Metrics for Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.1MiB allocated

analyze45.0ms (0.6%)

Memory

1.0MiB live, 72.6MiB 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
50%	49.9%	49.9%	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
75%	74.9%	25%	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
87.5%	87.4%	12.5%	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
93.8%	93.6%	6.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.0s (14.3%)

Memory

4.8MiB live, 1 386.7MiB allocated

Samples

704.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 439.0ms

ival-mult: 296.0ms (67.4% of total)

ival-div: 55.0ms (12.5% of total)

ival-add: 38.0ms (8.7% of total)

ival-sub: 36.0ms (8.2% of total)

ival-true: 7.0ms (1.6% of total)

exact: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain125.0ms (1.7%)

Memory

-4.8MiB live, 245.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
70	-	-	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
28	-	-	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0	-	-	`z`
0	-	-	`(*.f64 x x)`
0	-	-	`(*.f64 y #s(literal 2 binary64))`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`y`
0	-	-	`(*.f64 z z)`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`	o/n	63	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	151
↳	`(*.f64 y y)`	overflow	67
↳	`(*.f64 x x)`	overflow	73
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	120
↳	`(*.f64 z z)`	overflow	59
`-.f64`	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	nan-rescue	28	0
↳	`(*.f64 y y)`	overflow	67
↳	`(*.f64 x x)`	overflow	73
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	120
↳	`(*.f64 z z)`	overflow	59
`/.f64`	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`	u/n	6	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	6
↳	`(*.f64 y y)`	underflow	59
↳	`(*.f64 x x)`	underflow	62
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	17
↳	`(*.f64 z z)`	underflow	68
`/.f64`	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`	o/o	1	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	151
↳	`(*.f64 y y)`	overflow	67
↳	`(*.f64 x x)`	overflow	73
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	120
↳	`(*.f64 z z)`	overflow	59
↳	`(*.f64 y #s(literal 2 binary64))`	overflow	1

Confusion

	Predicted +	Predicted -
+	84	0
-	0	172

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	84	0	0
-	0	0	172

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	172
1	70
2	14

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

41.0ms

512×

valid

Compiler

Compiled 117 to 37 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 15.0ms (62.2% of total)

ival-div: 3.0ms (12.4% of total)

ival-sub: 2.0ms (8.3% of total)

ival-add: 2.0ms (8.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess192.0ms (2.7%)

Memory

21.0MiB live, 215.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 972×	`lower-fma.f64`
12 972×	`lower-fma.f32`
3 732×	`lower-*.f32`
3 724×	`lower-*.f64`
2 414×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	138
1	147	135
2	489	135
3	2191	135
4	6834	117
0	11	15
0	18	15
1	32	15
2	69	15
3	136	15
4	295	15
5	630	15
6	1505	13
7	3475	13
8	7859	13
0	8033	12

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs z)

(abs x)

(negabs y)

Compiler

Compiled 15 to 11 computations (26.7% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.7%	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify153.0ms (2.1%)

Memory

-19.2MiB live, 132.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	128	(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

Rules

12 972×	`lower-fma.f64`
12 972×	`lower-fma.f32`
3 732×	`lower-*.f32`
3 724×	`lower-*.f64`
2 414×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
0	18	49
1	32	49
2	69	49
3	136	49
4	295	49
5	630	49
6	1505	47
7	3475	47
8	7859	47
0	8033	44

Stop Event

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

Calls

Call 1

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

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

localize31.0ms (0.4%)

Memory

0.4MiB live, 37.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	6.292939851622882	(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	16.1892665750384	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 51 to 13 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (58.5% of total)

ival-div: 2.0ms (19.5% of total)

ival-sub: 1.0ms (9.8% of total)

ival-add: 1.0ms (9.8% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

5 → 120

Calls

Call 1

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

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

Calls

9 calls:

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

simplify124.0ms (1.7%)

Memory

8.9MiB live, 131.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 488×	`lower-fma.f64`
7 488×	`lower-fma.f32`
4 752×	`lower-*.f64`
4 752×	`lower-*.f32`
1 676×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	1206
1	196	1206
2	566	1204
3	2177	1064
4	6044	1040
0	8183	954

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite270.0ms (3.7%)

Memory

-21.0MiB live, 262.9MiB allocated

Rules

5 846×	`lower-*.f32`
5 838×	`lower-*.f64`
5 096×	`lower-fma.f64`
5 096×	`lower-fma.f32`
4 708×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
0	18	39
1	68	39
2	569	39
0	8301	36

Stop Event

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

Counts

5 → 528

Calls

Call 1

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

Outputs
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eval88.0ms (1.2%)

Memory: 24.8MiB live, 97.7MiB allocated
Compiler: Compiled 18 944 to 1 651 computations (91.3% saved)

prune37.0ms (0.5%)

Memory

6.9MiB live, 44.2MiB allocated

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	636	12	648
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	637	12	649

Accuracy

100.0%

Counts

649 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.4%	(fma.f64 (neg.f64 z) (.f64 z (/.f64 #s(literal 1/2 binary64) y)) (.f64 (/.f64 (fma.f64 y y (*.f64 x x)) y) #s(literal 1/2 binary64)))
	73.0%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64))) (.f64 y #s(literal 2 binary64)))
	73.0%	(/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64)))
▶	33.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
	73.0%	(/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
▶	73.0%	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
▶	99.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64)))
	69.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	28.4%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
▶	59.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
	65.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)))
▶	35.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 288 to 234 computations (18.8% saved)

simplify208.0ms (2.9%)

Memory

-6.8MiB live, 141.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 y z)
cost-diff	0	(+.f64 y z)
cost-diff	448	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(/.f64 (*.f64 z z) y)
cost-diff	0	(-.f64 y (/.f64 (*.f64 z z) y))
cost-diff	0	(.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 y #s(literal 2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
cost-diff	0	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(/.f64 (-.f64 x z) y)
cost-diff	0	(fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64)))

Rules

16 274×	`lower-fma.f32`
16 270×	`lower-fma.f64`
3 432×	`lower-+.f32`
3 428×	`lower-+.f64`
3 112×	`lower-*.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	34	224
0	54	222
1	98	217
2	210	217
3	538	217
4	1743	217
5	5419	211
0	8236	211

