Metrics for Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze52.0ms (0.8%)

Memory

-4.4MiB live, 87.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
50%	49.9%	49.9%	0.1%	0%	0%	0%	4
50%	49.9%	49.9%	0.1%	0%	0%	0%	5
50%	49.9%	49.9%	0.1%	0%	0%	0%	6
75%	74.9%	25%	0.1%	0%	0%	0%	7
75%	74.9%	25%	0.1%	0%	0%	0%	8
75%	74.9%	25%	0.1%	0%	0%	0%	9
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	10
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	11
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	12

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample988.0ms (15.6%)

Memory

-11.3MiB live, 1 326.9MiB allocated

Samples

620.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 391.0ms

ival-sub: 189.0ms (48.3% of total)

ival-mult: 109.0ms (27.9% of total)

ival-div: 75.0ms (19.2% of total)

exact: 8.0ms (2% of total)

ival-true: 6.0ms (1.5% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain127.0ms (2%)

Memory

3.5MiB live, 162.8MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`z`
-	-	`#s(literal 4 binary64)`
-	-	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`
-	-	`y`
-	-	`(-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))`
-	-	`(*.f64 z #s(literal 1/2 binary64))`
-	-	`(-.f64 x y)`
-	-	`#s(literal 1/2 binary64)`
-	-	`(.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))))`
-	-	`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

32.0ms

512×

valid

Compiler

Compiled 91 to 34 computations (62.6% saved)

Precisions

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

ival-mult: 6.0ms (37.7% of total)

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

ival-div: 3.0ms (18.8% of total)

exact: 1.0ms (6.3% of total)

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

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

preprocess239.0ms (3.8%)

Memory

-3.2MiB live, 113.0MiB allocated

Algorithm

1×	egg-herbie

Rules

2 736×	`lower-fma.f64`
2 736×	`lower-fma.f32`
1 156×	`div-sub`
1 152×	`lower-*.f32`
1 148×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	109
1	126	101
2	405	99
3	1525	81
4	5505	81
0	10	11
0	15	11
1	28	11
2	68	11
3	169	9
4	409	9
5	976	9
6	2577	9
7	4574	9
8	4888	9
9	4898	9
10	4907	9
11	4907	9
12	5219	9
13	5428	9
14	5444	9
15	5444	9
16	5444	9
17	5476	9
18	5583	9
0	5583	8

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Outputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(fma.f64 (/.f64 #s(literal -4 binary64) z) (-.f64 y x) #s(literal -2 binary64))

Compiler

Compiled 11 to 10 computations (9.1% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune6.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify185.0ms (2.9%)

Memory

21.8MiB live, 92.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	0	(.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))))
cost-diff	128	(-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))
cost-diff	320	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Rules

2 736×	`lower-fma.f64`
2 736×	`lower-fma.f32`
1 156×	`div-sub`
1 152×	`lower-*.f32`
1 148×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
0	15	38
1	28	38
2	68	38
3	169	36
4	409	36
5	976	36
6	2577	36
7	4574	36
8	4888	36
9	4898	36
10	4907	36
11	4907	36
12	5219	36
13	5428	36
14	5444	36
15	5444	36
16	5444	36
17	5476	36
18	5583	36
0	5583	33

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))))
#s(literal 4 binary64)
(-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))
(-.f64 x y)
x
y
(*.f64 z #s(literal 1/2 binary64))
z
#s(literal 1/2 binary64)

Outputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(fma.f64 (/.f64 #s(literal -4 binary64) z) (-.f64 y x) #s(literal -2 binary64))
(.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)) #s(literal 4 binary64))
#s(literal 4 binary64)
(-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(-.f64 x y)
x
y
(*.f64 z #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) z)
z
#s(literal 1/2 binary64)

localize66.0ms (1%)

Memory

-13.8MiB live, 37.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(*.f64 z #s(literal 1/2 binary64))
accuracy	0	(.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))))
accuracy	0.01953125	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Samples

43.0ms

256×

valid

Compiler

Compiled 40 to 12 computations (70% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sub: 3.0ms (37.9% of total)

ival-mult: 3.0ms (37.9% of total)

ival-div: 2.0ms (25.3% of total)

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.3%)

Memory

-11.8MiB live, 21.9MiB allocated

Counts

5 → 144

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())
#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())
#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1/2 z)) y) (taylor 0 z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1/2 z)) y) (taylor 0 z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ x (* -1/2 z)) y) (taylor 0 z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (- x y)) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor 0 z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor 0 z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor 0 z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor 0 z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt -2 (taylor inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1/2 z) (taylor inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (+ 1/2 (/ y z)))) (taylor inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (+ 1/2 (/ y z)))) (taylor inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (+ 1/2 (/ y z)))) (taylor inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -2 z) (taylor inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 4 (/ (- x y) z)) 2)) (taylor inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 4 (/ (- x y) z)) 2)) (taylor inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* z (- (* 4 (/ (- x y) z)) 2)) (taylor inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor inf z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor inf z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor inf z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 z) (taylor inf z) (#s(alt (.f64 z #s(literal 1/2 binary64)) (patch (.f64 z #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor -inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor -inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor -inf z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1/2 z) (taylor -inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/2 (* -1 (/ (- x y) z))))) (taylor -inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/2 (* -1 (/ (- x y) z))))) (taylor -inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 1/2 (* -1 (/ (- x y) z))))) (taylor -inf z) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -2 z) (taylor -inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 2 (* -4 (/ (- x y) z))))) (taylor -inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 2 (* -4 (/ (- x y) z))))) (taylor -inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ 2 (* -4 (/ (- x y) z))))) (taylor -inf z) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x)))) (taylor inf x) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x)))) (taylor inf x) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) (patch (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) (patch (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (- (- x y) (* z 1/2)) (* 4 (- (- x y) (* z 1/2))) (- x y) (* z 1/2))
1.0ms	z	@	inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (- (- x y) (* z 1/2)) (* 4 (- (- x y) (* z 1/2))) (- x y) (* z 1/2))
1.0ms	y	@	0	((/ (* 4 (- (- x y) (* z 1/2))) z) (- (- x y) (* z 1/2)) (* 4 (- (- x y) (* z 1/2))) (- x y) (* z 1/2))
1.0ms	z	@	-inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (- (- x y) (* z 1/2)) (* 4 (- (- x y) (* z 1/2))) (- x y) (* z 1/2))
1.0ms	z	@	0	((/ (* 4 (- (- x y) (* z 1/2))) z) (- (- x y) (* z 1/2)) (* 4 (- (- x y) (* z 1/2))) (- x y) (* z 1/2))

simplify121.0ms (1.9%)

Memory

40.9MiB live, 112.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 634×	`lower-fma.f64`
9 634×	`lower-fma.f32`
3 970×	`lower-*.f64`
3 970×	`lower-*.f32`
1 970×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	890
1	390	889
2	1127	887
3	3264	885
0	8225	800

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 139

Calls

Call 1

Inputs
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(- x y)
(- (+ x (* -1/2 z)) y)
(- (+ x (* -1/2 z)) y)
(- (+ x (* -1/2 z)) y)
(* 4 (- x y))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -1/2 z)
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* -2 z)
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -1/2 z)
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -2 z)
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(- x (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(* 4 (- x (* 1/2 z)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -4 (/ y z))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* -1 y)
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(* -4 y)
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(* -4 y)
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(* -1 (+ y (* 1/2 z)))
(- x (+ y (* 1/2 z)))
(- x (+ y (* 1/2 z)))
(- x (+ y (* 1/2 z)))
(* -4 (+ y (* 1/2 z)))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(* -1 y)
(- x y)
(- x y)
(- x y)
(* 4 (/ x z))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
x
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(* 4 x)
(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* 4 (/ x z))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
x
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(* 4 x)
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))

