Metrics for Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 11 to 11 computations (0% saved)

sample992.0ms (29.5%)

Memory

11.1MiB live, 1 124.5MiB allocated

Samples

713.0ms	8 255×	0	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 258.0ms

ival-div: 133.0ms (51.6% of total)

ival-mult: 70.0ms (27.2% of total)

ival-sub: 38.0ms (14.7% of total)

exact: 8.0ms (3.1% of total)

ival-true: 6.0ms (2.3% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess64.0ms (1.9%)

Memory

12.7MiB live, 49.2MiB allocated

Algorithm

1×	egg-herbie

Rules

352×	`lower-fma.f64`
352×	`lower-fma.f32`
256×	`lower-*.f32`
254×	`lower-*.f64`
172×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	87
1	76	84
2	153	81
3	332	81
4	616	81
5	1057	81
6	1210	81
7	1234	81
8	1234	81
0	9	9
0	13	9
1	18	9
2	31	9
3	40	9
4	64	9
5	108	9
6	189	9
7	312	9
8	447	9
9	514	9
10	549	9
11	550	9
0	550	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Outputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(fma.f64 x (.f64 y #s(literal 1/2 binary64)) (.f64 z #s(literal -1/8 binary64)))

Symmetry

(sort x y)

explain98.0ms (2.9%)

Memory

-31.3MiB live, 171.3MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 8 binary64)`
-	-	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
-	-	`z`
-	-	`(*.f64 x y)`
-	-	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
-	-	`(/.f64 z #s(literal 8 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

38.0ms

512×

valid

Compiler

Compiled 78 to 40 computations (48.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 9.0ms (53.6% of total)

ival-mult: 4.0ms (23.8% of total)

ival-sub: 2.0ms (11.9% of total)

exact: 1.0ms (6% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Compiler

Compiled 12 to 9 computations (25% saved)

simplify31.0ms (0.9%)

Memory

9.5MiB live, 48.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	128	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
✓	cost-diff	384	(/.f64 z #s(literal 8 binary64))
✓	cost-diff	384	(/.f64 (*.f64 x y) #s(literal 2 binary64))

Rules

352×	`lower-fma.f64`
352×	`lower-fma.f32`
256×	`lower-*.f32`
254×	`lower-*.f64`
88×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
0	13	25
1	18	25
2	31	25
3	40	25
4	64	25
5	108	25
6	189	25
7	312	25
8	447	25
9	514	25
10	549	25
11	550	25
0	550	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
x
y
#s(literal 2 binary64)
(/.f64 z #s(literal 8 binary64))
z
#s(literal 8 binary64)

Outputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(fma.f64 x (.f64 y #s(literal 1/2 binary64)) (.f64 z #s(literal -1/8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(.f64 x (.f64 y #s(literal 1/2 binary64)))
(*.f64 x y)
x
y
#s(literal 2 binary64)
(/.f64 z #s(literal 8 binary64))
(*.f64 z #s(literal 1/8 binary64))
z
#s(literal 8 binary64)

localize48.0ms (1.4%)

Memory

-3.9MiB live, 38.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 z #s(literal 8 binary64))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Samples

38.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-sub: 24.0ms (80.1% of total)

ival-div: 3.0ms (10% of total)

ival-mult: 2.0ms (6.7% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (/.f64 (.f64 x y) #s(literal 2 binary64)) (patch (/.f64 (.f64 x y) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor 0 z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor 0 z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor 0 z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor 0 z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor -inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor -inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor -inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 z) (taylor -inf z) (#s(alt (/.f64 z #s(literal 8 binary64)) (patch (/.f64 z #s(literal 8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor 0 x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor 0 y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x))) (taylor inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x))) (taylor inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x))) (taylor inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor -inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) (patch (-.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(- (/ (* x y) 2) (/ z 8))
1.0ms	y	@	0	(/ (* x y) 2)
1.0ms	x	@	inf	(/ (* x y) 2)
1.0ms	x	@	0	(/ (* x y) 2)
1.0ms	y	@	inf	(/ (* x y) 2)

simplify263.0ms (7.8%)