Stop Event

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

Calls

Call 1

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

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

localize120.0ms (1.7%)

Memory

-22.1MiB live, 109.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y z)
accuracy	0	(*.f64 x x)
accuracy	1.5038897356333616	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
accuracy	16.21679972498638	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(*.f64 z z)
accuracy	0.01171875	(-.f64 y (/.f64 (*.f64 z z) y))
accuracy	9.249873315677467	(/.f64 (*.f64 z z) y)
accuracy	21.847184574442124	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	0	(*.f64 x x)
accuracy	16.1892665750384	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
accuracy	36.45769804617819	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	41.163078547981854	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))
accuracy	0	(*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64))
accuracy	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64)))
accuracy	0.0078125	(/.f64 (-.f64 x z) y)
accuracy	0.0625	(fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y)

Samples

90.0ms

256×

valid

Compiler

Compiled 195 to 30 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 43.0ms (58.1% of total)

ival-add: 20.0ms (27% of total)

ival-div: 6.0ms (8.1% of total)

ival-sub: 4.0ms (5.4% of total)

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

exact: 0.0ms (0% of total)

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

series49.0ms (0.7%)

Memory

21.3MiB live, 59.5MiB allocated

Counts

19 → 528

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	y	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* 1/2 y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* z z) (+ (* (+ y z) (- y z)) (* x x)))
6.0ms	x	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* 1/2 y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* z z) (+ (* (+ y z) (- y z)) (* x x)))
4.0ms	z	@	0	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* 1/2 y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* z z) (+ (* (+ y z) (- y z)) (* x x)))
4.0ms	y	@	-inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* 1/2 y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* z z) (+ (* (+ y z) (- y z)) (* x x)))
3.0ms	z	@	inf	((/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* 1/2 y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (- (+ (* x x) (* y y)) (* z z)) (* x x) (* y 2) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (- y (/ (* z z) y)) 1/2) (- y (/ (* z z) y)) (/ (* z z) y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* z z) (+ (* (+ y z) (- y z)) (* x x)))

simplify164.0ms (2.3%)

Memory

-7.8MiB live, 114.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6 988×	`lower-fma.f64`
6 988×	`lower-fma.f32`
3 726×	`lower-*.f64`
3 726×	`lower-*.f32`
2 506×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	364	6225
1	1187	5855
2	4054	5654
0	8213	5347

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 514

Calls

Call 1

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

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

rewrite206.0ms (2.8%)

Memory

7.6MiB live, 155.0MiB allocated

Rules

5 092×	`lower-/.f32`
5 084×	`lower-/.f64`
4 388×	`lower-fma.f32`
4 384×	`lower-fma.f64`
4 350×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	196
0	54	196
1	216	191
2	1930	191
0	8649	191

Stop Event

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

Counts

19 → 643

Calls

Call 1

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

Outputs
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eval218.0ms (3%)

Memory: 18.0MiB live, 209.2MiB allocated
Compiler: Compiled 25 026 to 2 751 computations (89% saved)

prune224.0ms (3.1%)

Memory

-166.8MiB live, 140.8MiB allocated

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	1 166	9	1 175
Fresh	1	6	7
Picked	2	3	5
Done	0	0	0
Total	1 169	18	1 187

Accuracy

100.0%

Counts

1 187 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.4%	(fma.f64 (neg.f64 z) (.f64 z (/.f64 #s(literal 1/2 binary64) y)) (.f64 (/.f64 (fma.f64 y y (*.f64 x x)) y) #s(literal 1/2 binary64)))
	73.0%	(/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64)))
✓	33.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
▶	73.0%	(/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
	33.8%	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
	28.3%	(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z)) (/.f64 #s(literal 1/2 binary64) y))
	75.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal 1 binary64) y) (.f64 (/.f64 y x) z)) (.f64 (/.f64 y x) y)) (+.f64 z x) y) #s(literal 1/2 binary64)))
▶	99.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)))
▶	69.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	65.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))
	28.4%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
✓	59.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
	59.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 #s(literal 1 binary64) (/.f64 y (.f64 z z)))) #s(literal 1/2 binary64)))
▶	31.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
▶	65.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)))
	59.3%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (-.f64 (fma.f64 (/.f64 (/.f64 x z) z) (/.f64 x y) (/.f64 y (.f64 z z))) (/.f64 #s(literal 1 binary64) y)) (*.f64 z z))) #s(literal 1/2 binary64)))
✓	35.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))
	63.6%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) #s(approx (* (- y (/ (* z z) y)) 1/2) (.f64 (.f64 #s(literal -1/2 binary64) y) (fma.f64 (/.f64 z y) (/.f64 z y) #s(literal -1 binary64)))))

Compiler

Compiled 432 to 339 computations (21.5% saved)

simplify246.0ms (3.4%)

Memory

23.7MiB live, 150.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 y z)
cost-diff	0	(+.f64 y z)
cost-diff	0	(/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))
cost-diff	832	(/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
cost-diff	0	(+.f64 z x)
cost-diff	0	(*.f64 (+.f64 z x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)))
cost-diff	0	(/.f64 x y)
cost-diff	0	(fma.f64 (/.f64 x y) x y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 z y)
cost-diff	0	(*.f64 (/.f64 z y) #s(literal -1/2 binary64))
cost-diff	0	(.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
cost-diff	0	(/.f64 (-.f64 x z) y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)))
cost-diff	1088	(fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y))

Rules

19 012×	`lower-fma.f32`
19 004×	`lower-fma.f64`
3 558×	`lower-+.f32`
3 554×	`lower-+.f64`
3 418×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	277
0	61	280
1	111	260
2	251	260
3	716	260
4	2005	260
5	5464	256
0	8093	248

Stop Event

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

Calls

Call 1

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

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

localize162.0ms (2.2%)