Outputs
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x))) z)
(- x y)
(-.f64 x y)
(- (+ x (* -1/2 z)) y)
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- (+ x (* -1/2 z)) y)
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- (+ x (* -1/2 z)) y)
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* 4 (- x y))
(*.f64 (-.f64 y x) #s(literal -4 binary64))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1/2 z)
(*.f64 #s(literal -1/2 binary64) z)
(* z (- (/ x z) (+ 1/2 (/ y z))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -2 z)
(*.f64 #s(literal -2 binary64) z)
(* z (- (* 4 (/ (- x y) z)) 2))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* z (- (* 4 (/ (- x y) z)) 2))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* z (- (* 4 (/ (- x y) z)) 2))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1/2 z)
(*.f64 #s(literal -1/2 binary64) z)
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -2 z)
(*.f64 #s(literal -2 binary64) z)
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 1/2 z)
(*.f64 #s(literal 1/2 binary64) z)
(* 4 (/ (- x (* 1/2 z)) z))
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- x (* 1/2 z))
(fma.f64 #s(literal -1/2 binary64) z x)
(- (+ x (* -1 y)) (* 1/2 z))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- (+ x (* -1 y)) (* 1/2 z))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- (+ x (* -1 y)) (* 1/2 z))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* 4 (- x (* 1/2 z)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) z x) #s(literal 4 binary64))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -4 (/ (+ y (* 1/2 z)) z))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (+ y (* 1/2 z)))
(fma.f64 #s(literal -1/2 binary64) z (neg.f64 y))
(- x (+ y (* 1/2 z)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- x (+ y (* 1/2 z)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- x (+ y (* 1/2 z)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -4 (+ y (* 1/2 z)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) z y) #s(literal -4 binary64))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(* 4 (/ x z))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
x
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* 4 (/ x z))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
x
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)))
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)

rewrite203.0ms (3.2%)

Memory

-9.9MiB live, 199.4MiB allocated

Rules

4 820×	`lower-fma.f64`
4 820×	`lower-fma.f32`
4 390×	`lower-*.f32`
4 386×	`lower-*.f64`
3 134×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	15	33
1	60	33
2	470	33
3	6831	33
0	8009	30

Stop Event

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

Counts

5 → 338

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))
(.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64))))
(-.f64 x y)
(*.f64 z #s(literal 1/2 binary64))

Outputs
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eval83.0ms (1.3%)

Memory: -4.9MiB live, 104.4MiB allocated
Compiler: Compiled 10 342 to 1 382 computations (86.6% saved)

prune15.0ms (0.2%)

Memory

-11.0MiB live, 37.7MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	468	9	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	9	478

Accuracy

100.0%

Counts

478 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.3%	(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)
	67.4%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (fma.f64 #s(literal -1/2 binary64) z x))) z)
▶	69.3%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
	37.1%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
▶	36.5%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
▶	67.3%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
	37.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
	67.2%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
▶	33.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Compiler

Compiled 148 to 154 computations (-4.1% saved)

simplify99.0ms (1.6%)

Memory

14.3MiB live, 87.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	0	#s(approx (- (- x y) (* z 1/2)) (-.f64 x y))
cost-diff	0	(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)))
cost-diff	0	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
cost-diff	0	(/.f64 #s(literal 4 binary64) z)
cost-diff	0	(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
cost-diff	0	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
cost-diff	0	(*.f64 #s(literal -4 binary64) y)
cost-diff	0	#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y))
cost-diff	0	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
cost-diff	0	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
cost-diff	128	(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x)))
cost-diff	256	(neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))
cost-diff	320	(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)
cost-diff	1728	(fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))

Rules

4 880×	`lower-fma.f32`
4 874×	`lower-fma.f64`
2 244×	`lower-*.f32`
2 234×	`lower-*.f64`
1 942×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	227
0	57	227
1	114	219
2	259	216
3	875	210
4	2717	186
5	5470	186
0	8126	176

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)
(.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z)))
#s(literal 4 binary64)
(fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))
(neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
y
(*.f64 x x)
x
(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x)))
#s(literal 1 binary64)
(neg.f64 (+.f64 y x))
(+.f64 y x)
(*.f64 #s(literal -1/2 binary64) z)
#s(literal -1/2 binary64)
z
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(literal -2 binary64)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y))
(*.f64 #s(literal -4 binary64) y)
#s(literal -4 binary64)
y
z
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/.f64 #s(literal 4 binary64) z)
#s(literal 4 binary64)
z
x
#s(literal -2 binary64)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)))
#s(literal 4 binary64)
#s(approx (- (- x y) (* z 1/2)) (-.f64 x y))
(-.f64 x y)
x
y
z

Outputs
(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)
(fma.f64 (/.f64 #s(literal -4 binary64) z) (-.f64 y x) #s(literal -2 binary64))
(.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) z (-.f64 y x)) #s(literal -4 binary64))
#s(literal 4 binary64)
(fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))
(fma.f64 z #s(literal -1/2 binary64) (-.f64 x y))
(neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))
(*.f64 (-.f64 y x) (+.f64 x y))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(neg.f64 y)
y
(*.f64 x x)
x
(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x)))
(/.f64 #s(literal -1 binary64) (+.f64 x y))
#s(literal 1 binary64)
(neg.f64 (+.f64 y x))
(-.f64 (neg.f64 y) x)
(+.f64 y x)
(+.f64 x y)
(*.f64 #s(literal -1/2 binary64) z)
(*.f64 z #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
z
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(literal -2 binary64)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y))
(*.f64 #s(literal -4 binary64) y)
#s(literal -4 binary64)
y
z
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/.f64 #s(literal 4 binary64) z)
#s(literal 4 binary64)
z
x
#s(literal -2 binary64)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
(.f64 #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)) (/.f64 #s(literal 4 binary64) z))
(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)))
(.f64 #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)) #s(literal 4 binary64))
#s(literal 4 binary64)
#s(approx (- (- x y) (* z 1/2)) (-.f64 x y))
(-.f64 x y)
x
y
z

localize92.0ms (1.5%)

Memory

2.2MiB live, 117.6MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)))
accuracy	0.01953125	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
accuracy	19.74755844288937	#s(approx (- (- x y) (* z 1/2)) (-.f64 x y))
accuracy	0	(/.f64 #s(literal 4 binary64) z)
accuracy	0.1171875	(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
accuracy	20.853766884663642	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
accuracy	0	(*.f64 #s(literal -4 binary64) y)
accuracy	0.01953125	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
accuracy	41.391940354515555	#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y))
accuracy	42.853177701924274	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x)))
accuracy	0.01953125	(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)
accuracy	1.4999834856333614	(fma.f64 (neg.f64 y) y (*.f64 x x))
accuracy	25.900313199376072	(fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))

Samples

70.0ms

256×

valid

Compiler

Compiled 209 to 33 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 18.0ms (43.6% of total)

ival-div: 12.0ms (29.1% of total)

ival-add: 5.0ms (12.1% of total)

ival-neg: 3.0ms (7.3% of total)

ival-sub: 2.0ms (4.8% of total)

exact: 1.0ms (2.4% of total)

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

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

series46.0ms (0.7%)

Memory

14.4MiB live, 89.2MiB allocated

Counts

16 → 468

Calls

Call 1

Inputs
#s(alt (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) (patch (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) #<representation binary64>) () ())
#s(alt (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (patch (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (patch (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z) #<representation binary64>) () ())
#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -4 binary64) y) (patch (.f64 #s(literal -4 binary64) y) #<representation binary64>) () ())
#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) #<representation binary64>) () ())
#s(alt #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) (patch #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) #<representation binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 y) y (.f64 x x)) (patch (fma.f64 (neg.f64 y) y (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) (patch (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y)))) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) (patch (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y)))) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) (patch (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y)))) (taylor 0 z) (#s(alt (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) (patch (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (- x y)) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 x)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 x)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 x)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (- x y)) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) (patch #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) (patch #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) (patch #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) (patch #s(approx (- (- x y) (* z 1/2)) (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 y) y (.f64 x x)) (patch (fma.f64 (neg.f64 y) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 y) y (.f64 x x)) (patch (fma.f64 (neg.f64 y) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 y) y (.f64 x x)) (patch (fma.f64 (neg.f64 y) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (neg.f64 y) y (.f64 x x)) (patch (fma.f64 (neg.f64 y) y (.f64 x x)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
7.0ms	y	@	0	((+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z)) (/ (* 4 (+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z))) z) (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x))) (/ (* 4 (- (- x y) (* z 1/2))) z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* -4 y) (/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ 4 z) x) -2) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y) (+ (* (neg y) y) (* x x)))
4.0ms	y	@	inf	((+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z)) (/ (* 4 (+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z))) z) (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x))) (/ (* 4 (- (- x y) (* z 1/2))) z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* -4 y) (/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ 4 z) x) -2) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y) (+ (* (neg y) y) (* x x)))
4.0ms	x	@	inf	((+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z)) (/ (* 4 (+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z))) z) (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x))) (/ (* 4 (- (- x y) (* z 1/2))) z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* -4 y) (/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ 4 z) x) -2) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y) (+ (* (neg y) y) (* x x)))
3.0ms	x	@	0	((+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z)) (/ (* 4 (+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z))) z) (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x))) (/ (* 4 (- (- x y) (* z 1/2))) z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* -4 y) (/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ 4 z) x) -2) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y) (+ (* (neg y) y) (* x x)))
3.0ms	z	@	0	((+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z)) (/ (* 4 (+ (* (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x)))) (* -1/2 z))) z) (neg (+ (* (neg y) y) (* x x))) (/ 1 (neg (+ y x))) (/ (* 4 (- (- x y) (* z 1/2))) z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* -4 y) (/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ 4 z) x) -2) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y) (+ (* (neg y) y) (* x x)))

