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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample718.0ms (29.2%)

Memory

-16.2MiB live, 1 061.0MiB allocated

Samples

472.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 287.0ms

ival-div: 146.0ms (50.9% of total)

ival-mult: 80.0ms (27.9% of total)

ival-sub: 43.0ms (15% of total)

exact: 8.0ms (2.8% of total)

ival-true: 6.0ms (2.1% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

explain135.0ms (5.5%)

Memory

17.3MiB live, 142.7MiB 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

28.0ms

512×

valid

Compiler

Compiled 63 to 31 computations (50.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-div: 6.0ms (45.2% of total)

ival-mult: 4.0ms (30.2% of total)

ival-sub: 2.0ms (15.1% of total)

exact: 1.0ms (7.5% of total)

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

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

preprocess78.0ms (3.2%)

Memory

-23.3MiB live, 52.0MiB 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 #s(literal 1/2 binary64) (.f64 y x) (.f64 #s(literal -1/8 binary64) z))

Symmetry

(sort x y)

Compiler

Compiled 9 to 9 computations (0% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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 9 to 9 computations (0% saved)

simplify18.0ms (0.7%)

Memory

13.3MiB live, 13.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize19.0ms (0.8%)

Memory

20.9MiB live, 20.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 (*.f64 x y) #s(literal 2 binary64))
accuracy	0	(/.f64 z #s(literal 8 binary64))
accuracy	0	(*.f64 x y)
accuracy	0.0078125	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Samples

14.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-div: 3.0ms (45.6% of total)

ival-mult: 2.0ms (30.4% of total)

ival-sub: 1.0ms (15.2% of total)

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

exact: 0.0ms (0% of total)

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

series36.0ms (1.5%)

Memory

-39.6MiB live, 11.3MiB 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 (* 1/8 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 (* 1/2 (* 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 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 (/.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 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 (/.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 (* 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 (* -1/8 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 (* 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 (* 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 (.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 (* 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 (* 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 (.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 (* 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 (* 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 (* -1/8 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 (* 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 (* 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 (.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 (* 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 (* 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 (.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 (* 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>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
28.0ms	z	@	0	((/ (* x y) 2) (/ z 8) (- (/ (* x y) 2) (/ z 8)) (* x y))
1.0ms	x	@	0	((/ (* x y) 2) (/ z 8) (- (/ (* x y) 2) (/ z 8)) (* x y))
1.0ms	z	@	inf	((/ (* x y) 2) (/ z 8) (- (/ (* x y) 2) (/ z 8)) (* x y))
1.0ms	z	@	-inf	((/ (* x y) 2) (/ z 8) (- (/ (* x y) 2) (/ z 8)) (* x y))
1.0ms	y	@	-inf	((/ (* x y) 2) (/ z 8) (- (/ (* x y) 2) (/ z 8)) (* x y))

simplify132.0ms (5.4%)

Memory

22.9MiB live, 137.8MiB 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	859	508
4	1956	508
5	4016	508
6	6381	508
0	8111	481

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite159.0ms (6.5%)

Memory

8.4MiB live, 126.1MiB allocated

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
(.f64 (.f64 #s(literal 1/2 binary64) y) x)
(.f64 (.f64 #s(literal 1/2 binary64) x) y)
(.f64 (.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 y #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 y x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 y x)) #s(literal -1/2 binary64)))
(.f64 (neg.f64 x) (.f64 y #s(literal -1/2 binary64)))
(.f64 (neg.f64 y) (.f64 x #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 y x) #s(literal -1/2 binary64)))
(.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))
(.f64 (.f64 y #s(literal 1/2 binary64)) x)
(.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 y x)))
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(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/64 binary64) z) z (fma.f64 (.f64 (.f64 y x) z) #s(literal 1/16 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) z) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/64 binary64) z) z (fma.f64 (.f64 (.f64 y x) z) #s(literal 1/16 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64))))))
(-.f64 (.f64 (.f64 #s(literal 8 binary64) (.f64 y x)) #s(literal 1/16 binary64)) (.f64 (*.f64 z #s(literal 2 binary64)) #s(literal 1/16 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 y x))))
(-.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 (*.f64 y x) #s(literal -1/2 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) (*.f64 #s(literal 1/8 binary64) z))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) z (.f64 #s(literal 1/2 binary64) (.f64 y x)))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) z) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) z (.f64 #s(literal 1/2 binary64) (*.f64 y x))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/64 binary64) z) z (fma.f64 (.f64 (.f64 y x) z) #s(literal 1/16 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) #s(literal 2 binary64))))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) z) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/64 binary64) z) z (fma.f64 (.f64 (.f64 y x) z) #s(literal 1/16 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y x)) #s(literal 2 binary64)))))))
(+.f64 (.f64 (.f64 #s(literal 8 binary64) (.f64 y x)) #s(literal 1/16 binary64)) (neg.f64 (.f64 (*.f64 z #s(literal 2 binary64)) #s(literal 1/16 binary64))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 y x)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) (*.f64 #s(literal -1/8 binary64) z))
(.f64 (.f64 #s(literal 1 binary64) y) x)
(.f64 (.f64 #s(literal 1 binary64) x) y)
(*.f64 (neg.f64 (neg.f64 x)) y)
(*.f64 (neg.f64 (neg.f64 y)) x)
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) y))
(.f64 #s(literal 1 binary64) (.f64 y x))
(.f64 (.f64 y x) #s(literal 1 binary64))
(.f64 y (.f64 x #s(literal 1 binary64)))
(*.f64 y (neg.f64 (neg.f64 x)))
(*.f64 y x)
(.f64 x (.f64 y #s(literal 1 binary64)))
(*.f64 x (neg.f64 (neg.f64 y)))
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) y))