Memory

-19.8MiB live, 101.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.12337875976844202	(/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
accuracy	1.5038897356333616	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
accuracy	16.43391311115592	(/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))
accuracy	0	(*.f64 (+.f64 z x) #s(literal 1/2 binary64))
accuracy	0.0078125	(/.f64 (-.f64 x z) y)
accuracy	0.13671875	(.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))
accuracy	21.74842710881393	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)))
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))
accuracy	0.05078125	(fma.f64 (/.f64 x y) x y)
accuracy	19.72715701103321	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
accuracy	0	(/.f64 z y)
accuracy	0.0078125	(*.f64 (/.f64 z y) #s(literal -1/2 binary64))
accuracy	0.15625	(.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)
accuracy	44.03239035959762	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
accuracy	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)))
accuracy	0.0078125	(/.f64 (-.f64 x z) y)
accuracy	0.046875	(fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y))
accuracy	2.824357547927631	(fma.f64 (/.f64 (-.f64 x z) y) x y)

Samples

121.0ms

256×

valid

Compiler

Compiled 242 to 38 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-add: 44.0ms (57.5% of total)

ival-mult: 19.0ms (24.8% of total)

ival-div: 9.0ms (11.8% of total)

ival-sub: 3.0ms (3.9% of total)

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

exact: 0.0ms (0% of total)

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

series129.0ms (1.8%)

Memory

-3.5MiB live, 69.5MiB allocated

Counts

23 → 684

Calls

Call 1

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

Outputs
#s(alt (+ y (/ (pow x 2) y)) (taylor 0 z) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) (patch (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #<representation binary64>) () ())) ())
#s(alt (+ y (+ (* z (+ (* -1 (/ x y)) (/ x y))) (/ (pow x 2) y))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) (patch (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #<representation binary64>) () ())) ())
#s(alt (+ y (+ (* z (+ (* -1 (/ x y)) (+ (* -1 (/ z y)) (/ x y)))) (/ (pow x 2) y))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) (patch (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #<representation binary64>) () ())) ())
#s(alt (+ y (+ (* z (+ (* -1 (/ x y)) (+ (* -1 (/ z y)) (/ x y)))) (/ (pow x 2) y))) (taylor 0 z) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) (patch (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y))) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y))) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y))) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (+ y (/ (pow x 2) y))) (taylor 0 z) (#s(alt (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* z (+ (* -1 (/ x y)) (/ x y)))) (* 1/2 (+ y (/ (pow x 2) y)))) (taylor 0 z) (#s(alt (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (+ y (/ (pow x 2) y))) (* z (+ (* -1/2 (/ z y)) (* 1/2 (+ (* -1 (/ x y)) (/ x y)))))) (taylor 0 z) (#s(alt (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (+ y (/ (pow x 2) y))) (* z (+ (* -1/2 (/ z y)) (* 1/2 (+ (* -1 (/ x y)) (/ x y)))))) (taylor 0 z) (#s(alt (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 z) (#s(alt (/.f64 (-.f64 x z) y) (patch (/.f64 (-.f64 x z) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ z y)) (/ x y)) (taylor 0 z) (#s(alt (/.f64 (-.f64 x z) y) (patch (/.f64 (-.f64 x z) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ z y)) (/ x y)) (taylor 0 z) (#s(alt (/.f64 (-.f64 x z) y) (patch (/.f64 (-.f64 x z) y) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ z y)) (/ x y)) (taylor 0 z) (#s(alt (/.f64 (-.f64 x z) y) (patch (/.f64 (-.f64 x z) y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y))) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y))) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y))) (taylor 0 z) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (pow z 2) y)) (taylor 0 z) (#s(alt (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) (patch (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ y (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ y (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ y (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) x y) (patch (fma.f64 (/.f64 x y) x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (/ 1 y) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) x y) (patch (fma.f64 (/.f64 x y) x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (/ 1 y) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) x y) (patch (fma.f64 (/.f64 x y) x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (/ 1 y) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x y) x y) (patch (fma.f64 (/.f64 x y) x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) (patch (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (+ (* -1 (/ z y)) (/ z y)) x)) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) (patch (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (/ z y)) (/ z y))) (* 1/2 (/ (pow z 2) (* x y)))) x)) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) (patch (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (/ z y)) (/ z y))) (* 1/2 (/ (pow z 2) (* x y)))) x)) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) (patch (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ z x)) 1/2))) (taylor -inf x) (#s(alt (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ z x)) 1/2))) (taylor -inf x) (#s(alt (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ z x)) 1/2))) (taylor -inf x) (#s(alt (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 z x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 z x) (patch (+.f64 z x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ z x)) 1))) (taylor -inf x) (#s(alt (+.f64 z x) (patch (+.f64 z x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ z x)) 1))) (taylor -inf x) (#s(alt (+.f64 z x) (patch (+.f64 z x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ z x)) 1))) (taylor -inf x) (#s(alt (+.f64 z x) (patch (+.f64 z x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (patch (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ y (* -1 (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (patch (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ y (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (patch (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ y (* -1 (/ (* y (* (pow (+ y z) 3) (pow (- y z) 3))) (pow x 6)))) (+ (* -1 (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (patch (/.f64 y (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) x y) (patch (fma.f64 (/.f64 (-.f64 x z) y) x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ z (* x y))) (/ 1 y))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) x y) (patch (fma.f64 (/.f64 (-.f64 x z) y) x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ y x)) (/ z y)) x)) (/ 1 y))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) x y) (patch (fma.f64 (/.f64 (-.f64 x z) y) x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ y x)) (/ z y)) x)) (/ 1 y))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 (-.f64 x z) y) x y) (patch (fma.f64 (/.f64 (-.f64 x z) y) x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
37.0ms	y	@	inf	((+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) 1/2) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) -1/2) z) (* (/ z y) -1/2) (/ z y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (+ z x) 1/2) (/ (- x z) y)) (* (+ z x) 1/2) (+ z x) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ y z) (- y z) (+ (* (/ (- x z) y) x) y) (+ (* (+ y z) (- y z)) (* x x)) (* x x))
6.0ms	y	@	0	((+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) 1/2) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) -1/2) z) (* (/ z y) -1/2) (/ z y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (+ z x) 1/2) (/ (- x z) y)) (* (+ z x) 1/2) (+ z x) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ y z) (- y z) (+ (* (/ (- x z) y) x) y) (+ (* (+ y z) (- y z)) (* x x)) (* x x))
5.0ms	y	@	-inf	((+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) 1/2) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) -1/2) z) (* (/ z y) -1/2) (/ z y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (+ z x) 1/2) (/ (- x z) y)) (* (+ z x) 1/2) (+ z x) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ y z) (- y z) (+ (* (/ (- x z) y) x) y) (+ (* (+ y z) (- y z)) (* x x)) (* x x))
4.0ms	x	@	inf	((+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) 1/2) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) -1/2) z) (* (/ z y) -1/2) (/ z y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (+ z x) 1/2) (/ (- x z) y)) (* (+ z x) 1/2) (+ z x) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ y z) (- y z) (+ (* (/ (- x z) y) x) y) (+ (* (+ y z) (- y z)) (* x x)) (* x x))
4.0ms	z	@	inf	((+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) z) (+ (* (/ (- x z) y) x) y)) 1/2) (/ (- x z) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (/ z y) -1/2) z) (* (/ z y) -1/2) (/ z y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ x y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* (+ z x) 1/2) (/ (- x z) y)) (* (+ z x) 1/2) (+ z x) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ y z) (- y z) (+ (* (/ (- x z) y) x) y) (+ (* (+ y z) (- y z)) (* x x)) (* x x))