simplify165.0ms (2.6%)

Memory

-43.0MiB live, 253.2MiB allocated

Algorithm

1×	egg-herbie

Rules

5 978×	`lower-fma.f64`
5 978×	`lower-fma.f32`
3 690×	`lower-*.f64`
3 690×	`lower-*.f32`
3 086×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	341	4780
1	1056	4662
2	3056	4516
0	8596	4203

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 461

Calls

Call 1

Inputs
(+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y)))
(+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y))))
(+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y))))
(+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y))))
(* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z))
(/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z)
(/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z)
(/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (- x y))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (/ x z))
(/ (+ (* -2 z) (* 4 x)) z)
(/ (+ (* -2 z) (* 4 x)) z)
(/ (+ (* -2 z) (* 4 x)) z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (- x y))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(- x y)
(- (+ x (* -1/2 z)) y)
(- (+ x (* -1/2 z)) y)
(- (+ x (* -1/2 z)) y)
(* -1/2 z)
(* z (- (+ (* -1 (/ (pow y 2) (* z (+ x y)))) (/ (pow x 2) (* z (+ x y)))) 1/2))
(* z (- (+ (* -1 (/ (pow y 2) (* z (+ x y)))) (/ (pow x 2) (* z (+ x y)))) 1/2))
(* z (- (+ (* -1 (/ (pow y 2) (* z (+ x y)))) (/ (pow x 2) (* z (+ x y)))) 1/2))
-2
(- (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) 2)
(- (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) 2)
(- (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) 2)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(/ 4 z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* -1/2 z)
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* -1/2 z)
(* -1 (* z (+ 1/2 (* -1 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)))))
-2
(- (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) 2)
(- (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) 2)
(- (* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z)) 2)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(/ 4 z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1/2 z)
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(+ x (* -1/2 z))
(+ x (+ (* -1 y) (* -1/2 z)))
(+ x (+ (* -1 y) (* -1/2 z)))
(+ x (+ (* -1 y) (* -1/2 z)))
(* 4 (/ (+ x (* -1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (+ x (* -1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (+ x (* -1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (+ x (* -1/2 z)) z)))
(* -1 (pow x 2))
(- (pow y 2) (pow x 2))
(- (pow y 2) (pow x 2))
(- (pow y 2) (pow x 2))
(/ -1 x)
(- (/ y (pow x 2)) (/ 1 x))
(- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(- (* y (+ (* y (- (/ y (pow x 4)) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (- x (* 1/2 z)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(* -4 y)
(* -4 y)
(* -4 y)
(* -4 y)
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (- x (* 1/2 z)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(- x (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(pow x 2)
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* -1 (pow y 2)) (pow x 2))
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(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(pow y 2)
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(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(/ -1 y)
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(pow y 2)
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(/ -1 y)
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(pow y 2)
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(- (* -1 (pow x 2)) (* -1 (pow y 2)))
(- (* -1 (pow x 2)) (* -1 (pow y 2)))
(/ -1 y)
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(- (* x (+ (* -1 (/ x (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))
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(+ (* -1 (pow y 2)) (pow x 2))
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x
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(* -1 (pow x 2))
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(/ -1 x)
(/ (- (/ y x) 1) x)
(/ (- (* -1 (/ (pow y 2) (pow x 2))) (+ 1 (* -1 (/ y x)))) x)
(/ (- (/ (pow y 3) (pow x 3)) (+ 1 (+ (* -1 (/ y x)) (/ (pow y 2) (pow x 2))))) x)
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x
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(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(/ -1 x)
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x
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(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))

Outputs
(+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y)))
(fma.f64 (neg.f64 y) (/.f64 y (+.f64 x y)) (*.f64 x (/.f64 x (+.f64 x y))))
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(+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y))))
(fma.f64 (neg.f64 y) (/.f64 y (+.f64 x y)) (fma.f64 x (/.f64 x (+.f64 x y)) (*.f64 z #s(literal -1/2 binary64))))
(+ (* -1 (/ (pow y 2) (+ x y))) (+ (* -1/2 z) (/ (pow x 2) (+ x y))))
(fma.f64 (neg.f64 y) (/.f64 y (+.f64 x y)) (fma.f64 x (/.f64 x (+.f64 x y)) (*.f64 z #s(literal -1/2 binary64))))
(* 4 (/ (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))) z))
(.f64 (fma.f64 (neg.f64 y) (/.f64 y (+.f64 x y)) (.f64 x (/.f64 x (+.f64 x y)))) (/.f64 #s(literal 4 binary64) z))
(/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z)
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(/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z)
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(/ (+ (* -2 z) (* 4 (+ (* -1 (/ (pow y 2) (+ x y))) (/ (pow x 2) (+ x y))))) z)
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(* 4 (/ (- x y) z))
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(/ (+ (* -2 z) (* 4 (- x y))) z)
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(+ (* -2 z) (* 4 (- x y)))
(fma.f64 (-.f64 x y) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) z))
(+ (* -2 z) (* 4 (- x y)))
(fma.f64 (-.f64 x y) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) z))
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
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(/ (+ (* -2 z) (* 4 (- x y))) z)
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(/ (+ (* -2 z) (* 4 (- x y))) z)
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(/ (+ (* -2 z) (* 4 x)) z)
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(/ (+ (* -2 z) (* 4 x)) z)
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(/ (+ (* -2 z) (* 4 x)) z)
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(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
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(/ (+ (* -2 z) (* 4 (- x y))) z)
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(/ (+ (* -2 z) (* 4 (- x y))) z)
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(* 4 (- x y))
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(+ (* -2 z) (* 4 (- x y)))
(fma.f64 (-.f64 x y) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) z))
(+ (* -2 z) (* 4 (- x y)))
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(+ (* -2 z) (* 4 (- x y)))
(fma.f64 (-.f64 x y) #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) z))
(- x y)
(-.f64 x y)
(- (+ x (* -1/2 z)) y)
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(- (+ x (* -1/2 z)) y)
(fma.f64 z #s(literal -1/2 binary64) (-.f64 x y))
(* -1/2 z)
(*.f64 z #s(literal -1/2 binary64))
(* z (- (+ (* -1 (/ (pow y 2) (* z (+ x y)))) (/ (pow x 2) (* z (+ x y)))) 1/2))
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rewrite174.0ms (2.8%)

Memory

5.7MiB live, 279.8MiB allocated

Rules

5 864×	`lower-fma.f32`
5 858×	`lower-fma.f64`
4 124×	`lower-/.f32`
4 114×	`lower-/.f64`
3 912×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	174
0	57	172
1	218	150
2	1662	150
0	8581	141

Stop Event

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

Counts

16 → 497

Calls

Call 1

Inputs
(fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (.f64 #s(literal -1/2 binary64) z))
(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)
(neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y))
(*.f64 #s(literal -4 binary64) y)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/.f64 #s(literal 4 binary64) z)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)))
#s(approx (- (- x y) (* z 1/2)) (-.f64 x y))
(-.f64 x y)
(fma.f64 (neg.f64 y) y (*.f64 x x))

