 y.im #s(literal 2 binary64)) x.im (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))))
(fma.f64 (.f64 y.im #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x.im) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(fma.f64 (.f64 x.im #s(literal 2 binary64)) y.im (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal -2 binary64)))))
(fma.f64 (.f64 x.im #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) y.im) (+.f64 (.f64 x.re y.re) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x.re y.re)))
(*.f64 x.re y.re)
(*.f64 x.re (neg.f64 (-.f64 #s(literal 0 binary64) y.re)))
(*.f64 y.re x.re)
(*.f64 y.re (neg.f64 (-.f64 #s(literal 0 binary64) x.re)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x.re y.re)))
(.f64 #s(literal 1 binary64) (.f64 x.re y.re))
(*.f64 (-.f64 #s(literal 0 binary64) y.re) (-.f64 #s(literal 0 binary64) x.re))
(*.f64 (-.f64 #s(literal 0 binary64) x.re) (-.f64 #s(literal 0 binary64) y.re))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) y.re)) x.re)
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x.re)) y.re)
(+.f64 x.im (neg.f64 (-.f64 x.im (*.f64 x.im y.im))))
(+.f64 x.im (.f64 #s(literal -1 binary64) (-.f64 x.im (.f64 x.im y.im))))
(+.f64 x.im (.f64 (-.f64 x.im (.f64 x.im y.im)) #s(literal -1 binary64)))
(+.f64 x.im (+.f64 (.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im))) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(+.f64 y.im (neg.f64 (-.f64 y.im (*.f64 x.im y.im))))
(+.f64 y.im (.f64 #s(literal -1 binary64) (-.f64 y.im (.f64 x.im y.im))))
(+.f64 y.im (.f64 (-.f64 y.im (.f64 x.im y.im)) #s(literal -1 binary64)))
(+.f64 y.im (+.f64 (.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im))) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(+.f64 (*.f64 x.im y.im) #s(literal 0 binary64))
(+.f64 (-.f64 #s(literal 0 binary64) y.im) (neg.f64 (*.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im)))))
(+.f64 (-.f64 #s(literal 0 binary64) y.im) (.f64 #s(literal -1 binary64) (.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im)))))
(+.f64 (-.f64 #s(literal 0 binary64) y.im) (.f64 (.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im))) #s(literal -1 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) y.im) (+.f64 (-.f64 y.im (.f64 x.im y.im)) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(+.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 x.im (*.f64 y.im #s(literal 2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) x.im) (neg.f64 (*.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im)))))
(+.f64 (-.f64 #s(literal 0 binary64) x.im) (.f64 #s(literal -1 binary64) (.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im)))))
(+.f64 (-.f64 #s(literal 0 binary64) x.im) (.f64 (.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im))) #s(literal -1 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) x.im) (+.f64 (-.f64 x.im (.f64 x.im y.im)) (.f64 x.im (*.f64 y.im #s(literal 2 binary64)))))
(+.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (.f64 (.f64 x.im y.im) #s(literal 3 binary64)))
(+.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (neg.f64 (.f64 (.f64 x.im y.im) #s(literal -3 binary64))))
(+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(+.f64 (.f64 (.f64 x.im y.im) #s(literal -3 binary64)) (neg.f64 (.f64 (.f64 x.im y.im) #s(literal -4 binary64))))
(+.f64 (.f64 (.f64 x.im y.im) #s(literal 3 binary64)) (.f64 x.im (.f64 y.im #s(literal -2 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 x.im y.im) #s(literal 3 binary64))) (.f64 x.im (*.f64 y.im #s(literal -2 binary64))))
(+.f64 (.f64 (.f64 (.f64 x.im y.im) #s(literal 3 binary64)) #s(literal 1 binary64)) (.f64 x.im (*.f64 y.im #s(literal -2 binary64))))