Memory

-10.3MiB live, 181.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4 218×	`lower-fma.f64`
4 218×	`lower-fma.f32`
3 690×	`lower-*.f64`
3 690×	`lower-*.f32`
2 036×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	508
1	123	508
2	350	508
3	861	508
4	1961	508
5	4019	508
6	6382	508
0	8114	481

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

Outputs
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* -1/8 z)
(*.f64 z #s(literal -1/8 binary64))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1/8 z)
(*.f64 z #s(literal -1/8 binary64))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1/8 z)
(*.f64 z #s(literal -1/8 binary64))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1/8 z)
(*.f64 z #s(literal -1/8 binary64))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x y) (.f64 z #s(literal -1/8 binary64)))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)

rewrite323.0ms (9.6%)

Memory

-4.8MiB live, 276.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 312×	`lower-fma.f64`
5 312×	`lower-fma.f32`
4 784×	`lower-*.f32`
4 782×	`lower-*.f64`
3 460×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
0	13	20
1	56	20
2	486	20
0	8677	19

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 221

Calls

Call 1

Inputs
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 z #s(literal 8 binary64))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(*.f64 x y)

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x y))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 (*.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (*.f64 x y) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y))))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 x y)) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
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(.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (.f64 (.f64 z (.f64 z z)) #s(literal -1/512 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) x) (fma.f64 y (.f64 x (.f64 #s(literal 1/16 binary64) z)) (.f64 z (.f64 #s(literal 1/64 binary64) z)))))))
(.f64 (neg.f64 (fma.f64 x (.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) x) (.f64 (.f64 z z) #s(literal -1/64 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 z #s(literal -1/8 binary64) (neg.f64 (.f64 (.f64 x y) #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (*.f64 x y)))
(neg.f64 (neg.f64 (*.f64 x y)))
(*.f64 x y)
(*.f64 x (neg.f64 (neg.f64 y)))
(.f64 x (.f64 y #s(literal 1 binary64)))
(*.f64 y x)
(*.f64 y (neg.f64 (neg.f64 x)))
(.f64 y (.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x y))
(.f64 #s(literal -1 binary64) (neg.f64 (.f64 x y)))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 (neg.f64 y)) x)
(*.f64 (neg.f64 (neg.f64 x)) y)
(.f64 (.f64 #s(literal 1 binary64) x) y)
(.f64 (.f64 #s(literal 1 binary64) y) x)

eval50.0ms (1.5%)

Memory: 13.4MiB live, 50.8MiB allocated
Compiler: Compiled 5 252 to 611 computations (88.4% saved)

prune50.0ms (1.5%)

Memory

21.5MiB live, 60.0MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	314	3	317
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	315	3	318

Accuracy

100.0%

Counts

318 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
▶	51.8%	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
▶	49.8%	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))

Status

Accuracy

Program

▶

100.0%

(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x (*.f64 z #s(literal -1/8 binary64)))

▶

51.8%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

▶

49.8%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y)))

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify27.0ms (0.8%)

Memory

-18.0MiB live, 20.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 z #s(literal -1/8 binary64))
✓	cost-diff	(*.f64 y #s(literal 1/2 binary64))
✓	cost-diff	(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
✓	cost-diff	(*.f64 z #s(literal -1/8 binary64))
✓	cost-diff	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
✓	cost-diff	(*.f64 x y)
✓	cost-diff	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	cost-diff	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))

Rules

352×	`lower-fma.f32`
350×	`lower-fma.f64`
256×	`lower-*.f32`
248×	`lower-*.f64`
100×	`distribute-lft-neg-in`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	18	63
0	24	64
1	37	64
2	54	64
3	63	64
4	88	64
5	134	64
6	224	64
7	369	61
8	537	61
9	578	61
10	611	61
11	612	61
0	612	61

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
#s(literal 1/2 binary64)
(*.f64 x y)
x
y
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
(*.f64 z #s(literal -1/8 binary64))
z
#s(literal -1/8 binary64)
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
(*.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
x
(*.f64 z #s(literal -1/8 binary64))
z
#s(literal -1/8 binary64)