Outputs
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eval157.0ms (2.5%)

Memory: 37.2MiB live, 233.4MiB allocated
Compiler: Compiled 18 635 to 2 531 computations (86.4% saved)

prune27.0ms (0.4%)

Memory

-18.8MiB live, 64.6MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	956	2	958
Fresh	1	3	4
Picked	2	3	5
Done	0	0	0
Total	959	8	967

Accuracy

100.0%

Counts

967 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.3%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
▶	61.4%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
▶	37.1%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
✓	36.5%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
▶	67.4%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
▶	37.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
▶	67.2%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
✓	33.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Compiler

Compiled 96 to 106 computations (-10.4% saved)

simplify165.0ms (2.6%)

Memory

-0.8MiB live, 109.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))
cost-diff	0	(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))))
cost-diff	0	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
cost-diff	1024	(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
cost-diff	0	(/.f64 y z)
cost-diff	0	(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
cost-diff	0	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
cost-diff	128	(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))
cost-diff	0	(*.f64 x #s(literal 4 binary64))
cost-diff	0	#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64)))
cost-diff	0	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
cost-diff	0	(/.f64 #s(literal 4 binary64) z)
cost-diff	0	(*.f64 (/.f64 #s(literal 4 binary64) z) x)
cost-diff	0	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
cost-diff	0	(/.f64 x z)
cost-diff	0	(fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))
cost-diff	0	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

Rules

5 454×	`lower-fma.f32`
5 452×	`lower-fma.f64`
2 526×	`lower-*.f32`
2 516×	`lower-*.f64`
1 220×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	225
0	48	225
1	79	225
2	140	225
3	288	219
4	677	199
5	1591	199
6	4128	199
7	6186	199
8	7083	199
9	7445	199
10	7566	199
11	7724	199
12	7968	199
0	8006	189

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
(fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))
(/.f64 x z)
x
z
#s(literal 4 binary64)
#s(literal -2 binary64)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(/.f64 #s(literal 4 binary64) z)
#s(literal 4 binary64)
z
x
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64)))
(*.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
z
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))
(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
#s(literal -1/2 binary64)
(/.f64 y z)
y
z
#s(literal 4 binary64)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))))
#s(literal 4 binary64)
#s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))
#s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(-.f64 #s(literal 1 binary64) (/.f64 y x))
#s(literal 1 binary64)
(/.f64 y x)
y
x
z

Outputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
(fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/.f64 x z)
x
z
#s(literal 4 binary64)
#s(literal -2 binary64)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(/.f64 #s(literal 4 binary64) z)
#s(literal 4 binary64)
z
x
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64)))
(*.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
z
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 #s(literal -4 binary64) (/.f64 y z) #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))
(fma.f64 #s(literal -4 binary64) (/.f64 y z) #s(literal -2 binary64))
(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
#s(literal -1/2 binary64)
(/.f64 y z)
y
z
#s(literal 4 binary64)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
(.f64 #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (-.f64 x y))) (/.f64 #s(literal 4 binary64) z))
(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))))
(.f64 #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (-.f64 x y))) #s(literal 4 binary64))
#s(literal 4 binary64)
#s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))
#s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (-.f64 x y)))
#s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))
#s(approx (- x y) (-.f64 x y))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(-.f64 x y)
(-.f64 #s(literal 1 binary64) (/.f64 y x))
#s(literal 1 binary64)
(/.f64 y x)
y
x
z

localize87.0ms (1.4%)

Memory

24.1MiB live, 104.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))
accuracy	0.01953125	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
accuracy	9.93148808092665	(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
accuracy	19.74755844288937	#s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))
accuracy	0	(/.f64 y z)
accuracy	0	(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
accuracy	0	(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))
accuracy	21.009577969406998	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
accuracy	0	(*.f64 x #s(literal 4 binary64))
accuracy	0.01953125	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
accuracy	40.77746202017822	#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64)))
accuracy	0	(/.f64 #s(literal 4 binary64) z)
accuracy	0.21875	(*.f64 (/.f64 #s(literal 4 binary64) z) x)
accuracy	40.232516878074144	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
accuracy	0	(fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))
accuracy	0	(/.f64 x z)
accuracy	20.853766884663642	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

Samples

71.0ms

256×

valid

Compiler

Compiled 155 to 27 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 34.0ms (62% of total)

ival-div: 13.0ms (23.7% of total)

ival-sub: 5.0ms (9.1% of total)

ival-add: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series45.0ms (0.7%)

Memory

-7.3MiB live, 68.4MiB allocated

Counts

18 → 504

Calls

Call 1

Inputs
#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) (patch (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())
#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 4 binary64) z) x) (patch (.f64 (/.f64 #s(literal 4 binary64) z) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z) #<representation binary64>) () ())
#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 4 binary64)) (patch (.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) (patch (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) (patch (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #<representation binary64>) () ())
#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) (patch #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) #<representation binary64>) () ())
#s(alt #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) (patch #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) #<representation binary64>) () ())

Outputs
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor 0 z) (#s(alt (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) (patch (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 x)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) (patch (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 x)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) (patch (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 x)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) (patch (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ())
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ())
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ())
#s(alt (/ x z) (taylor 0 z) (#s(alt (/.f64 x z) (patch (/.f64 x z) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 4 binary64) z) x) (patch (.f64 (/.f64 #s(literal 4 binary64) z) x) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 4 binary64) z) x) (patch (.f64 (/.f64 #s(literal 4 binary64) z) x) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 4 binary64) z) x) (patch (.f64 (/.f64 #s(literal 4 binary64) z) x) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 4 binary64) z) x) (patch (.f64 (/.f64 #s(literal 4 binary64) z) x) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ 4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal 4 binary64) z) (patch (/.f64 #s(literal 4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (patch (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (- x y)) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ y z)) (taylor 0 z) (#s(alt (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) (patch (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -4 y) (* -2 z)) z) (taylor 0 z) (#s(alt (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) (patch (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -4 y) (* -2 z)) z) (taylor 0 z) (#s(alt (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) (patch (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -4 y) (* -2 z)) z) (taylor 0 z) (#s(alt (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) (patch (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ y z)) (taylor 0 z) (#s(alt (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) (patch (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 z) y) z) (taylor 0 z) (#s(alt (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) (patch (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 z) y) z) (taylor 0 z) (#s(alt (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) (patch (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 z) y) z) (taylor 0 z) (#s(alt (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) (patch (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #<representation binary64>) () ())) ())
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ())
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ())
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ())
#s(alt (/ y z) (taylor 0 z) (#s(alt (/.f64 y z) (patch (/.f64 y z) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (- x y)) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 z) (* 4 (- x y))) (taylor 0 z) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
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#s(alt (* 4 x) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) (patch #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 4 binary64)) (patch (.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 4 binary64)) (patch (.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 4 binary64)) (patch (.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 4 binary64)) (patch (.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) (patch #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) (patch (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) (patch (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) (patch (.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) (patch #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) (patch #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) (patch #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) (patch #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) (patch #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) (patch #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) (patch #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) (patch #s(approx (- x y) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
9.0ms	z	@	-inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ x z) 4) -2) (/ x z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* (/ 4 z) x) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* x 4) (* (- -1/2 (/ y z)) 4) (/ (* 4 (- (- x y) (* z 1/2))) z) (- -1/2 (/ y z)) (/ y z) (* (- 1 (/ y x)) x) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y))
6.0ms	x	@	-inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ x z) 4) -2) (/ x z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* (/ 4 z) x) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* x 4) (* (- -1/2 (/ y z)) 4) (/ (* 4 (- (- x y) (* z 1/2))) z) (- -1/2 (/ y z)) (/ y z) (* (- 1 (/ y x)) x) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y))
2.0ms	x	@	inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ x z) 4) -2) (/ x z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* (/ 4 z) x) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* x 4) (* (- -1/2 (/ y z)) 4) (/ (* 4 (- (- x y) (* z 1/2))) z) (- -1/2 (/ y z)) (/ y z) (* (- 1 (/ y x)) x) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y))
2.0ms	y	@	-inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ x z) 4) -2) (/ x z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* (/ 4 z) x) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* x 4) (* (- -1/2 (/ y z)) 4) (/ (* 4 (- (- x y) (* z 1/2))) z) (- -1/2 (/ y z)) (/ y z) (* (- 1 (/ y x)) x) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y))
2.0ms	z	@	0	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ x z) 4) -2) (/ x z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* (/ 4 z) x) (/ 4 z) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (* x 4) (* (- -1/2 (/ y z)) 4) (/ (* 4 (- (- x y) (* z 1/2))) z) (- -1/2 (/ y z)) (/ y z) (* (- 1 (/ y x)) x) (/ (* 4 (- (- x y) (* z 1/2))) z) (* 4 (- (- x y) (* z 1/2))) (- (- x y) (* z 1/2)) (- x y))

simplify347.0ms (5.5%)