(+.f64 (+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) x.im) (*.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im))))
(+.f64 (+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) y.im) (*.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im))))
(+.f64 (+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) y.im)) (-.f64 y.im (*.f64 x.im y.im)))
(+.f64 (+.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x.im)) (-.f64 x.im (*.f64 x.im y.im)))
(+.f64 (+.f64 (.f64 (.f64 x.im y.im) #s(literal 3 binary64)) (.f64 x.im y.im)) (.f64 (*.f64 x.im y.im) #s(literal -3 binary64)))
(+.f64 (+.f64 (.f64 (.f64 x.im y.im) #s(literal 3 binary64)) (.f64 x.im (.f64 y.im #s(literal 2 binary64)))) (.f64 (.f64 x.im y.im) #s(literal -4 binary64)))
(-.f64 x.im (-.f64 x.im (*.f64 x.im y.im)))
(-.f64 y.im (-.f64 y.im (*.f64 x.im y.im)))
(-.f64 (*.f64 x.im y.im) #s(literal 0 binary64))
(-.f64 (-.f64 #s(literal 0 binary64) y.im) (*.f64 y.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x.im))))
(-.f64 #s(literal 0 binary64) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(-.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 x.im (*.f64 y.im #s(literal -2 binary64))))
(-.f64 (-.f64 #s(literal 0 binary64) x.im) (*.f64 x.im (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y.im))))
(-.f64 (.f64 x.im (.f64 y.im #s(literal -2 binary64))) (.f64 (.f64 x.im y.im) #s(literal -3 binary64)))
(-.f64 (.f64 x.im (.f64 y.im #s(literal 2 binary64))) (*.f64 x.im y.im))
(-.f64 (.f64 (.f64 x.im y.im) #s(literal -3 binary64)) (.f64 (.f64 x.im y.im) #s(literal -4 binary64)))
(-.f64 (.f64 (.f64 x.im y.im) #s(literal 3 binary64)) (.f64 x.im (.f64 y.im #s(literal 2 binary64))))
(fma.f64 x.im y.im #s(literal 0 binary64))
(fma.f64 x.im (-.f64 #s(literal 0 binary64) y.im) (.f64 x.im (.f64 y.im #s(literal 2 binary64))))
(fma.f64 x.im (.f64 y.im #s(literal 2 binary64)) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 y.im x.im #s(literal 0 binary64))
(fma.f64 y.im (-.f64 #s(literal 0 binary64) x.im) (.f64 x.im (.f64 y.im #s(literal 2 binary64))))
(fma.f64 y.im (.f64 x.im #s(literal 2 binary64)) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 (.f64 x.im y.im) #s(literal -1 binary64) (.f64 x.im (*.f64 y.im #s(literal 2 binary64))))
(fma.f64 (*.f64 x.im y.im) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x.im y.im) #s(literal 2 binary64) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 (-.f64 #s(literal 0 binary64) y.im) x.im (.f64 x.im (.f64 y.im #s(literal 2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) y.im) (-.f64 #s(literal 0 binary64) x.im) #s(literal 0 binary64))
(fma.f64 (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) y.im (.f64 x.im (.f64 y.im #s(literal 2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) (-.f64 #s(literal 0 binary64) y.im) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x.im y.im) (.f64 x.im (*.f64 y.im #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x.im y.im) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) (.f64 x.im (*.f64 y.im #s(literal 2 binary64))))
(fma.f64 #s(literal 2 binary64) (.f64 x.im y.im) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 (.f64 y.im #s(literal 2 binary64)) x.im (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 (.f64 x.im #s(literal 2 binary64)) y.im (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(neg.f64 (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(*.f64 x.im y.im)
(*.f64 y.im x.im)
(.f64 (.f64 x.im y.im) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y.im) (-.f64 #s(literal 0 binary64) x.im))
(.f64 (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x.im) (-.f64 #s(literal 0 binary64) y.im))
(.f64 #s(literal -1 binary64) (.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(.f64 #s(literal 1 binary64) (.f64 x.im y.im))