eval71.0ms (2.9%)

Memory: -15.6MiB live, 63.9MiB allocated
Compiler: Compiled 4 979 to 612 computations (87.7% saved)

prune6.0ms (0.2%)

Memory

19.7MiB live, 19.7MiB 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 #s(literal -1/8 binary64) z))
▶	52.3%	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64)))
▶	49.1%	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Status

Accuracy

Program

▶

100.0%

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

▶

52.3%

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

▶

49.1%

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

Compiler

Compiled 18 to 21 computations (-16.7% saved)

simplify32.0ms (1.3%)

Memory

-30.8MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 #s(literal -1/8 binary64) z)
cost-diff	0	(*.f64 y #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 #s(literal -1/8 binary64) z))
cost-diff	0	(*.f64 y x)
cost-diff	0	(.f64 (.f64 y x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 #s(literal -1/8 binary64) z)
cost-diff	0	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

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	63
1	38	63
2	54	63
3	63	63
4	88	63
5	134	63
6	224	63
7	369	61
8	533	61
9	574	61
10	607	61
11	608	61
0	608	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 -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64)))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(*.f64 y x)
y
x
#s(literal 1/2 binary64)
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 #s(literal -1/8 binary64) z))
(*.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
x
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z

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

localize47.0ms (1.9%)

Memory

2.9MiB live, 40.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 #s(literal -1/8 binary64) z))
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	0	(*.f64 #s(literal -1/8 binary64) z)
accuracy	0	(.f64 (.f64 y x) #s(literal 1/2 binary64))
accuracy	0	(*.f64 y x)
accuracy	30.5565577056322	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 #s(literal -1/8 binary64) z)
accuracy	32.58006263710924	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Samples

38.0ms

256×

valid

Compiler

Compiled 56 to 19 computations (66.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 9.0ms (58.2% of total)

ival-div: 3.0ms (19.4% of total)

ival-sub: 1.0ms (6.5% of total)

ival-add: 1.0ms (6.5% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.4%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

7 → 180

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (* (* y x) 1/2) (* y x) (+ (* (* y 1/2) x) (* -1/8 z)) (* y 1/2))
1.0ms	y	@	inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (* (* y x) 1/2) (* y x) (+ (* (* y 1/2) x) (* -1/8 z)) (* y 1/2))
1.0ms	y	@	0	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (* (* y x) 1/2) (* y x) (+ (* (* y 1/2) x) (* -1/8 z)) (* y 1/2))
1.0ms	x	@	-inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (* (* y x) 1/2) (* y x) (+ (* (* y 1/2) x) (* -1/8 z)) (* y 1/2))
1.0ms	x	@	0	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (* (* y x) 1/2) (* y x) (+ (* (* y 1/2) x) (* -1/8 z)) (* y 1/2))

simplify124.0ms (5.1%)

Memory

10.0MiB live, 87.2MiB 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	859	1104
4	1967	1104
5	4046	1104
6	6405	1104
0	8135	1023

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

rewrite161.0ms (6.6%)

Memory

15.1MiB live, 125.7MiB allocated

Rules

4 322×	`lower-/.f64`
4 322×	`lower-/.f32`
4 102×	`lower-*.f32`
4 094×	`lower-*.f64`
3 786×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	50
0	24	50
1	88	48
2	739	48
0	8927	48

Stop Event

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

Counts

7 → 203

Calls

Call 1

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

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

eval73.0ms (3%)

Memory: -3.7MiB live, 80.4MiB allocated
Compiler: Compiled 5 226 to 575 computations (89% saved)

prune21.0ms (0.8%)

Memory

-3.7MiB live, 33.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	414	3	417

Accuracy

100.0%

Counts

417 → 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 #s(literal -1/8 binary64) z))