Memory

-11.2MiB live, 143.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 976×	`lower-fma.f64`
9 976×	`lower-fma.f32`
4 510×	`lower-*.f64`
4 510×	`lower-*.f32`
2 626×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	3218
1	465	3217
2	1352	3089
3	3871	3089
0	8173	2822

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 496

Calls

Call 1

Inputs
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (/ x z))
(/ (+ (* -2 z) (* 4 x)) z)
(/ (+ (* -2 z) (* 4 x)) z)
(/ (+ (* -2 z) (* 4 x)) z)
(/ x z)
(/ x z)
(/ x z)
(/ x z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(/ 4 z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (- x y))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(* -4 (/ y z))
(/ (+ (* -4 y) (* -2 z)) z)
(/ (+ (* -4 y) (* -2 z)) z)
(/ (+ (* -4 y) (* -2 z)) z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* -1 (/ y z))
(/ (- (* -1/2 z) y) z)
(/ (- (* -1/2 z) y) z)
(/ (- (* -1/2 z) y) z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* 4 (- x y))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(+ (* -2 z) (* 4 (- x y)))
(- x y)
(- (+ x (* -1/2 z)) y)
(- (+ x (* -1/2 z)) y)
(- (+ x (* -1/2 z)) y)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(/ x z)
(/ x z)
(/ x z)
(/ x z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(/ 4 z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
-2
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-1/2
(- (* -1 (/ y z)) 1/2)
(- (* -1 (/ y z)) 1/2)
(- (* -1 (/ y z)) 1/2)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* z (- (* 4 (/ (- x y) z)) 2))
(* -1/2 z)
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* z (- (/ x z) (+ 1/2 (/ y z))))
(* z (- (/ x z) (+ 1/2 (/ y z))))
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(/ x z)
(/ x z)
(/ x z)
(/ x z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(/ 4 z)
(/ 4 z)
(/ 4 z)
(/ 4 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
-2
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-1/2
(- (* -1 (/ y z)) 1/2)
(- (* -1 (/ y z)) 1/2)
(- (* -1 (/ y z)) 1/2)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(* -2 z)
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1 (* z (+ 2 (* -4 (/ (- x y) z)))))
(* -1/2 z)
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* -1 (* z (+ 1/2 (* -1 (/ (- x y) z)))))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (- x (* 1/2 z)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
-2
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
-1/2
(- (* -1 (/ y z)) 1/2)
(- (* -1 (/ y z)) 1/2)
(- (* -1 (/ y z)) 1/2)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(* 4 (- x (* 1/2 z)))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(+ (* -4 y) (* 4 (- x (* 1/2 z))))
(- x (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
(- (+ x (* -1 y)) (* 1/2 z))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -4 (/ y z))
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(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
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(* -4 (/ y z))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* -4 (/ y z))
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(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* -4 y)
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(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* -4 (/ y z))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
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(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* -1 (/ y z))
(* -1 (* y (+ (* 1/2 (/ 1 y)) (/ 1 z))))
(* -1 (* y (+ (* 1/2 (/ 1 y)) (/ 1 z))))
(* -1 (* y (+ (* 1/2 (/ 1 y)) (/ 1 z))))
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(* -1 y)
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(* y (- (/ x y) 1))
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(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* -4 y)
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* y (- (* 4 (/ (- x (* 1/2 z)) y)) 4))
(* -1 y)
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(* y (- (/ x y) (+ 1 (* 1/2 (/ z y)))))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -4 y)
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -4 (/ y z))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (/ y z))
(* -1 (* y (+ (* 1/2 (/ 1 y)) (/ 1 z))))
(* -1 (* y (+ (* 1/2 (/ 1 y)) (/ 1 z))))
(* -1 (* y (+ (* 1/2 (/ 1 y)) (/ 1 z))))
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -4 y)
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 4 (* -4 (/ (- x (* 1/2 z)) y)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- x (* 1/2 z)) y)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
-2
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(- (* 4 (/ x z)) 2)
(/ x z)
(/ x z)
(/ x z)
(/ x z)
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
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(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(* -4 (+ y (* 1/2 z)))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(* -1 y)
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(* -4 (+ y (* 1/2 z)))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(+ (* -4 (+ y (* 1/2 z))) (* 4 x))
(* -1 (+ y (* 1/2 z)))
(- x (+ y (* 1/2 z)))
(- x (+ y (* 1/2 z)))
(- x (+ y (* 1/2 z)))
(* -1 y)
(- x y)
(- x y)
(- x y)
(* 4 (/ x z))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* 4 (/ x z))
(* x (- (* 4 (/ 1 z)) (* 2 (/ 1 x))))
(* x (- (* 4 (/ 1 z)) (* 2 (/ 1 x))))
(* x (- (* 4 (/ 1 z)) (* 2 (/ 1 x))))
(/ x z)
(/ x z)
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(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
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(* 4 (/ x z))
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(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
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(* x (+ 4 (* -4 (/ (+ y (* 1/2 z)) x))))
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(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 (/ x z))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
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(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
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x
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
(* x (+ 1 (* -1 (/ (+ y (* 1/2 z)) x))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* 4 (/ x z))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* 4 (/ x z))
(* -1 (* x (- (* 2 (/ 1 x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 2 (/ 1 x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 2 (/ 1 x)) (* 4 (/ 1 z)))))
(/ x z)
(/ x z)
(/ x z)
(/ x z)
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(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* 4 (/ x z))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* 4 x)
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 (/ x z))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* 4 (/ x z))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* 4 x)
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
x
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
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x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))

Outputs
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 x)) z)
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/ (+ (* -2 z) (* 4 x)) z)
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/ (+ (* -2 z) (* 4 x)) z)
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/ x z)
(/.f64 x z)
(/ x z)
(/.f64 x z)
(/ x z)
(/.f64 x z)
(/ x z)
(/.f64 x z)
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(* 4 (- x y))
(*.f64 (-.f64 y x) #s(literal -4 binary64))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(/ (+ (* -4 y) (* -2 z)) z)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(/ (+ (* -4 y) (* -2 z)) z)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(/ (+ (* -4 y) (* -2 z)) z)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(* -1 (/ y z))
(/.f64 (neg.f64 y) z)
(/ (- (* -1/2 z) y) z)
(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
(/ (- (* -1/2 z) y) z)
(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
(/ (- (* -1/2 z) y) z)
(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
(/ y z)
(/.f64 y z)
(/ y z)
(/.f64 y z)
(/ y z)
(/.f64 y z)
(/ y z)
(/.f64 y z)
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/.f64 (*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))) z)
(* 4 (- x y))
(*.f64 (-.f64 y x) #s(literal -4 binary64))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(+ (* -2 z) (* 4 (- x y)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(- x y)
(-.f64 x y)
(- (+ x (* -1/2 z)) y)
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- (+ x (* -1/2 z)) y)
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(- (+ x (* -1/2 z)) y)
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(- (* 4 (/ x z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(- (* 4 (/ x z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(- (* 4 (/ x z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(/ x z)
(/.f64 x z)
(/ x z)
(/.f64 x z)
(/ x z)
(/.f64 x z)
(/ x z)
(/.f64 x z)
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 x z) #s(literal 4 binary64))
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
(/ 4 z)
(/.f64 #s(literal 4 binary64) z)
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -2 z)
(*.f64 #s(literal -2 binary64) z)
(* z (- (* 4 (/ (- x y) z)) 2))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(* z (- (* 4 (/ (- x y) z)) 2))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(* z (- (* 4 (/ (- x y) z)) 2))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
-2
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(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
(* -1 (* x (- (* 4 (/ (+ y (* 1/2 z)) x)) 4)))
(*.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) z (-.f64 x y)))
x
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
(* -1 (* x (- (+ (* 1/2 (/ z x)) (/ y x)) 1)))
(fma.f64 #s(literal -1/2 binary64) z (-.f64 x y))
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)

rewrite329.0ms (5.2%)