simplify156.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

2018×	`-lowering-.f32`
2018×	`-lowering-.f64`
2008×	`fma-lowering-fma.f32`
2008×	`fma-lowering-fma.f64`
1940×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	438
1	150	426
2	450	426
3	1565	426
4	6440	426
0	8131	426

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* -1 (* x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(* x.re y.re)
(* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))
(* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))
(* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))
(* x.re y.re)
(* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))
(* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))
(* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))
(* -1 (* x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(* x.re y.re)
(* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))
(* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))
(* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))
(* x.re y.re)
(* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))
(* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))
(* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))
(* x.re y.re)
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(* -1 (* x.im y.im))
(* x.im (- (/ (* x.re y.re) x.im) y.im))
(* x.im (- (/ (* x.re y.re) x.im) y.im))
(* x.im (- (/ (* x.re y.re) x.im) y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))
(* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))
(* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))
(* x.re y.re)
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(* -1 (* x.im y.im))
(* y.im (- (/ (* x.re y.re) y.im) x.im))
(* y.im (- (/ (* x.re y.re) y.im) x.im))
(* y.im (- (/ (* x.re y.re) y.im) x.im))
(* -1 (* x.im y.im))
(* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))
(* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))
(* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)

Outputs
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re (+ y.re (* -1 (/ (* x.im y.im) x.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re y.re)
(*.f64 x.re y.re)
(* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* x.re (+ (* -1 y.re) (/ (* x.im y.im) x.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(- (* x.re y.re) (* x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re y.re)
(*.f64 x.re y.re)
(* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* y.re (+ x.re (* -1 (/ (* x.im y.im) y.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re y.re)
(*.f64 x.re y.re)
(* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* y.re (+ (* -1 x.re) (/ (* x.im y.im) y.re))))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* x.re y.re)
(*.f64 x.re y.re)
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* x.im (- (/ (* x.re y.re) x.im) y.im))
(.f64 x.im (-.f64 (/.f64 (.f64 x.re y.re) x.im) y.im))
(* x.im (- (/ (* x.re y.re) x.im) y.im))
(.f64 x.im (-.f64 (/.f64 (.f64 x.re y.re) x.im) y.im))
(* x.im (- (/ (* x.re y.re) x.im) y.im))
(.f64 x.im (-.f64 (/.f64 (.f64 x.re y.re) x.im) y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))
(.f64 x.im (-.f64 (/.f64 (.f64 x.re y.re) x.im) y.im))
(* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))
(.f64 x.im (-.f64 (/.f64 (.f64 x.re y.re) x.im) y.im))
(* -1 (* x.im (- (* -1 (/ (* x.re y.re) x.im)) (* -1 y.im))))
(.f64 x.im (-.f64 (/.f64 (.f64 x.re y.re) x.im) y.im))
(* x.re y.re)
(*.f64 x.re y.re)
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(+ (* -1 (* x.im y.im)) (* x.re y.re))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* y.im (- (/ (* x.re y.re) y.im) x.im))
(.f64 y.im (-.f64 (/.f64 (.f64 x.re y.re) y.im) x.im))
(* y.im (- (/ (* x.re y.re) y.im) x.im))
(.f64 y.im (-.f64 (/.f64 (.f64 x.re y.re) y.im) x.im))
(* y.im (- (/ (* x.re y.re) y.im) x.im))
(.f64 y.im (-.f64 (/.f64 (.f64 x.re y.re) y.im) x.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))
(.f64 y.im (-.f64 (/.f64 (.f64 x.re y.re) y.im) x.im))
(* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))
(.f64 y.im (-.f64 (/.f64 (.f64 x.re y.re) y.im) x.im))
(* -1 (* y.im (- (* -1 (/ (* x.re y.re) y.im)) (* -1 x.im))))
(.f64 y.im (-.f64 (/.f64 (.f64 x.re y.re) y.im) x.im))
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)

eval42.0ms (1.7%)

Compiler: Compiled 5174 to 615 computations (88.1% saved)

prune58.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	390	2	392
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	390	3	393

Accuracy

100.0%

Counts

393 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
▶	54.1%	(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
▶	51.2%	(*.f64 x.re y.re)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x.im y.im)
✓	cost-diff	(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
✓	cost-diff	(*.f64 x.re y.re)

Rules

78×	`fma-define`
72×	`sum3-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
28×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	15	15
2	26	15
3	44	15
4	61	15
5	84	15
6	108	15
7	118	15
8	155	15
9	184	15
0	184	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x.re y.re)
x.re
y.re
(- 0 (* x.im y.im))
0
(* x.im y.im)
x.im
y.im

Outputs
(* x.re y.re)
(*.f64 x.re y.re)
x.re
y.re
(- 0 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
0
#s(literal 0 binary64)
(* x.im y.im)
(*.f64 x.im y.im)
x.im
y.im

localize35.0ms (1.4%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
✓	accuracy	100.0%	(*.f64 x.im y.im)
✓	accuracy	100.0%	(*.f64 x.re y.re)

Results

27.0ms

256×

valid

Compiler

Compiled 21 to 9 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 5.0ms (70.9% of total)

ival-sub: 1.0ms (14.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

3 → 72

Calls

Call 1

Inputs
#<alt (* x.re y.re)>
#<alt (- 0 (* x.im y.im))>
#<alt (* x.im y.im)>

Outputs
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* x.re y.re)>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x.im	@	0	(- 0 (* x.im y.im))
0.0ms	x.im	@	-inf	(- 0 (* x.im y.im))
0.0ms	x.im	@	inf	(- 0 (* x.im y.im))
0.0ms	y.im	@	-inf	(- 0 (* x.im y.im))
0.0ms	y.im	@	inf	(- 0 (* x.im y.im))

rewrite23.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

78×	`fma-define`
72×	`sum3-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
28×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	26	10
3	44	10
4	61	10
5	84	10
6	108	10
7	118	10
8	155	10
9	184	10
0	184	10