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 x (.f64 y #s(literal 1/2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(.f64 x (.f64 y #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 x y)
x
y
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
(*.f64 z #s(literal -1/8 binary64))
z
#s(literal -1/8 binary64)
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
(fma.f64 x (.f64 y #s(literal 1/2 binary64)) (.f64 z #s(literal -1/8 binary64)))
(*.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
x
(*.f64 z #s(literal -1/8 binary64))
z
#s(literal -1/8 binary64)

localize48.0ms (1.4%)

Memory

8.6MiB live, 49.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
✓	accuracy	100.0%	(*.f64 z #s(literal -1/8 binary64))
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 z #s(literal -1/8 binary64))
✓	accuracy	51.8%	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	accuracy	49.8%	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))

Samples

26.0ms

256×

valid

Compiler

Compiled 56 to 18 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 8.0ms (50.2% of total)

ival-div: 5.0ms (31.4% of total)

ival-sub: 1.0ms (6.3% of total)

ival-add: 1.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

7 → 180

Calls

Call 1

Inputs
#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())
#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())
#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 z #s(literal -1/8 binary64))) (patch #s(approx (- (/ ( x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())
#s(alt (.f64 z #s(literal -1/8 binary64)) (patch (.f64 z #s(literal -1/8 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* -1/8 z) (taylor 0 x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor 0 y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (* x y)) (* 1/8 z)) (taylor 0 y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x))) (taylor inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x))) (taylor inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x))) (taylor inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor -inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (patch #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) (taylor -inf y) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor 0 x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y))) (taylor inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor -inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* x y)) (taylor 0 z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 z) (* 1/2 (* x y))) (taylor 0 z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 1/2 (/ (* x y) z)) 1/8)) (taylor inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 z) (taylor -inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) (taylor -inf z) (#s(alt (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) (patch (fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

45 calls:

Time	Variable		Point	Expression
0.0ms	y	@	-inf	(* y 1/2)
0.0ms	y	@	inf	(* y 1/2)
0.0ms	z	@	0	(* z -1/8)
0.0ms	y	@	0	(* y 1/2)
0.0ms	y	@	0	(+ (* (* y 1/2) x) (* z -1/8))

simplify242.0ms (7.2%)

Memory

-8.3MiB live, 183.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4 218×	`lower-fma.f64`
4 218×	`lower-fma.f32`
3 690×	`lower-*.f64`
3 690×	`lower-*.f32`
2 036×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	1104
1	123	1104
2	350	1104
3	860	1104
4	1966	1104
5	4045	1104
6	6408	1104
0	8139	1023

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)

Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)

rewrite366.0ms (10.9%)

Memory

11.1MiB live, 476.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 796×	`lower-/.f64`
4 796×	`lower-/.f32`
4 618×	`lower-*.f32`
4 610×	`lower-*.f64`
4 164×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	50
0	24	51
1	86	48
2	744	48
0	8270	48

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

7 → 232

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(*.f64 x y)
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
(*.f64 z #s(literal -1/8 binary64))
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
(*.f64 y #s(literal 1/2 binary64))

