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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze45.0ms (0.6%)

Memory

27.3MiB live, 108.3MiB 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 (12.8%)

Memory

19.8MiB live, 1 311.7MiB allocated

Samples

686.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 419.0ms

ival-mult: 241.0ms (57.6% of total)

ival-div: 89.0ms (21.3% of total)

ival-sub: 37.0ms (8.8% of total)

ival-add: 36.0ms (8.6% of total)

ival-true: 7.0ms (1.7% of total)

exact: 5.0ms (1.2% of total)

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

Bogosity

explain140.0ms (1.8%)

Memory

10.6MiB live, 208.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
68	-	-	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
26	-	-	`(-.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	65	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	151
↳	`(*.f64 y y)`	overflow	65
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	114
↳	`(*.f64 z z)`	overflow	63
`-.f64`	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	nan-rescue	26	0
↳	`(*.f64 y y)`	overflow	65
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	114
↳	`(*.f64 z z)`	overflow	63
`/.f64`	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`	u/n	3	0
↳	`(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	3
↳	`(*.f64 y y)`	underflow	57
↳	`(*.f64 x x)`	underflow	49
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	8
↳	`(*.f64 z z)`	underflow	64

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	74
2	10

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms

512×

valid

Compiler

Compiled 117 to 37 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 14.0ms (61.5% of total)

ival-div: 3.0ms (13.2% of total)

ival-sub: 2.0ms (8.8% of total)

ival-add: 2.0ms (8.8% of total)

ival-true: 1.0ms (4.4% of total)

exact: 0.0ms (0% of total)

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

preprocess207.0ms (2.6%)

Memory

-32.0MiB live, 241.7MiB allocated

Algorithm

1×	egg-herbie

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB 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)

simplify160.0ms (2%)

Memory

39.5MiB live, 220.6MiB 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))

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

-3.5MiB live, 88.5MiB 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	5.644512672471853	(-.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	15.835004251285199	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Samples

23.0ms

256×

valid

Compiler

Compiled 51 to 13 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 10.0ms (71.3% of total)

ival-div: 2.0ms (14.3% of total)

ival-sub: 1.0ms (7.1% of total)

ival-add: 1.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series53.0ms (0.7%)

Memory

-24.7MiB live, 13.8MiB 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>) () ())) ())
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Calls

9 calls:

Time	Variable		Point	Expression
42.0ms	x	@	-inf	((- (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (* x x) (* y y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)))
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)))

simplify125.0ms (1.6%)

Memory

8.7MiB live, 127.4MiB allocated

Algorithm

1×	egg-herbie

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))

rewrite238.0ms (3%)

Memory

5.9MiB live, 257.1MiB allocated

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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eval124.0ms (1.6%)

Memory: -22.4MiB live, 138.2MiB allocated
Compiler: Compiled 18 944 to 1 651 computations (91.3% saved)

prune25.0ms (0.3%)

Memory

-14.9MiB live, 74.4MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	635	13	648
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	636	13	649

Accuracy

100.0%

Counts

649 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.9%	(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)))
	36.4%	(/.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z))) (.f64 x x)) (*.f64 y #s(literal 2 binary64)))
▶	25.8%	(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y z) (-.f64 y z)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 (+.f64 x y) (-.f64 x y) (.f64 z z))))
	47.3%	(/.f64 (-.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (/.f64 #s(literal 2 binary64) z) (/.f64 y z))) (.f64 #s(literal 2 binary64) y)) (.f64 (.f64 #s(literal 2 binary64) y) (*.f64 (/.f64 #s(literal 2 binary64) z) (/.f64 y z))))
	32.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
▶	74.0%	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
	18.6%	(.f64 (/.f64 (fma.f64 (.f64 z z) (fma.f64 z z (fma.f64 y y (.f64 x x))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) y)) (/.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (fma.f64 (.f64 z z) (fma.f64 z z (fma.f64 y y (.f64 x x))) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 2 binary64)))))
▶	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)))
▶	67.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	30.4%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
	61.0%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
	66.7%	#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)))
▶	34.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 470 to 292 computations (37.9% saved)

simplify201.0ms (2.6%)

Memory

37.1MiB live, 194.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	280
0	71	280
1	136	277
2	348	277
3	1526	277
4	7962	277
0	8606	277

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

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

localize135.0ms (1.7%)

Memory

-18.7MiB live, 58.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	1.7499807332389217	(fma.f64 (+.f64 x y) (-.f64 x y) (*.f64 z z))
accuracy	6.8589609850533275	(.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 (+.f64 x y) (-.f64 x y) (*.f64 z z)))
accuracy	11.777294209924948	(-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 y z) (-.f64 y z)) #s(literal 2 binary64)))
accuracy	37.1922990877124	(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y z) (-.f64 y z)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) y) (fma.f64 (+.f64 x y) (-.f64 x y) (.f64 z z))))
accuracy	0	(+.f64 y z)
accuracy	0	(*.f64 x x)
accuracy	0.9999889904222409	(fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))
accuracy	15.854535501285199	(.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64))
accuracy	0.0546875	(fma.f64 (/.f64 x y) x y)
accuracy	20.562616096895457	#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 #s(literal 1/2 binary64) y)
accuracy	41.802503459050826	#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	0.01953125	(/.f64 (-.f64 x z) y)
accuracy	0.07421875	(fma.f64 (/.f64 (-.f64 x z) y) (+.f64 z x) y)