Stop Event

1×	iter limit
1×	saturated

Counts

3 → 30

Calls

Call 1

Inputs
(* x.re y.re)
(- 0 (* x.im y.im))
(* x.im y.im)

Outputs
(*.f64 x.re y.re)
(*.f64 y.re x.re)
(+.f64 #s(literal 0 binary64) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(+.f64 (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(-.f64 (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)) #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) x.im (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 #s(literal 0 binary64) y.im (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 x.im #s(literal 0 binary64) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 x.im (-.f64 #s(literal 0 binary64) y.im) #s(literal 0 binary64))
(fma.f64 y.im #s(literal 0 binary64) (*.f64 x.im (-.f64 #s(literal 0 binary64) y.im)))
(fma.f64 y.im (-.f64 #s(literal 0 binary64) x.im) #s(literal 0 binary64))
(fma.f64 (*.f64 x.im y.im) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) y.im #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x.im y.im) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) y.im) x.im #s(literal 0 binary64))
(neg.f64 (*.f64 x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(*.f64 y.im (-.f64 #s(literal 0 binary64) x.im))
(.f64 (.f64 x.im y.im) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x.im) y.im)
(.f64 #s(literal -1 binary64) (.f64 x.im y.im))
(*.f64 (-.f64 #s(literal 0 binary64) y.im) x.im)
(+.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(+.f64 (*.f64 x.im y.im) #s(literal 0 binary64))
(-.f64 (*.f64 x.im y.im) #s(literal 0 binary64))
(fma.f64 x.im y.im #s(literal 0 binary64))
(fma.f64 y.im x.im #s(literal 0 binary64))
(*.f64 x.im y.im)
(*.f64 y.im x.im)

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

88×	`sum3-define`
76×	`fma-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
28×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	14	240
2	27	240
3	31	240
4	35	240
5	57	240
6	89	240
7	101	240
8	124	240
9	191	240
0	191	240

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

Inputs
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* x.re y.re)
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)

Outputs
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* x.re y.re)
(*.f64 x.re y.re)
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* -1 (* x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)

eval11.0ms (0.4%)

Compiler: Compiled 493 to 44 computations (91.1% saved)

prune5.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	102	3	105

Accuracy

100.0%

Counts

105 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
✓	51.2%	(*.f64 x.re y.re)
▶	54.1%	(neg.f64 (*.f64 x.im y.im))

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(neg.f64 (*.f64 x.im y.im))
✓	cost-diff	0	(*.f64 x.im y.im)

Rules

88×	`sum3-define`
76×	`fma-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
24×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
1	13	9
2	22	9
3	32	9
4	54	9
5	86	9
6	98	9
7	121	9
8	188	9
0	188	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(neg (* x.im y.im))
(* x.im y.im)
x.im
y.im

Outputs
(neg (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* x.im y.im)
(*.f64 x.im y.im)
x.im
y.im

localize28.0ms (1.1%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x.im y.im)
✓	accuracy	100.0%	(neg.f64 (*.f64 x.im y.im))

Results

21.0ms

256×

valid

Compiler

Compiled 14 to 7 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (51.7% of total)

ival-neg: 1.0ms (25.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (* x.im y.im)>
#<alt (neg (* x.im y.im))>

Outputs
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* x.im y.im)>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>
#<alt (* -1 (* x.im y.im))>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x.im	@	inf	(neg (* x.im y.im))
0.0ms	x.im	@	0	(* x.im y.im)
0.0ms	x.im	@	-inf	(neg (* x.im y.im))
0.0ms	y.im	@	-inf	(neg (* x.im y.im))
0.0ms	y.im	@	inf	(neg (* x.im y.im))

rewrite20.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

88×	`sum3-define`
76×	`fma-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
24×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	13	7
2	22	7
3	32	7
4	54	7
5	86	7
6	98	7
7	121	7
8	188	7
0	188	7

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 28

Calls

Call 1

Inputs
(* x.im y.im)
(neg (* x.im y.im))