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 x (.f64 y #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x y))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 x y)) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y))))
(/.f64 (neg.f64 (neg.f64 (*.f64 x y))) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 x y)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64))
(.f64 x (.f64 y #s(literal 1/2 binary64)))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -1 binary64)))
(.f64 (.f64 x y) #s(literal 1/2 binary64))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(.f64 (neg.f64 (.f64 x y)) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 y #s(literal 1/2 binary64))))
(.f64 (.f64 x #s(literal 1/2 binary64)) y)
(.f64 #s(literal -1 binary64) (.f64 (*.f64 x y) #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)))))
(.f64 (neg.f64 (neg.f64 (.f64 x y))) #s(literal 1/2 binary64))
(*.f64 x y)
(*.f64 y x)
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 z #s(literal -1/8 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 z #s(literal 1/8 binary64)))
(neg.f64 (*.f64 z #s(literal 1/8 binary64)))
(/.f64 z #s(literal -8 binary64))
(/.f64 (neg.f64 z) #s(literal 8 binary64))
(/.f64 (.f64 (.f64 z (.f64 z z)) #s(literal 1/512 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 z z) #s(literal 1/64 binary64) (.f64 #s(literal 0 binary64) (.f64 z #s(literal 1/8 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 8 binary64) z)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8 binary64) z))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 8 binary64) (neg.f64 z)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (/.f64 #s(literal 8 binary64) z)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 8 binary64) z) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -8 binary64) (neg.f64 (neg.f64 z))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 8 binary64) z))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 8 binary64) z))))
(/.f64 (neg.f64 (neg.f64 z)) #s(literal -8 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 z))) #s(literal 8 binary64))
(pow.f64 (neg.f64 (/.f64 #s(literal 8 binary64) z)) #s(literal -1 binary64))
(*.f64 z #s(literal -1/8 binary64))
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(.f64 (-.f64 (.f64 (.f64 z z) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 x y) (.f64 x y)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 z #s(literal -1/8 binary64)) (.f64 x (.f64 y #s(literal 1/2 binary64))))))
(/.f64 y #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) y)))
(/.f64 (neg.f64 y) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 y)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) y) #s(literal -1 binary64))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(.f64 #s(literal 1 binary64) (.f64 y #s(literal 1/2 binary64)))
(*.f64 (neg.f64 y) #s(literal -1/2 binary64))

eval112.0ms (3.3%)

Memory: 14.2MiB live, 91.4MiB allocated
Compiler: Compiled 5 941 to 585 computations (90.2% saved)

prune64.0ms (1.9%)

Memory

-5.6MiB live, 115.3MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	447	0	447
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	447	3	450

Accuracy

100.0%

Counts

450 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x (*.f64 z #s(literal -1/8 binary64)))

✓

51.8%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

✓

49.8%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y)))

Compiler

Compiled 57 to 34 computations (40.4% saved)

regimes16.0ms (0.5%)

Memory

-3.7MiB live, 35.7MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Outputs
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))

Calls

7 calls:

3.0ms	z
2.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	y
2.0ms	(/.f64 (*.f64 x y) #s(literal 2 binary64))
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
100.0%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
100.0%	1	`(*.f64 x y)`
100.0%	1	`(/.f64 z #s(literal 8 binary64))`

Compiler

Compiled 44 to 33 computations (25% saved)

regimes28.0ms (0.8%)

Memory

-8.8MiB live, 46.5MiB allocated

Counts

2 → 3

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))

Outputs

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y)))

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y)))

Calls

7 calls:

18.0ms	x
2.0ms	(/.f64 (*.f64 x y) #s(literal 2 binary64))
2.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	z
2.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Results

Accuracy	Segments	Branch
74.9%	3	`x`
74.7%	3	`y`
74.9%	3	`z`
70.1%	5	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
81.7%	3	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
81.7%	3	`(*.f64 x y)`
74.9%	3	`(/.f64 z #s(literal 8 binary64))`

Compiler

Compiled 44 to 33 computations (25% saved)

regimes36.0ms (1.1%)

Memory

-18.2MiB live, 21.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

Calls

7 calls:

1.0ms	x
1.0ms	(/.f64 z #s(literal 8 binary64))
1.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
1.0ms	z
1.0ms	y

Results

Accuracy	Segments	Branch
51.8%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
51.8%	1	`y`
51.8%	1	`x`
51.8%	1	`z`
51.8%	1	`(/.f64 z #s(literal 8 binary64))`
51.8%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
51.8%	1	`(*.f64 x y)`

Compiler

Compiled 44 to 33 computations (25% saved)

bsearch25.0ms (0.7%)

Memory

36.5MiB live, 36.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	2.4836775676313938e-67	3.6986692349244306e-63
12.0ms	-3.2190339100778275e-36	-5.292618972239464e-54

Samples

12.0ms

288×

valid

Compiler

Compiled 303 to 231 computations (23.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 3.0ms (55.4% of total)

ival-sub: 1.0ms (18.5% of total)

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

exact: 0.0ms (0% of total)

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

simplify11.0ms (0.3%)

Memory

-27.5MiB live, 12.1MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	76
1	28	76