simplify210.0ms (2.9%)

Memory

24.7MiB live, 139.0MiB allocated

Algorithm

1×	egg-herbie

Rules

7 082×	`lower-fma.f64`
7 082×	`lower-fma.f32`
4 568×	`lower-*.f64`
4 568×	`lower-*.f32`
2 674×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	674	8643
1	2257	7723
0	8824	7342

Stop Event

1×	iter limit
1×	node limit

Counts

684 → 661

Calls

Call 1

Inputs
(+ y (/ (pow x 2) y))
(+ y (+ (* z (+ (* -1 (/ x y)) (/ x y))) (/ (pow x 2) y)))
(+ y (+ (* z (+ (* -1 (/ x y)) (+ (* -1 (/ z y)) (/ x y)))) (/ (pow x 2) y)))
(+ y (+ (* z (+ (* -1 (/ x y)) (+ (* -1 (/ z y)) (/ x y)))) (/ (pow x 2) y)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(* 1/2 (+ y (/ (pow x 2) y)))
(+ (* 1/2 (* z (+ (* -1 (/ x y)) (/ x y)))) (* 1/2 (+ y (/ (pow x 2) y))))
(+ (* 1/2 (+ y (/ (pow x 2) y))) (* z (+ (* -1/2 (/ z y)) (* 1/2 (+ (* -1 (/ x y)) (/ x y))))))
(+ (* 1/2 (+ y (/ (pow x 2) y))) (* z (+ (* -1/2 (/ z y)) (* 1/2 (+ (* -1 (/ x y)) (/ x y))))))
(/ x y)
(+ (* -1 (/ z y)) (/ x y))
(+ (* -1 (/ z y)) (/ x y))
(+ (* -1 (/ z y)) (/ x y))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
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z
(+ x z)
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(pow x 2)
(pow x 2)
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(/ (pow x 2) y)
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(* x (+ (* -1 (/ z (* x y))) (/ 1 y)))
(* x (+ (* -1 (/ z (* x y))) (/ 1 y)))
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x
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(/ (pow x 2) y)
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Outputs
(+ y (/ (pow x 2) y))
(fma.f64 (/.f64 x y) x y)
(+ y (+ (* z (+ (* -1 (/ x y)) (/ x y))) (/ (pow x 2) y)))
(fma.f64 (+.f64 #s(literal 0 binary64) (/.f64 x y)) x y)
(+ y (+ (* z (+ (* -1 (/ x y)) (+ (* -1 (/ z y)) (/ x y)))) (/ (pow x 2) y)))
(fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y)
(+ y (+ (* z (+ (* -1 (/ x y)) (+ (* -1 (/ z y)) (/ x y)))) (/ (pow x 2) y)))
(fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y)
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(.f64 (/.f64 (fma.f64 x x (.f64 y y)) y) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(fma.f64 (.f64 z (/.f64 z y)) #s(literal -1/2 binary64) (.f64 (/.f64 (fma.f64 x x (*.f64 y y)) y) #s(literal 1/2 binary64)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(fma.f64 (.f64 z (/.f64 z y)) #s(literal -1/2 binary64) (.f64 (/.f64 (fma.f64 x x (*.f64 y y)) y) #s(literal 1/2 binary64)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(fma.f64 (.f64 z (/.f64 z y)) #s(literal -1/2 binary64) (.f64 (/.f64 (fma.f64 x x (*.f64 y y)) y) #s(literal 1/2 binary64)))
(* 1/2 (+ y (/ (pow x 2) y)))
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(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (*.f64 z (/.f64 (/.f64 z y) x)) #s(literal 1/2 binary64) #s(literal 0 binary64)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (/ z y)) (/ z y))) (* 1/2 (/ (pow z 2) (* x y)))) x)) (* 1/2 (/ 1 y))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (*.f64 z (/.f64 (/.f64 z y) x)) #s(literal 1/2 binary64) #s(literal 0 binary64)) x)) x) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (/ z x)) 1/2)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 z x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(* -1 (* x (- (* -1/2 (/ z x)) 1/2)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 z x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(* -1 (* x (- (* -1/2 (/ z x)) 1/2)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 z x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
x
(* -1 (* x (- (* -1 (/ z x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 z x) #s(literal -1 binary64) #s(literal -1 binary64)))
(* -1 (* x (- (* -1 (/ z x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 z x) #s(literal -1 binary64) #s(literal -1 binary64)))
(* -1 (* x (- (* -1 (/ z x)) 1)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 z x) #s(literal -1 binary64) #s(literal -1 binary64)))
(* 1/2 (/ (pow x 2) y))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) y))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (fma.f64 (neg.f64 z) z (.f64 y y)) y) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (fma.f64 (neg.f64 z) z (.f64 y y)) y) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (fma.f64 (neg.f64 z) z (.f64 y y)) y) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ (+ y (* -1 (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (neg.f64 y) (.f64 (/.f64 (+.f64 z y) x) (/.f64 (-.f64 y z) x)) y) (.f64 x x))
(/ (- (+ y (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2))) (pow x 2))
(/.f64 (fma.f64 y (-.f64 (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 (+.f64 z y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 (+.f64 z y) x) (/.f64 (-.f64 y z) x))) y) (*.f64 x x))
(/ (- (+ y (* -1 (/ (* y (* (pow (+ y z) 3) (pow (- y z) 3))) (pow x 6)))) (+ (* -1 (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (neg.f64 y) (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 3 binary64)) (pow.f64 (+.f64 z y) #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) y) (fma.f64 (.f64 (+.f64 z y) y) (/.f64 (/.f64 (-.f64 y z) x) x) (.f64 (neg.f64 y) (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 (+.f64 z y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 x x))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(* (pow x 2) (+ (* -1 (/ z (* x y))) (/ 1 y)))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (/.f64 z y) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ y x)) (/ z y)) x)) (/ 1 y)))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (-.f64 (/.f64 z y) (/.f64 y x)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ y x)) (/ z y)) x)) (/ 1 y)))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 (-.f64 (/.f64 z y) (/.f64 y x)) x)) x) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (+.f64 z y) x) (/.f64 (-.f64 y z) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (+.f64 z y) x) (/.f64 (-.f64 y z) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (+.f64 z y) x) (/.f64 (-.f64 y z) x) #s(literal 1 binary64)) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite293.0ms (4.1%)