Outputs
(+.f64 (*.f64 x.im y.im) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(-.f64 (*.f64 x.im y.im) #s(literal 0 binary64))
(fma.f64 x.im y.im #s(literal 0 binary64))
(fma.f64 y.im x.im #s(literal 0 binary64))
(*.f64 x.im y.im)
(*.f64 y.im x.im)
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)))
(-.f64 (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(fma.f64 x.im #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)))
(fma.f64 x.im (-.f64 #s(literal 0 binary64) y.im) #s(literal 0 binary64))
(fma.f64 y.im #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)))
(fma.f64 y.im (-.f64 #s(literal 0 binary64) x.im) #s(literal 0 binary64))
(fma.f64 (*.f64 x.im y.im) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) x.im (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)))
(fma.f64 #s(literal 0 binary64) y.im (-.f64 #s(literal 0 binary64) (*.f64 x.im y.im)))
(fma.f64 #s(literal -1 binary64) (*.f64 x.im y.im) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x.im) y.im #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) y.im) x.im #s(literal 0 binary64))
(neg.f64 (*.f64 x.im y.im))
(*.f64 x.im (-.f64 #s(literal 0 binary64) y.im))
(*.f64 y.im (-.f64 #s(literal 0 binary64) x.im))
(.f64 (.f64 x.im y.im) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x.im y.im))
(*.f64 (-.f64 #s(literal 0 binary64) x.im) y.im)
(*.f64 (-.f64 #s(literal 0 binary64) y.im) x.im)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

88×	`sum3-define`
76×	`fma-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
24×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	168
1	10	168
2	23	168
3	27	168
4	31	168
5	53	168
6	85	168
7	97	168
8	120	168
9	187	168
0	187	168

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* x.im y.im)
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))
(* -1 (* x.im y.im))

Outputs
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* x.im y.im)
(*.f64 x.im y.im)
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(* -1 (* x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))

eval9.0ms (0.3%)

Compiler: Compiled 384 to 42 computations (89.1% saved)

prune7.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	76	3	79

Accuracy

100.0%

Counts

79 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
✓	51.2%	(*.f64 x.re y.re)
✓	54.1%	(neg.f64 (*.f64 x.im y.im))

Compiler

Compiled 49 to 28 computations (42.9% saved)

regimes16.0ms (0.6%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 x.re y.re)
(neg.f64 (*.f64 x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Outputs
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Calls

7 calls:

3.0ms	x.im
2.0ms	x.re
2.0ms	y.re
2.0ms	y.im
2.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Results

Accuracy	Segments	Branch
99.2%	1	`x.re`
99.2%	1	`x.im`
99.2%	1	`y.re`
99.2%	1	`y.im`
99.2%	1	`(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))`
99.2%	1	`(*.f64 x.re y.re)`
99.2%	1	`(*.f64 x.im y.im)`

Compiler

Compiled 45 to 33 computations (26.7% saved)

regimes12.0ms (0.5%)

Counts

3 → 3

Calls

Call 1

Inputs
(*.f64 x.re y.re)
(neg.f64 (*.f64 x.im y.im))
(-.f64 #s(literal 0 binary64) (*.f64 x.im y.im))

Outputs
(*.f64 x.re y.re)
(neg.f64 (*.f64 x.im y.im))
(*.f64 x.re y.re)

Calls

6 calls:

3.0ms	x.re
2.0ms	y.re
2.0ms	x.im
2.0ms	y.im
2.0ms	(*.f64 x.re y.re)

Results

Accuracy	Segments	Branch
75.7%	3	`x.re`
73.8%	3	`x.im`
77.7%	3	`y.re`
74.0%	3	`y.im`
81.5%	3	`(*.f64 x.re y.re)`
80.2%	3	`(*.f64 x.im y.im)`

Compiler

Compiled 34 to 26 computations (23.5% saved)

regimes7.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x.re y.re)

Outputs
(*.f64 x.re y.re)

Calls

5 calls:

1.0ms	y.re
1.0ms	x.re
1.0ms	y.im
1.0ms	x.im
1.0ms	(*.f64 x.re y.re)

Results

Accuracy	Segments	Branch
51.2%	1	`x.im`
51.2%	1	`y.im`
51.2%	1	`x.re`
51.2%	1	`y.re`
51.2%	1	`(*.f64 x.re y.re)`

Compiler

Compiled 27 to 21 computations (22.2% saved)

bsearch51.0ms (2%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	4.2438349158991646e-30	1.46705082371955e-26
39.0ms	-3.715828573757422e-17	-1.2493548187596497e-20