Memory

25.3MiB live, 190.4MiB allocated

Rules

4 142×	`lower-/.f32`
4 130×	`lower-/.f64`
3 822×	`lower-*.f32`
3 812×	`lower-*.f64`
3 652×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	198
0	48	198
1	179	198
2	1220	198
0	8472	190

Stop Event

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

Counts

18 → 288

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
(fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))
(/.f64 x z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(/.f64 #s(literal 4 binary64) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64)))
(*.f64 x #s(literal 4 binary64))
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
(-.f64 #s(literal -1/2 binary64) (/.f64 y z))
(/.f64 y z)
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
(.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))))
#s(approx (- (- x y) (* z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))
#s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))

Outputs
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eval164.0ms (2.6%)

Memory: 0.6MiB live, 236.6MiB allocated
Compiler: Compiled 8 741 to 1 100 computations (87.4% saved)

prune30.0ms (0.5%)

Memory

-33.0MiB live, 93.5MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	783	1	784
Fresh	0	0	0
Picked	0	5	5
Done	0	3	3
Total	783	9	792

Accuracy

100.0%

Counts

792 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.3%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
✓	61.4%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
✓	37.1%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
✓	36.5%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
✓	67.4%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
▶	67.1%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
✓	37.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
✓	67.2%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
✓	33.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Compiler

Compiled 63 to 71 computations (-12.7% saved)

simplify185.0ms (2.9%)

Memory

24.1MiB live, 63.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

cost-diff

(/.f64 #s(literal -4 binary64) z)

cost-diff

(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))

cost-diff

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

Rules

2 736×	`lower-fma.f32`
2 734×	`lower-fma.f64`
1 548×	`div-sub`
1 152×	`lower-*.f64`
1 152×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
0	18	31
1	35	31
2	79	31
3	178	29
4	418	29
5	1056	29
6	2648	29
7	4699	29
8	5447	29
9	5466	29
10	5474	29
11	5474	29
12	5810	29
13	5979	29
14	5979	29
15	5979	29
16	5979	29
17	6011	29
18	6123	29
0	6123	28

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(/.f64 #s(literal -4 binary64) z)
#s(literal -4 binary64)
z
y
#s(literal -2 binary64)

Outputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64))
(/.f64 #s(literal -4 binary64) z)
#s(literal -4 binary64)
z
y
#s(literal -2 binary64)

localize40.0ms (0.6%)

Memory

-18.5MiB live, 55.0MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

accuracy

(/.f64 #s(literal -4 binary64) z)

accuracy

0.1171875

(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))

accuracy

21.009577969406998

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

Samples

29.0ms

256×

valid

Compiler

Compiled 27 to 17 computations (37% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 10.0ms (46.3% of total)

ival-sub: 6.0ms (27.8% of total)

ival-div: 4.0ms (18.5% of total)

ival-add: 1.0ms (4.6% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs

#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())

#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())

#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())

Outputs
#s(alt (* 4 (/ (- x y) z)) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -2 z) (* 4 (- x y))) z) (taylor 0 z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ y z)) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -4 y) (* -2 z)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -4 y) (* -2 z)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -4 y) (* -2 z)) z) (taylor 0 z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor 0 z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt -2 (taylor inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor -inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor -inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 4 (/ (- x y) z)) 2) (taylor -inf z) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor -inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor -inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor -inf z) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor -inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor -inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor -inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (/ -4 z) (taylor -inf z) (#s(alt (/.f64 #s(literal -4 binary64) z) (patch (/.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ (- x (* 1/2 z)) z)) (taylor 0 y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z))) (taylor 0 y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z))) (taylor 0 y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z))) (taylor 0 y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -4 (/ y z)) 2) (taylor 0 y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ y z)) (taylor inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))) (taylor inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))) (taylor inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))) (taylor inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ y z)) (taylor inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y))))) (taylor inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y))))) (taylor inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y))))) (taylor inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ y z)) (taylor -inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))) (taylor -inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))) (taylor -inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))) (taylor -inf y) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ y z)) (taylor -inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z))))) (taylor -inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z))))) (taylor -inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z))))) (taylor -inf y) (#s(alt (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) (patch (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (/ (+ y (* 1/2 z)) z)) (taylor 0 x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z))) (taylor 0 x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z))) (taylor 0 x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z))) (taylor 0 x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z)))) (taylor inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z)))) (taylor inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z)))) (taylor inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (/ x z)) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z))))) (taylor -inf x) (#s(alt #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (patch #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ -4 z) y) -2) (/ -4 z))
1.0ms	z	@	0	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ -4 z) y) -2) (/ -4 z))
1.0ms	z	@	-inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ -4 z) y) -2) (/ -4 z))
1.0ms	y	@	inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ -4 z) y) -2) (/ -4 z))
1.0ms	y	@	-inf	((/ (* 4 (- (- x y) (* z 1/2))) z) (+ (* (/ -4 z) y) -2) (/ -4 z))

simplify166.0ms (2.6%)

Memory

16.2MiB live, 183.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 356×	`lower-fma.f64`
14 356×	`lower-fma.f32`
4 056×	`lower-*.f64`
4 056×	`lower-*.f32`
2 104×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	530
1	179	530
2	463	528
3	1168	528
4	2883	474
0	8476	427

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 4 (/ (- x y) z))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(/ (+ (* -2 z) (* 4 (- x y))) z)
(* -4 (/ y z))
(/ (+ (* -4 y) (* -2 z)) z)
(/ (+ (* -4 y) (* -2 z)) z)
(/ (+ (* -4 y) (* -2 z)) z)
(/ -4 z)
(/ -4 z)
(/ -4 z)
(/ -4 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(/ -4 z)
(/ -4 z)
(/ -4 z)
(/ -4 z)
-2
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
(- (* 4 (/ (- x y) z)) 2)
-2
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(/ -4 z)
(/ -4 z)
(/ -4 z)
(/ -4 z)
(* 4 (/ (- x (* 1/2 z)) z))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
-2
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(- (* -4 (/ y z)) 2)
(* -4 (/ y z))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(* -4 (/ y z))
(* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y)))))
(* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y)))))
(* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y)))))
(* -4 (/ y z))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(* -4 (/ y z))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(* -4 (/ (+ y (* 1/2 z)) z))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(* 4 (/ x z))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(* 4 (/ x z))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))

Outputs
(* 4 (/ (- x y) z))
(*.f64 (/.f64 (-.f64 x y) z) #s(literal 4 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(/ (+ (* -2 z) (* 4 (- x y))) z)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(/ (+ (* -4 y) (* -2 z)) z)
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) z y) z) #s(literal -4 binary64))
(/ (+ (* -4 y) (* -2 z)) z)
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) z y) z) #s(literal -4 binary64))
(/ (+ (* -4 y) (* -2 z)) z)
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) z y) z) #s(literal -4 binary64))
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
-2
#s(literal -2 binary64)
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(- (* 4 (/ (- x y) z)) 2)
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(/ -4 z)
(/.f64 #s(literal -4 binary64) z)
(* 4 (/ (- x (* 1/2 z)) z))
(fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ y z)) (* 4 (/ (- x (* 1/2 z)) z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
-2
#s(literal -2 binary64)
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(- (* -4 (/ y z)) 2)
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* y (- (* 4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y)))))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y)))))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -1 (* y (+ (* 4 (/ 1 z)) (* 2 (/ 1 y)))))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* y (+ (* -4 (/ (- (/ x z) 1/2) y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -4 (/ y z))
(*.f64 (/.f64 #s(literal -4 binary64) z) y)
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -1 (* y (+ (* 2 (/ 1 y)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))
(* -4 (/ (+ y (* 1/2 z)) z))
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) z y) z) #s(literal -4 binary64))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(+ (* -4 (/ (+ y (* 1/2 z)) z)) (* 4 (/ x z)))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* x (+ (* -4 (/ (+ y (* 1/2 z)) (* x z))) (* 4 (/ 1 z))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* 4 (/ x z))
(*.f64 (/.f64 #s(literal 4 binary64) z) x)
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))
(* -1 (* x (- (* 4 (/ (+ 1/2 (/ y z)) x)) (* 4 (/ 1 z)))))
(fma.f64 (/.f64 #s(literal 4 binary64) z) (-.f64 x y) #s(literal -2 binary64))

rewrite281.0ms (4.4%)