✓

52.3%

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

✓

49.1%

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

Compiler

Compiled 45 to 39 computations (13.3% saved)

regimes32.0ms (1.3%)

Memory

-12.8MiB live, 26.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

Calls

7 calls:

19.0ms	z
2.0ms	y
2.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 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 23 to 33 computations (-43.5% saved)

regimes11.0ms (0.5%)

Memory

20.7MiB live, 20.7MiB allocated

Counts

2 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

7 calls:

2.0ms	z
2.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
1.0ms	(/.f64 (*.f64 x y) #s(literal 2 binary64))
1.0ms	x

Results

Accuracy	Segments	Branch
78.0%	3	`x`
71.9%	3	`y`
73.8%	3	`z`
68.3%	5	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
80.4%	3	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
80.4%	3	`(*.f64 x y)`
73.8%	3	`(/.f64 z #s(literal 8 binary64))`

Compiler

Compiled 23 to 33 computations (-43.5% saved)

regimes28.0ms (1.2%)

Memory

-25.3MiB live, 17.2MiB 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 #s(literal -1/8 binary64) z))

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

Calls

7 calls:

20.0ms	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
49.1%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
49.1%	1	`y`
49.1%	1	`z`
49.1%	1	`(/.f64 z #s(literal 8 binary64))`
49.1%	1	`x`
49.1%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
49.1%	1	`(*.f64 x y)`

Compiler

Compiled 23 to 33 computations (-43.5% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	4.812411174543885e-68	1.3927360634769449e-64
0.0ms	-3.777080850038337e+96	-5.892228205505686e+89

Compiler

Compiled 12 to 15 computations (-25% saved)

simplify57.0ms (2.3%)

Memory

-4.6MiB live, 34.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	76
1	29	76

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x y) #s(literal -2000000000000000099723307943817786034020536970876924303149785861223976798198611630768918030712832 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 (*.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 (*.f64 x y) #s(literal 6070840288205403/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 (*.f64 y x) #s(literal 1/2 binary64)))))

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

Outputs
(fma.f64 (.f64 y #s(literal 1/2 binary64)) x (.f64 #s(literal -1/8 binary64) z))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 z #s(literal -1/8 binary64)))
(if (<=.f64 (.f64 x y) #s(literal -2000000000000000099723307943817786034020536970876924303149785861223976798198611630768918030712832 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 (.f64 x y) #s(literal 6070840288205403/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 (.f64 x y) #s(literal -2000000000000000099723307943817786034020536970876924303149785861223976798198611630768918030712832 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 (.f64 x y) #s(literal 1/2 binary64))) (if (<=.f64 (.f64 x y) #s(literal 6070840288205403/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 z #s(literal -1/8 binary64))) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 (.f64 x y) #s(literal 1/2 binary64)))))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 z #s(literal -1/8 binary64)))

soundness446.0ms (18.1%)

Memory

19.2MiB live, 242.1MiB 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	859	508
4	1956	508
5	4016	508
6	6381	508
0	8111	481

Stop Event

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

Compiler

Compiled 68 to 48 computations (29.4% saved)

preprocess43.0ms (1.8%)

Memory: 20.1MiB live, 110.2MiB allocated
Remove: (sort x y)
Compiler: Compiled 146 to 102 computations (30.1% 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	63
1	38	63
2	54	63
3	63	63
4	88	63
5	134	63
6	224	63
7	369	61
8	533	61
9	574	61
10	607	61
11	608	61
0	608	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	63
1	38	63
2	54	63
3	63	63
4	88	63
5	134	63
6	224	63
7	369	61
8	533	61
9	574	61
10	607	61
11	608	61
0	608	61

start0.0ms (0%)

analyze0.0ms (0%)

sample718.0ms (29.2%)

explain135.0ms (5.5%)

preprocess78.0ms (3.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify18.0ms (0.7%)

localize19.0ms (0.8%)

series36.0ms (1.5%)

simplify132.0ms (5.4%)

rewrite159.0ms (6.5%)

eval71.0ms (2.9%)

prune6.0ms (0.2%)

simplify32.0ms (1.3%)

localize47.0ms (1.9%)

series10.0ms (0.4%)

simplify124.0ms (5.1%)

rewrite161.0ms (6.6%)

eval73.0ms (3%)

prune21.0ms (0.8%)

regimes32.0ms (1.3%)

regimes11.0ms (0.5%)

regimes28.0ms (1.2%)

bsearch1.0ms (0%)

simplify57.0ms (2.3%)

soundness446.0ms (18.1%)

preprocess43.0ms (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	63
1	38	63
2	54	63
3	63	63
4	88	63
5	134	63
6	224	63
7	369	61
8	533	61
9	574	61
10	607	61
11	608	61
0	608	61