Memory

1.9MiB live, 247.9MiB allocated

Rules

5 132×	`lower-/.f32`
5 122×	`lower-/.f64`
4 008×	`lower-*.f32`
3 994×	`lower-*.f64`
2 694×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	248
0	61	248
1	248	232
2	2167	232
0	8297	229

Stop Event

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

Counts

23 → 829

Calls

Call 1

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

Outputs
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eval325.0ms (4.5%)

Memory: 35.6MiB live, 591.7MiB allocated
Compiler: Compiled 45 438 to 5 212 computations (88.5% saved)

prune87.0ms (1.2%)

Memory

-18.4MiB live, 229.7MiB allocated

Pruning

16 alts after pruning (10 fresh and 6 done)

	Pruned	Kept	Total
New	1 819	7	1 826
Fresh	7	3	10
Picked	2	3	5
Done	0	3	3
Total	1 828	16	1 844

Accuracy

100.0%

Counts

1 844 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.0%	(/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64)))
✓	33.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
▶	41.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))))
▶	33.8%	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
	28.4%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) z) z) y))
	31.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (/.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) z)) (/.f64 y z)))
✓	69.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	65.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))
▶	31.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z))
✓	59.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
✓	31.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
	54.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 #s(literal 1 binary64) y) (.f64 (/.f64 y x) z)) (*.f64 (/.f64 y x) y))))
✓	65.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)))
▶	31.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z))
	66.6%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ x y) x) y) (*.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y)) #s(literal 1/2 binary64)))
✓	35.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 283 to 247 computations (12.7% saved)

simplify123.0ms (1.7%)

Memory

21.4MiB live, 176.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (neg.f64 z) z (*.f64 y y))
cost-diff	0	#s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))
cost-diff	0	(/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))))
cost-diff	384	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))))
cost-diff	0	(/.f64 y z)
cost-diff	0	(*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z))
cost-diff	384	(/.f64 #s(literal -1/2 binary64) (/.f64 y z))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) y)
cost-diff	0	(*.f64 z (/.f64 #s(literal -1/2 binary64) y))
cost-diff	0	(.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z))
cost-diff	0	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
cost-diff	0	(pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	7168	(/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64)))

Rules

10 078×	`lower-fma.f32`
10 074×	`lower-fma.f64`
3 060×	`lower-*.f32`
3 050×	`lower-*.f64`
1 624×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	255
0	61	255
1	98	251
2	174	249
3	356	249
4	1080	249
5	2961	246
6	6487	246
0	8276	243

Stop Event

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

Calls

Call 1

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

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

localize158.0ms (2.2%)

Memory

-25.8MiB live, 176.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12337875976844202	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))))
accuracy	2.9999669712667223	(fma.f64 (neg.f64 z) z (*.f64 y y))
accuracy	16.43391311115592	(/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))))
accuracy	20.63540099957118	#s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))
accuracy	0	(/.f64 y z)
accuracy	0.15625	(*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)
accuracy	0.40036174612100717	(/.f64 #s(literal -1/2 binary64) (/.f64 y z))
accuracy	44.03239035959762	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0	(*.f64 x x)
accuracy	16.21679972498638	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
accuracy	36.45769804617819	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
accuracy	0	(/.f64 #s(literal -1/2 binary64) y)
accuracy	0.15625	(.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)
accuracy	0.23953878162065376	(*.f64 z (/.f64 #s(literal -1/2 binary64) y))
accuracy	44.03239035959762	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z))
accuracy	0	(*.f64 x x)
accuracy	0.7649794231070471	(pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64))
accuracy	1.5038897356333616	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
accuracy	15.646768167869048	(/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64)))

Samples

137.0ms

256×

valid

Compiler

Compiled 216 to 35 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 15.0ms (34.8% of total)

ival-mult: 14.0ms (32.4% of total)

ival-pow: 5.0ms (11.6% of total)

ival-add: 4.0ms (9.3% of total)

ival-sub: 2.0ms (4.6% of total)

exact: 1.0ms (2.3% of total)

ival-neg: 1.0ms (2.3% of total)

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

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

series48.0ms (0.7%)