Memory

-12.1MiB live, 190.7MiB allocated

Rules

6 016×	`lower-fma.f32`
6 014×	`lower-fma.f64`
5 518×	`lower-*.f64`
5 518×	`lower-*.f32`
3 850×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
0	18	27
1	85	27
2	654	27
0	8502	26

Stop Event

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

Counts

3 → 75

Calls

Call 1

Inputs

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

(fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))

(/.f64 #s(literal -4 binary64) z)

Outputs
#<batchref>
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eval52.0ms (0.8%)

Memory: -12.7MiB live, 25.8MiB allocated
Compiler: Compiled 2 035 to 316 computations (84.5% saved)

prune8.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	0	0
Picked	1	0	1
Done	1	7	8
Total	148	8	156

Accuracy

100.0%

Counts

156 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.3%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
✓	61.4%	(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
✓	37.1%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
✓	36.5%	(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
	67.2%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))
✓	67.4%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
✓	37.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
✓	33.0%	#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Compiler

Compiled 174 to 125 computations (28.2% saved)

regimes31.0ms (0.5%)

Memory

-23.6MiB live, 49.5MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (fma.f64 #s(literal -1/2 binary64) z x))) z)
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) #s(approx (- x y) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)))) z)
(/.f64 (.f64 #s(literal 4 binary64) (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 y x))) (*.f64 #s(literal -1/2 binary64) z))) z)

Outputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Calls

5 calls:

8.0ms	x
8.0ms	(-.f64 x y)
5.0ms	z
5.0ms	y
4.0ms	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`
100.0%	1	`(-.f64 x y)`

Compiler

Compiled 17 to 23 computations (-35.3% saved)

regimes28.0ms (0.4%)

Memory

-0.6MiB live, 43.7MiB allocated

Counts

11 → 3

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)
(/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (fma.f64 #s(literal -1/2 binary64) z x))) z)

Outputs

(/.f64 (*.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) (-.f64 x y))) z)

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))

(/.f64 (*.f64 #s(literal 4 binary64) #s(approx (- (- x y) (* z 1/2)) (-.f64 x y))) z)

Calls

5 calls:

10.0ms	y
4.0ms	(-.f64 x y)
4.0ms	z
4.0ms	x
4.0ms	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Results

Accuracy	Segments	Branch
91.2%	3	`x`
88.4%	3	`y`
87.2%	3	`z`
99.7%	3	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`
85.1%	4	`(-.f64 x y)`

Compiler

Compiled 17 to 23 computations (-35.3% saved)

regimes8.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

9 → 3

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 y z)) #s(literal 4 binary64)))

Outputs

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64)))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Results

Accuracy	Segments	Branch
89.3%	3	`x`
74.4%	3	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`

Compiler

Compiled 12 to 13 computations (-8.3% saved)

regimes4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

7 → 3

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

Outputs

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
89.2%	3	`x`

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))

Outputs

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
89.1%	3	`x`

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes11.0ms (0.2%)

Memory

-10.0MiB live, 25.9MiB allocated

Counts

5 → 3

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

Outputs

(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64)))

(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)

Calls

3 calls:

5.0ms	x
3.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
75.1%	5	`z`
72.4%	3	`y`
84.3%	3	`x`

Compiler

Compiled 3 to 9 computations (-200% saved)

regimes43.0ms (0.7%)

Memory

-4.9MiB live, 33.6MiB allocated

Counts

4 → 6

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)

Outputs
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)

Calls

5 calls:

2.0ms	z
2.0ms	y
2.0ms	x
2.0ms	(-.f64 x y)
2.0ms	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)

Results

Accuracy	Segments	Branch
65.7%	8	`z`
60.8%	4	`y`
75.7%	6	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`
51.1%	3	`(-.f64 x y)`
65.3%	6	`x`

Compiler

Compiled 17 to 23 computations (-35.3% saved)

regimes2.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

3 → 6

Calls

Call 1

Inputs

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))

(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)

Outputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))
(/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 #s(literal -4 binary64) y)) z)
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))

Calls

1 calls:

2.0ms

(/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z)

Results

Accuracy	Segments	Branch
75.6%	6	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`

Compiler

Compiled 11 to 10 computations (9.1% saved)

regimes2.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

2 → 3

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))

Outputs

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))

Calls

1 calls:

1.0ms

(/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z)

Results

Accuracy	Segments	Branch
66.9%	3	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`

Compiler

Compiled 11 to 10 computations (9.1% saved)

regimes21.0ms (0.3%)

Memory

-18.5MiB live, 19.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Outputs
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Calls

5 calls:

16.0ms	z
1.0ms	(-.f64 x y)
1.0ms	(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
33.0%	1	`(-.f64 x y)`
33.0%	1	`z`
33.0%	1	`y`
33.0%	1	`x`
33.0%	1	`(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)`

Compiler

Compiled 17 to 23 computations (-35.3% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	-1.9999999999931246	50513523751604.1
0.0ms	-4410437786244908.0	-392996137626037.8

Compiler

Compiled 14 to 16 computations (-14.3% saved)

bsearch63.0ms (1%)

Memory

-31.0MiB live, 78.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.2980180778250896e+37	1.2239104981111325e+38
45.0ms	-5.267077760016721e-53	-1.544842534211941e-68

Samples

45.0ms

256×

valid

Compiler

Compiled 238 to 304 computations (-27.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 16.0ms (76.1% of total)

ival-sub: 3.0ms (14.3% of total)

ival-div: 2.0ms (9.5% of total)

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

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.2980180778250896e+37	1.2239104981111325e+38
1.0ms	-5.267077760016721e-53	-1.544842534211941e-68

Compiler

Compiled 238 to 304 computations (-27.7% saved)

bsearch2.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.2980180778250896e+37	1.2239104981111325e+38
1.0ms	-5.267077760016721e-53	-1.544842534211941e-68

Compiler

Compiled 238 to 304 computations (-27.7% saved)

bsearch47.0ms (0.7%)

Memory

-15.1MiB live, 59.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
7.0ms	1.2980180778250896e+37	1.2239104981111325e+38
9.0ms	-5.937232381623184e+88	-1.5092556751104268e+88

Samples

10.0ms

160×

valid

Compiler

Compiled 157 to 203 computations (-29.3% saved)

Precisions

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

ival-sub: 2.0ms (41.4% of total)

ival-mult: 2.0ms (41.4% of total)

ival-div: 1.0ms (20.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

5×	left-value

Steps

Time	Left	Right
0.0ms	5.998928591029187e+243	9.805216964981731e+250
0.0ms	1.7787307418440813e+59	7.246242852207247e+59
0.0ms	-1.9999999999931246	50513523751604.1
0.0ms	-1788997.376049822	-2.000013664421237
0.0ms	-1.5087801844668285e+41	-1.4290773794268803e+40

Compiler

Compiled 14 to 16 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

5×	left-value

Steps

Time	Left	Right
0.0ms	5.998928591029187e+243	9.805216964981731e+250
0.0ms	1.7787307418440813e+59	7.246242852207247e+59
0.0ms	-1.9999999999931246	50513523751604.1
0.0ms	-1788997.376049822	-2.000013664421237
0.0ms	-3.567344526466399e+69	-8.154186589706192e+68

Compiler

Compiled 14 to 16 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	-1.9999999999931246	50513523751604.1
0.0ms	-4410437786244908.0	-392996137626037.8

Compiler

Compiled 14 to 16 computations (-14.3% saved)

simplify87.0ms (1.4%)