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x (*.f64 z #s(literal -1/8 binary64)))

(if (<=.f64 (*.f64 x y) #s(literal -2244866514940267/748288838313422294120286634350736906063837462003712 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y))) (if (<=.f64 (*.f64 x y) #s(literal 2408475456136177/926336713898529563388567880069503262826159877325124512315660672063305037119488 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64))) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y)))))

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

Outputs
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 z #s(literal -1/8 binary64)))
(if (<=.f64 (.f64 x y) #s(literal -2244866514940267/748288838313422294120286634350736906063837462003712 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y))) (if (<=.f64 (.f64 x y) #s(literal 2408475456136177/926336713898529563388567880069503262826159877325124512315660672063305037119488 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 z #s(literal -1/8 binary64))) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 x y)))))
(if (<=.f64 (.f64 y x) #s(literal -2244866514940267/748288838313422294120286634350736906063837462003712 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x))) (if (<=.f64 (.f64 y x) #s(literal 2408475456136177/926336713898529563388567880069503262826159877325124512315660672063305037119488 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 z #s(literal -1/8 binary64))) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

soundness389.0ms (11.6%)

Memory

15.9MiB live, 253.2MiB allocated

Rules

5 312×	`lower-fma.f64`
5 312×	`lower-fma.f32`
4 784×	`lower-*.f32`
4 782×	`lower-*.f64`
4 218×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
0	13	20
1	56	20
2	486	20
0	8677	19
0	42	508
1	123	508
2	350	508
3	861	508
4	1961	508
5	4019	508
6	6382	508
0	8114	481

Stop Event

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

Compiler

Compiled 83 to 46 computations (44.6% saved)

preprocess62.0ms (1.8%)

Memory: 18.8MiB live, 57.6MiB allocated
Remove: (sort x y)
Compiler: Compiled 132 to 66 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	9	25
0	13	25
1	18	25
2	31	25
3	40	25
4	64	25
5	108	25
6	189	25
7	312	25
8	447	25
9	514	25
10	549	25
11	550	25
0	550	24

Iter	Nodes	Cost
0	18	63
0	24	64
1	37	64
2	54	64
3	63	64
4	88	64
5	134	64
6	224	64
7	369	61
8	537	61
9	578	61
10	611	61
11	612	61
0	612	61

Iter	Nodes	Cost
0	9	25
0	13	25
1	18	25
2	31	25
3	40	25
4	64	25
5	108	25
6	189	25
7	312	25
8	447	25
9	514	25
10	549	25
11	550	25
0	550	24

Iter	Nodes	Cost
0	18	63
0	24	64
1	37	64
2	54	64
3	63	64
4	88	64
5	134	64
6	224	64
7	369	61
8	537	61
9	578	61
10	611	61
11	612	61
0	612	61

analyze0.0ms (0%)

sample992.0ms (29.5%)

preprocess64.0ms (1.9%)

explain98.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify31.0ms (0.9%)

localize48.0ms (1.4%)

series8.0ms (0.2%)

simplify263.0ms (7.8%)

rewrite323.0ms (9.6%)

eval50.0ms (1.5%)

prune50.0ms (1.5%)

simplify27.0ms (0.8%)

localize48.0ms (1.4%)

series7.0ms (0.2%)

simplify242.0ms (7.2%)

rewrite366.0ms (10.9%)

eval112.0ms (3.3%)

prune64.0ms (1.9%)

regimes16.0ms (0.5%)

regimes28.0ms (0.8%)

regimes36.0ms (1.1%)

bsearch25.0ms (0.7%)

simplify11.0ms (0.3%)

soundness389.0ms (11.6%)

preprocess62.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	25
0	13	25
1	18	25
2	31	25
3	40	25
4	64	25
5	108	25
6	189	25
7	312	25
8	447	25
9	514	25
10	549	25
11	550	25
0	550	24

Iter	Nodes	Cost
0	18	63
0	24	64
1	37	64
2	54	64
3	63	64
4	88	64
5	134	64
6	224	64
7	369	61
8	537	61
9	578	61
10	611	61
11	612	61
0	612	61