Memory

-24.0MiB live, 77.9MiB allocated

Counts

19 → 540

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)) (taylor 0 z) (#s(alt (/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64))) (patch (/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (/ (- (+ 1 (* -1 (/ (* (pow (+ y z) 3) (pow (- y z) 3)) (pow x 6)))) (+ (* -1 (/ (* (pow (+ y z) 2) (pow (- y z) 2)) (pow x 4))) (/ (* (+ y z) (- y z)) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (patch (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x))) (patch (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x))) (patch (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x))) (patch (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x))) (patch (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (patch #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (/ (pow z 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (patch #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (/ (pow z 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (patch #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (/ (pow z 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (patch #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (/.f64 #s(literal -1/2 binary64) (/.f64 y z)) z)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))))) (patch (/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (/ y (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y)))) (patch (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ y (* -1 (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y)))) (patch (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ y (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y)))) (patch (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ y (* -1 (/ (* y (* (pow (+ y z) 3) (pow (- y z) 3))) (pow x 6)))) (+ (* -1 (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y)))) (patch (/.f64 y #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))) (patch #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))) (patch #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))) (patch #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (.f64 y y))) (patch #s(approx (+ ( (+ y z) (- y z)) (* x x)) (fma.f64 (neg.f64 z) z (*.f64 y y))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1) (+ (* (+ y z) (- y z)) (* x x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* z (/ -1/2 y)) z) (* z (/ -1/2 y)) (/ -1/2 y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ -1/2 (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ -1/2 (/ y z)) z) (/ y z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ (* (neg z) z) (* y y)))
3.0ms	z	@	0	((/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1) (+ (* (+ y z) (- y z)) (* x x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* z (/ -1/2 y)) z) (* z (/ -1/2 y)) (/ -1/2 y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ -1/2 (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ -1/2 (/ y z)) z) (/ y z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ (* (neg z) z) (* y y)))
3.0ms	y	@	-inf	((/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1) (+ (* (+ y z) (- y z)) (* x x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* z (/ -1/2 y)) z) (* z (/ -1/2 y)) (/ -1/2 y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ -1/2 (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ -1/2 (/ y z)) z) (/ y z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ (* (neg z) z) (* y y)))
2.0ms	z	@	inf	((/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1) (+ (* (+ y z) (- y z)) (* x x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* z (/ -1/2 y)) z) (* z (/ -1/2 y)) (/ -1/2 y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ -1/2 (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ -1/2 (/ y z)) z) (/ y z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ (* (neg z) z) (* y y)))
2.0ms	y	@	0	((/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1) (+ (* (+ y z) (- y z)) (* x x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (* z (/ -1/2 y)) z) (* z (/ -1/2 y)) (/ -1/2 y) (* (/ 1/2 y) (- (+ (* x x) (* y y)) (* z z))) (- (+ (* x x) (* y y)) (* z z)) (* x x) (/ -1/2 (/ y z)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (/ -1/2 (/ y z)) z) (/ y z) (/ 1/2 (/ y (+ (* (+ y z) (- y z)) (* x x)))) (/ y (+ (* (+ y z) (- y z)) (* x x))) (+ (* (+ y z) (- y z)) (* x x)) (+ (* (neg z) z) (* y y)))

simplify247.0ms (3.4%)

Memory

10.2MiB live, 201.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 616×	`lower-fma.f64`
6 616×	`lower-fma.f32`
3 166×	`lower-*.f64`
3 166×	`lower-*.f32`
2 210×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	527	8117
1	1749	6896
2	7728	6875
0	8302	6543

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 540

Calls

Call 1

Inputs
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(/ 1 (+ (pow x 2) (pow y 2)))
(+ (* -1 (* z (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 2))) (/ y (pow (+ (pow x 2) (pow y 2)) 2))))) (/ 1 (+ (pow x 2) (pow y 2))))
(+ (* z (- (* z (- (/ 1 (pow (+ (pow x 2) (pow y 2)) 2)) (* -1 (/ (* (+ y (* -1 y)) (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 2))) (/ y (pow (+ (pow x 2) (pow y 2)) 2)))) (+ (pow x 2) (pow y 2)))))) (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 2))) (/ y (pow (+ (pow x 2) (pow y 2)) 2))))) (/ 1 (+ (pow x 2) (pow y 2))))
(+ (* z (- (* z (- (+ (* -1 (* z (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 3))) (+ (/ y (pow (+ (pow x 2) (pow y 2)) 3)) (/ (* (+ y (* -1 y)) (- (/ 1 (pow (+ (pow x 2) (pow y 2)) 2)) (* -1 (/ (* (+ y (* -1 y)) (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 2))) (/ y (pow (+ (pow x 2) (pow y 2)) 2)))) (+ (pow x 2) (pow y 2)))))) (+ (pow x 2) (pow y 2))))))) (/ 1 (pow (+ (pow x 2) (pow y 2)) 2))) (* -1 (/ (* (+ y (* -1 y)) (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 2))) (/ y (pow (+ (pow x 2) (pow y 2)) 2)))) (+ (pow x 2) (pow y 2)))))) (+ (* -1 (/ y (pow (+ (pow x 2) (pow y 2)) 2))) (/ y (pow (+ (pow x 2) (pow y 2)) 2))))) (/ 1 (+ (pow x 2) (pow y 2))))
(+ (pow x 2) (pow y 2))
(+ (* z (+ y (* -1 y))) (+ (pow x 2) (pow y 2)))
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (+ (pow x 2) (pow y 2)))
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (+ (pow x 2) (pow y 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (pow x 2) (pow y 2))
(+ (* -1 (pow z 2)) (+ (pow x 2) (pow y 2)))
(+ (* -1 (pow z 2)) (+ (pow x 2) (pow y 2)))
(+ (* -1 (pow z 2)) (+ (pow x 2) (pow y 2)))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* -1/2 (/ z y))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(+ (* -1/2 (/ (pow z 2) y)) (* 1/2 (/ (+ (pow x 2) (pow y 2)) y)))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(* -1/2 (/ (pow z 2) y))
(/ y z)
(/ y z)
(/ y z)
(/ y z)
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Outputs
(* 1/2 (/ (+ (pow x 2) (pow y 2)) y))
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(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ (+ y (* -1 (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (neg.f64 y) (.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x)) y) (.f64 x x))
(/ (- (+ y (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2))) (pow x 2))
(/.f64 (fma.f64 y (fma.f64 (/.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 z y) #s(literal 2 binary64)) (.f64 (-.f64 (neg.f64 z) y) (/.f64 (/.f64 (-.f64 y z) x) x))) y) (.f64 x x))
(/ (- (+ y (* -1 (/ (* y (* (pow (+ y z) 3) (pow (- y z) 3))) (pow x 6)))) (+ (* -1 (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (neg.f64 y) (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 3 binary64)) (pow.f64 (+.f64 z y) #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) y) (fma.f64 (/.f64 (.f64 (+.f64 z y) y) x) (/.f64 (-.f64 y z) x) (.f64 (neg.f64 y) (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 (+.f64 z y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* -1 (/ (* (+ y z) (- y z)) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (-.f64 (neg.f64 z) y) (/.f64 (/.f64 (-.f64 y z) x) x) #s(literal 1 binary64)) (*.f64 x x))
(/ (- (+ 1 (/ (* (pow (+ y z) 2) (pow (- y z) 2)) (pow x 4))) (/ (* (+ y z) (- y z)) (pow x 2))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 z y) #s(literal 2 binary64)) (fma.f64 (-.f64 (neg.f64 z) y) (/.f64 (/.f64 (-.f64 y z) x) x) #s(literal 1 binary64))) (*.f64 x x))
(/ (- (+ 1 (* -1 (/ (* (pow (+ y z) 3) (pow (- y z) 3)) (pow x 6)))) (+ (* -1 (/ (* (pow (+ y z) 2) (pow (- y z) 2)) (pow x 4))) (/ (* (+ y z) (- y z)) (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (neg.f64 (pow.f64 (+.f64 z y) #s(literal 3 binary64))) (/.f64 (pow.f64 (-.f64 y z) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (+.f64 z y) #s(literal 2 binary64))) (/.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (/ (pow z 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (/ (pow z 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (/ (pow z 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* (pow x 2) (+ (* 1/2 (/ (- y (/ (pow z 2) y)) (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (-.f64 y (/.f64 (.f64 z z) y)) x) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(* (pow x 2) (+ (* 1/2 (/ (* (+ y z) (- y z)) (* (pow x 2) y))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (-.f64 y z) y) (/.f64 (/.f64 (+.f64 z y) x) x) (/.f64 #s(literal 1 binary64) y)))
(/ y (pow x 2))
(/.f64 y (*.f64 x x))
(/ (+ y (* -1 (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2))
(/.f64 (fma.f64 (neg.f64 y) (.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x)) y) (.f64 x x))
(/ (- (+ y (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2))) (pow x 2))
(/.f64 (fma.f64 y (fma.f64 (/.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 z y) #s(literal 2 binary64)) (.f64 (-.f64 (neg.f64 z) y) (/.f64 (/.f64 (-.f64 y z) x) x))) y) (.f64 x x))
(/ (- (+ y (* -1 (/ (* y (* (pow (+ y z) 3) (pow (- y z) 3))) (pow x 6)))) (+ (* -1 (/ (* y (* (pow (+ y z) 2) (pow (- y z) 2))) (pow x 4))) (/ (* y (* (+ y z) (- y z))) (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (neg.f64 y) (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 3 binary64)) (pow.f64 (+.f64 z y) #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) y) (fma.f64 (/.f64 (.f64 (+.f64 z y) y) x) (/.f64 (-.f64 y z) x) (.f64 (neg.f64 y) (/.f64 (.f64 (pow.f64 (-.f64 y z) #s(literal 2 binary64)) (pow.f64 (+.f64 z y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (/ (* (+ y z) (- y z)) (pow x 2))))
(.f64 (fma.f64 (/.f64 (-.f64 y z) x) (/.f64 (+.f64 z y) x) #s(literal 1 binary64)) (.f64 x x))