Memory

-15.9MiB live, 72.5MiB allocated

Algorithm

1×	egg-herbie

Rules

20×	`-commutative-binary64-.f64`
12×	`+-commutative-binary64-+.f64`
12×	`sub-neg-binary64-neg.f64-+.f64--.f64`
8×	`neg-sub0-binary64--.f64-neg.f64`
8×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	739
1	98	739
2	112	739
3	120	739
4	125	739
5	126	739

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -4000000000000000 binary64)) (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64))) (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)))
(if (<=.f64 x #s(literal -6007280020246507/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (if (<=.f64 x #s(literal 27999999999999998236298794678974676992 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64))) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))))
(if (<=.f64 x #s(literal -6007280020246507/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (if (<=.f64 x #s(literal 27999999999999998236298794678974676992 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))))
(if (<=.f64 x #s(literal -6007280020246507/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (if (<=.f64 x #s(literal 27999999999999998236298794678974676992 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))))
(if (<=.f64 x #s(literal -30000000000000000549348798468895211528057383432372059017576067169820075810134834058100736 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 x #s(literal 120000000000000008632251347034389348352 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)))
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -100000000000000000620008645040778319495168 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1000000 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 199999999999999994337576099120928401699872656732354315812864 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 10000000000000000746505756498316957746327953001196155931630344001201154571357992362921494533074993280744790313201299421914675928345743408263359645135065900661507886387491188354180370195272228869449812405194846465661467225589890846083353893928960 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z))))))
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -2000000000000000145062872763058470252316748819293043911036420310958080 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1000000 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 199999999999999994337576099120928401699872656732354315812864 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 10000000000000000746505756498316957746327953001196155931630344001201154571357992362921494533074993280744790313201299421914675928345743408263359645135065900661507886387491188354180370195272228869449812405194846465661467225589890846083353893928960 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)))))))
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -4000000000000000 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

Outputs
(/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z)
(/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z)
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -4000000000000000 binary64)) (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64))) (/.f64 (.f64 #s(literal 4 binary64) #s(approx (- (- x y) ( z 1/2)) (-.f64 x y))) z)))
(if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -4000000000000000 binary64)) (/.f64 (.f64 #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)) #s(literal 4 binary64)) z) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -1 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64))) (/.f64 (.f64 #s(approx (- (- x y) ( z 1/2)) (-.f64 x y)) #s(literal 4 binary64)) z)))
(if (<=.f64 x #s(literal -6007280020246507/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (if (<=.f64 x #s(literal 27999999999999998236298794678974676992 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 y z) #s(literal -4 binary64) #s(literal -2 binary64))) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))))
(if (<=.f64 x #s(literal -6007280020246507/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64))) (if (<=.f64 x #s(literal 27999999999999998236298794678974676992 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 x z) #s(literal 4 binary64) #s(literal -2 binary64)))))
(if (<=.f64 x #s(literal -6007280020246507/883423532389192164791648750371459257913741948437809479060803100646309888 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64))) (if (<=.f64 x #s(literal 27999999999999998236298794678974676992 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal 4 binary64) z) x #s(literal -2 binary64)))))
(if (<=.f64 x #s(literal -30000000000000000549348798468895211528057383432372059017576067169820075810134834058100736 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 x #s(literal 120000000000000008632251347034389348352 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (fma.f64 (/.f64 #s(literal -4 binary64) z) y #s(literal -2 binary64))) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z)))
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -100000000000000000620008645040778319495168 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1000000 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 199999999999999994337576099120928401699872656732354315812864 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 10000000000000000746505756498316957746327953001196155931630344001201154571357992362921494533074993280744790313201299421914675928345743408263359645135065900661507886387491188354180370195272228869449812405194846465661467225589890846083353893928960 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z))))))
(if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -100000000000000000620008645040778319495168 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -1000000 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal 199999999999999994337576099120928401699872656732354315812864 binary64)) (/.f64 #s(approx (* 4 (- (- x y) (* z 1/2))) (.f64 x #s(literal 4 binary64))) z) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal 10000000000000000746505756498316957746327953001196155931630344001201154571357992362921494533074993280744790313201299421914675928345743408263359645135065900661507886387491188354180370195272228869449812405194846465661467225589890846083353893928960 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (*.f64 x #s(literal 4 binary64))) z))))))
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -2000000000000000145062872763058470252316748819293043911036420310958080 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1000000 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 199999999999999994337576099120928401699872656732354315812864 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal 10000000000000000746505756498316957746327953001196155931630344001201154571357992362921494533074993280744790313201299421914675928345743408263359645135065900661507886387491188354180370195272228869449812405194846465661467225589890846083353893928960 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)))))))
(if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -2000000000000000145062872763058470252316748819293043911036420310958080 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -1000000 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal 199999999999999994337576099120928401699872656732354315812864 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal 10000000000000000746505756498316957746327953001196155931630344001201154571357992362921494533074993280744790313201299421914675928345743408263359645135065900661507886387491188354180370195272228869449812405194846465661467225589890846083353893928960 binary64)) (/.f64 #s(approx ( 4 (- (- x y) (* z 1/2))) (.f64 #s(literal -4 binary64) y)) z) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x)))))))
(if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -4000000000000000 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (.f64 z #s(literal 1/2 binary64)))) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))))
(if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -4000000000000000 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (.f64 (/.f64 #s(literal 4 binary64) z) x)) (if (<=.f64 (/.f64 (.f64 (-.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) z)) #s(literal 4 binary64)) z) #s(literal -1 binary64)) #s(approx (/ ( 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64)) #s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) (*.f64 (/.f64 #s(literal 4 binary64) z) x))))
#s(approx (/ (* 4 (- (- x y) (* z 1/2))) z) #s(literal -2 binary64))

soundness988.0ms (15.6%)

Memory

21.6MiB live, 573.0MiB allocated

Rules

9 976×	`lower-fma.f64`
9 976×	`lower-fma.f32`
9 634×	`lower-fma.f64`
9 634×	`lower-fma.f32`
6 016×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	890
1	390	889
2	1127	887
3	3264	885
0	8225	800
0	15	27
0	18	27
1	85	27
2	654	27
0	8502	26
0	154	3218
1	465	3217
2	1352	3089
3	3871	3089
0	8173	2822
0	36	174
0	57	172
1	218	150
2	1662	150
0	8581	141

Stop Event

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

Compiler

Compiled 576 to 282 computations (51% saved)

preprocess202.0ms (3.2%)

Memory: 2.4MiB live, 162.7MiB allocated
Compiler: Compiled 896 to 202 computations (77.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze52.0ms (0.8%)

sample988.0ms (15.6%)

explain127.0ms (2%)

preprocess239.0ms (3.8%)

eval0.0ms (0%)

prune6.0ms (0.1%)

simplify185.0ms (2.9%)

localize66.0ms (1%)

series22.0ms (0.3%)

simplify121.0ms (1.9%)

rewrite203.0ms (3.2%)

eval83.0ms (1.3%)

prune15.0ms (0.2%)

simplify99.0ms (1.6%)

localize92.0ms (1.5%)

series46.0ms (0.7%)

simplify165.0ms (2.6%)

rewrite174.0ms (2.8%)

eval157.0ms (2.5%)

prune27.0ms (0.4%)

simplify165.0ms (2.6%)

localize87.0ms (1.4%)

series45.0ms (0.7%)

simplify347.0ms (5.5%)

rewrite329.0ms (5.2%)

eval164.0ms (2.6%)

prune30.0ms (0.5%)

simplify185.0ms (2.9%)

localize40.0ms (0.6%)

series7.0ms (0.1%)

simplify166.0ms (2.6%)

rewrite281.0ms (4.4%)

eval52.0ms (0.8%)

prune8.0ms (0.1%)

regimes31.0ms (0.5%)

regimes28.0ms (0.4%)

regimes8.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes11.0ms (0.2%)

regimes43.0ms (0.7%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes21.0ms (0.3%)

bsearch1.0ms (0%)

bsearch63.0ms (1%)

bsearch2.0ms (0%)

bsearch2.0ms (0%)

bsearch47.0ms (0.7%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify87.0ms (1.4%)

soundness988.0ms (15.6%)

preprocess202.0ms (3.2%)

end0.0ms (0%)

Profiling