Results

14.0ms

256×

valid

Compiler

Compiled 258 to 205 computations (20.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (48.2% of total)

ival-sub: 1.0ms (24.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify18.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	29	30
2	40	30
3	45	30
4	47	30

Stop Event

1×

saturated

Calls

Call 1

Inputs

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

(if (<=.f64 (*.f64 x.re y.re) #s(literal -8099983099314331/41538374868278621028243970633760768 binary64)) (*.f64 x.re y.re) (if (<=.f64 (*.f64 x.re y.re) #s(literal 1080192345553827/696898287454081973172991196020261297061888 binary64)) (neg.f64 (*.f64 x.im y.im)) (*.f64 x.re y.re)))

(*.f64 x.re y.re)

Outputs
(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
(if (<=.f64 (.f64 x.re y.re) #s(literal -8099983099314331/41538374868278621028243970633760768 binary64)) (.f64 x.re y.re) (if (<=.f64 (.f64 x.re y.re) #s(literal 1080192345553827/696898287454081973172991196020261297061888 binary64)) (neg.f64 (.f64 x.im y.im)) (*.f64 x.re y.re)))
(if (<=.f64 (.f64 x.re y.re) #s(literal -8099983099314331/41538374868278621028243970633760768 binary64)) (.f64 x.re y.re) (if (<=.f64 (.f64 x.re y.re) #s(literal 1080192345553827/696898287454081973172991196020261297061888 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x.im y.im)) (*.f64 x.re y.re)))
(*.f64 x.re y.re)

soundness441.0ms (17.2%)

Rules

2018×	`-lowering-.f32`
2018×	`-lowering-.f64`
2008×	`fma-lowering-fma.f32`
2008×	`fma-lowering-fma.f64`
1940×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	438
1	150	426
2	450	426
3	1565	426
4	6440	426
0	8131	426
0	8	10
1	15	10
2	26	10
3	44	10
4	61	10
5	84	10
6	108	10
7	118	10
8	155	10
9	184	10
0	184	10

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Compiler

Compiled 68 to 38 computations (44.1% saved)

preprocess32.0ms (1.2%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 184 to 100 computations (45.7% saved)

_multiplyComplex, real part

analyze0.0ms (0%)

sample1.1s (43.4%)

preprocess85.0ms (3.3%)

explain89.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify32.0ms (1.2%)

localize39.0ms (1.5%)

series6.0ms (0.2%)

rewrite182.0ms (7.1%)

simplify156.0ms (6.1%)

eval42.0ms (1.7%)

prune58.0ms (2.3%)

simplify9.0ms (0.4%)

localize35.0ms (1.4%)

series1.0ms (0%)

rewrite23.0ms (0.9%)

simplify16.0ms (0.6%)

eval11.0ms (0.4%)

prune5.0ms (0.2%)

simplify8.0ms (0.3%)

localize28.0ms (1.1%)

series1.0ms (0%)

rewrite20.0ms (0.8%)

simplify11.0ms (0.4%)

eval9.0ms (0.3%)

prune7.0ms (0.3%)

regimes16.0ms (0.6%)

regimes12.0ms (0.5%)

regimes7.0ms (0.3%)

bsearch51.0ms (2%)

simplify18.0ms (0.7%)

soundness441.0ms (17.2%)

preprocess32.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	240
1	14	240
2	27	240
3	31	240
4	35	240
5	57	240
6	89	240
7	101	240
8	124	240
9	191	240
0	191	240

Iter	Nodes	Cost
0	5	168
1	10	168
2	23	168
3	27	168
4	31	168
5	53	168
6	85	168
7	97	168
8	120	168
9	187	168
0	187	168

Iter	Nodes	Cost
0	8	240
1	14	240
2	27	240
3	31	240
4	35	240
5	57	240
6	89	240
7	101	240
8	124	240
9	191	240
0	191	240

Iter	Nodes	Cost
0	5	168
1	10	168
2	23	168
3	27	168
4	31	168
5	53	168
6	85	168
7	97	168
8	120	168
9	187	168
0	187	168

Iter	Nodes	Cost
0	8	240
1	14	240
2	27	240
3	31	240
4	35	240
5	57	240
6	89	240
7	101	240
8	124	240
9	191	240
0	191	240

Iter	Nodes	Cost
0	5	168
1	10	168
2	23	168
3	27	168
4	31	168
5	53	168
6	85	168
7	97	168
8	120	168
9	187	168
0	187	168