rewrite180.0ms (2.5%)

Memory

41.8MiB live, 273.2MiB allocated

Rules

4 882×	`lower-/.f32`
4 868×	`lower-/.f64`
4 266×	`lower-fma.f32`
4 262×	`lower-fma.f64`
3 928×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	221
0	61	221
1	214	215
2	1547	215
0	8512	215

Stop Event

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

Counts

19 → 948

Calls

Call 1

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

Outputs
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eval313.0ms (4.3%)

Memory: 12.2MiB live, 485.4MiB allocated
Compiler: Compiled 31 349 to 3 547 computations (88.7% saved)

prune88.0ms (1.2%)

Memory

-14.5MiB live, 184.1MiB allocated

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	1 532	5	1 537
Fresh	2	3	5
Picked	3	2	5
Done	0	6	6
Total	1 537	16	1 553

Accuracy

100.0%

Counts

1 553 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.3%	(/.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (pow (+ (* (+ y z) (- y z)) (* x x)) -1) (/.f64 #s(literal -1 binary64) (*.f64 z z))))
✓	33.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
	43.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 y #s(approx (+ (* (+ y z) (- y z)) (* x x)) (*.f64 (-.f64 y z) (+.f64 z y)))))
✓	33.8%	(.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ ( x x) (* y y)) (* z z)) (*.f64 x x)))
	87.5%	#s(approx (/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (.f64 (fma.f64 (/.f64 (-.f64 y z) y) (+.f64 z y) (/.f64 (.f64 x x) y)) #s(literal 1/2 binary64)))
	28.4%	#s(approx (/ (/ 1/2 y) (pow (+ (* (+ y z) (- y z)) (* x x)) -1)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
	31.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (/.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 y z)))
✓	69.2%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	65.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))
✓	59.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
✓	31.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
	54.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 (.f64 #s(literal 1 binary64) y) (.f64 (/.f64 y x) z)) (*.f64 (/.f64 y x) y))))
✓	65.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (+.f64 z x) #s(literal 1/2 binary64)) (/.f64 (-.f64 x z) y)))
✓	31.1%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z))
	66.6%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ x y) x) y) (*.f64 (fma.f64 (/.f64 x y) (/.f64 x y) #s(literal 1 binary64)) y)) #s(literal 1/2 binary64)))
✓	35.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 592 to 288 computations (51.4% saved)

regimes72.0ms (1%)

Memory

-14.2MiB live, 170.7MiB allocated

Counts

34 → 1

Calls

Call 1

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

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

Calls

6 calls:

15.0ms	y
14.0ms	(*.f64 z z)
11.0ms	z
10.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))
10.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`z`
99.9%	1	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 z z)`

Compiler

Compiled 24 to 28 computations (-16.7% saved)

regimes108.0ms (1.5%)

Memory

-8.7MiB live, 108.3MiB allocated

Counts

27 → 1

Calls

Call 1

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

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

Calls

6 calls:

65.0ms	y
9.0ms	(*.f64 z z)
8.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))
8.0ms	x
8.0ms	z

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`z`
99.9%	1	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 z z)`

Compiler

Compiled 24 to 28 computations (-16.7% saved)

regimes48.0ms (0.7%)

Memory

8.2MiB live, 50.1MiB allocated

Counts

15 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

6 calls:

22.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))
5.0ms	x
5.0ms	y
5.0ms	z
5.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.8%	2	`x`
88.6%	2	`y`
88.6%	2	`z`
96.7%	3	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
88.8%	2	`(*.f64 x x)`
88.6%	2	`(*.f64 z z)`

Compiler

Compiled 24 to 28 computations (-16.7% saved)

regimes4.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

11 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
92.8%	2	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes50.0ms (0.7%)

Memory

-22.4MiB live, 51.4MiB allocated

Counts

8 → 4

Calls

Call 1

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

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

Calls

6 calls:

5.0ms	(*.f64 z z)
3.0ms	y
3.0ms	x
3.0ms	z
3.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
57.9%	3	`z`
57.9%	3	`(*.f64 z z)`
57.3%	2	`y`
58.5%	4	`x`
56.1%	3	`(*.f64 x x)`
67.0%	4	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 24 to 28 computations (-16.7% saved)

regimes3.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

7 → 4

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
67.0%	4	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes3.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

6 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
61.1%	3	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

2 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

1.0ms

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

Results

Accuracy	Segments	Branch
61.1%	3	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes10.0ms (0.1%)

Memory

-15.3MiB live, 22.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

4.0ms	(*.f64 z z)
1.0ms	z
1.0ms	y
1.0ms	x
1.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
35.7%	1	`(*.f64 x x)`
35.7%	1	`x`
35.7%	1	`z`
35.7%	1	`(*.f64 z z)`
35.7%	1	`y`
35.7%	1	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`

Compiler

Compiled 24 to 28 computations (-16.7% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	0.0	9.362616724642038e-93

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.54705342093574e-76	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	2.514852871469583e+152	1.4316044352204975e+170
0.0ms	0.0	9.362616724642038e-93

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	2.514852871469583e+152	1.4316044352204975e+170
0.0ms	0.0	9.362616724642038e-93

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	0.0	9.362616724642038e-93

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	0.0	9.362616724642038e-93

Compiler

Compiled 18 to 17 computations (5.6% saved)

simplify30.0ms (0.4%)

Memory

13.4MiB live, 58.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	733
1	94	733
2	101	733
3	104	733
4	105	733

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -6518515124270355/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999999866701502061576872427769509559218343142920094012184839761211880836459879782283579221834689412014355010196297047064515110066507929878528 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) (/.f64 #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999999866701502061576872427769509559218343142920094012184839761211880836459879782283579221834689412014355010196297047064515110066507929878528 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z))))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Outputs
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y)) #s(literal 1/2 binary64)))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 (-.f64 x z) y) z (fma.f64 (/.f64 (-.f64 x z) y) x y))))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (neg.f64 z) (/.f64 z y) y) #s(literal 1/2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -6518515124270355/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -6518515124270355/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999999866701502061576872427769509559218343142920094012184839761211880836459879782283579221834689412014355010196297047064515110066507929878528 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) (/.f64 #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64))) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 499999999999999999866701502061576872427769509559218343142920094012184839761211880836459879782283579221834689412014355010196297047064515110066507929878528 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal +inf.0 binary64)) (/.f64 #s(approx (- (+ ( x x) (* y y)) (* z z)) (.f64 x x)) (.f64 #s(literal 2 binary64) y)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 499999999999999999866701502061576872427769509559218343142920094012184839761211880836459879782283579221834689412014355010196297047064515110066507929878528 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 499999999999999999866701502061576872427769509559218343142920094012184839761211880836459879782283579221834689412014355010196297047064515110066507929878528 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal +inf.0 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) y) #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x))) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z)))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 z (/.f64 #s(literal -1/2 binary64) y)) z))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal +inf.0 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) z))))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

soundness859.0ms (11.9%)

Memory

-7.2MiB live, 782.8MiB allocated

Rules

7 488×	`lower-fma.f64`
7 488×	`lower-fma.f32`
6 988×	`lower-fma.f64`
6 988×	`lower-fma.f32`
5 132×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	364	6225
1	1187	5855
2	4054	5654
0	8213	5347
0	37	248
0	61	248
1	248	232
2	2167	232
0	8297	229
0	34	196
0	54	196
1	216	191
2	1930	191
0	8649	191
0	71	1206
1	196	1206
2	566	1204
3	2177	1064
4	6044	1040
0	8183	954

Stop Event

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

Compiler

Compiled 531 to 192 computations (63.8% saved)

preprocess139.0ms (1.9%)

Memory: 13.5MiB live, 295.1MiB allocated
Remove: (negabs y)
Compiler: Compiled 1 242 to 376 computations (69.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze45.0ms (0.6%)

sample1.0s (14.3%)

explain125.0ms (1.7%)

preprocess192.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify153.0ms (2.1%)

localize31.0ms (0.4%)

series12.0ms (0.2%)

simplify124.0ms (1.7%)

rewrite270.0ms (3.7%)

eval88.0ms (1.2%)

prune37.0ms (0.5%)

simplify208.0ms (2.9%)

localize120.0ms (1.7%)

series49.0ms (0.7%)

simplify164.0ms (2.3%)

rewrite206.0ms (2.8%)

eval218.0ms (3%)

prune224.0ms (3.1%)

simplify246.0ms (3.4%)

localize162.0ms (2.2%)

series129.0ms (1.8%)

simplify210.0ms (2.9%)

rewrite293.0ms (4.1%)

eval325.0ms (4.5%)

prune87.0ms (1.2%)

simplify123.0ms (1.7%)

localize158.0ms (2.2%)

series48.0ms (0.7%)

simplify247.0ms (3.4%)

rewrite180.0ms (2.5%)

eval313.0ms (4.3%)

prune88.0ms (1.2%)

regimes72.0ms (1%)

regimes108.0ms (1.5%)

regimes48.0ms (0.7%)

regimes4.0ms (0.1%)

regimes50.0ms (0.7%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes10.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify30.0ms (0.4%)

soundness859.0ms (11.9%)

preprocess139.0ms (1.9%)

end0.0ms (0%)

Profiling