Samples

80.0ms

256×

valid

Compiler

Compiled 265 to 42 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 19.0ms (31.5% of total)

ival-pow2: 16.0ms (26.5% of total)

ival-div: 8.0ms (13.3% of total)

ival-add: 8.0ms (13.3% of total)

ival-sub: 6.0ms (9.9% of total)

ival-pow: 3.0ms (5% of total)

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

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

exact: 0.0ms (0% of total)

series147.0ms (1.9%)

Memory

-12.9MiB live, 72.1MiB allocated

Counts

21 → 612

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

Calls

9 calls:

Time	Variable		Point	Expression
52.0ms	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 y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* x x) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (pow x 4) (pow (* (+ y z) (- y z)) 2) (+ (* (+ y z) (- y z)) (* x x)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z))) (+ (* (+ x y) (- x y)) (* z z)))
10.0ms	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 y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* x x) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (pow x 4) (pow (* (+ y z) (- y z)) 2) (+ (* (+ y z) (- y z)) (* x x)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z))) (+ (* (+ x y) (- x y)) (* z z)))
8.0ms	y	@	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 y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* x x) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (pow x 4) (pow (* (+ y z) (- y z)) 2) (+ (* (+ y z) (- y z)) (* x x)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z))) (+ (* (+ x y) (- x y)) (* z z)))
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 y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* x x) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (pow x 4) (pow (* (+ y z) (- y z)) 2) (+ (* (+ y z) (- y z)) (* x x)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z))) (+ (* (+ x y) (- x y)) (* z z)))
6.0ms	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 y) x) y) 1/2) (+ (* (/ x y) x) y) (/ x y) (* (+ (* (+ y z) (- y z)) (* x x)) (/ 1/2 y)) (+ y z) (- y z) (* x x) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (pow x 4) (pow (* (+ y z) (- y z)) 2) (+ (* (+ y z) (- y z)) (* x x)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z))) (+ (* (+ x y) (- x y)) (* z z)))

simplify258.0ms (3.3%)

Memory

31.2MiB live, 186.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1020	9707
1	3496	8629
0	8864	8236

Stop Event

1×	iter limit
1×	node limit

Counts

612 → 598

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

rewrite371.0ms (4.7%)

Memory

-12.6MiB live, 258.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	228
0	71	228
1	308	225
2	2686	225
0	8556	225

Stop Event

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

Counts

21 → 733

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

Outputs
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eval285.0ms (3.6%)

Memory: 36.8MiB live, 308.7MiB allocated
Compiler: Compiled 41 250 to 4 109 computations (90% saved)

prune94.0ms (1.2%)

Memory

-30.1MiB live, 92.4MiB allocated

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	1 426	8	1 434
Fresh	6	2	8
Picked	3	2	5
Done	0	0	0
Total	1 435	12	1 447

Accuracy

100.0%

Counts

1 447 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
	30.4%	(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 (neg.f64 z) z)) (/.f64 #s(literal 1/2 binary64) y))
	32.6%	(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y))
▶	30.4%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
✓	67.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
▶	99.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z))) (+.f64 z x) y) #s(literal 1/2 binary64)))
▶	67.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))
	66.0%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 #s(approx (/ (- x z) y) (/.f64 (neg.f64 z) y)) (+.f64 z x) y) #s(literal 1/2 binary64)))
	92.6%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)))
▶	61.0%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (-.f64 y (/.f64 (.f64 z z) y)) #s(literal 1/2 binary64)))
	85.5%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64)))
✓	34.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 257 to 226 computations (12.1% saved)

simplify141.0ms (1.8%)

Memory

33.1MiB live, 103.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 y x))
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 z z)
cost-diff	0	(/.f64 (*.f64 z z) y)
cost-diff	0	(.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z))) (+.f64 z x) y)
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z))) (+.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 #s(literal 1 binary64) (/.f64 y (-.f64 x z))) (+.f64 z x) y) #s(literal 1/2 binary64)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	285
0	71	285
1	147	274
2	400	269
3	1713	269
4	7914	269
0	8547	263

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

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

localize160.0ms (2%)

Memory

-9.1MiB live, 151.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64))
accuracy	0.0546875	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y)
accuracy	0.23087221800160945	(/.f64 #s(literal 1 binary64) (/.f64 y x))
accuracy	20.562616096895457	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y x)) x y) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 z z)
accuracy	0.00390625	(-.f64 y (/.f64 (*.f64 z z) y))
accuracy	7.532590903774548	(/.f64 (*.f64 z z) y)
accuracy	21.56535559124465	#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	15.835004251285199	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
accuracy	38.5130881879458	#s(approx (- (+ (* x x) (* y y)) (* z z)) (*.f64 x x))
accuracy	0	(.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64))
accuracy	0	(*.f64 z z)
accuracy	7.532590903774548	(/.f64 (*.f64 z z) y)
accuracy	43.02953059971684	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
accuracy	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z))) (+.f64 z x) y) #s(literal 1/2 binary64)))
accuracy	0.015625	(/.f64 y (-.f64 x z))
accuracy	0.07421875	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z))) (+.f64 z x) y)
accuracy	0.40789809621754924	(/.f64 #s(literal 1 binary64) (/.f64 y (-.f64 x z)))

Samples

123.0ms

256×

valid

Compiler

Compiled 239 to 46 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-mult: 32.0ms (39.3% of total)

ival-add: 26.0ms (32% of total)

ival-div: 11.0ms (13.5% of total)

ival-sub: 7.0ms (8.6% of total)

ival-pow2: 3.0ms (3.7% of total)

ival-pow: 3.0ms (3.7% of total)

exact: 1.0ms (1.2% of total)

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

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

series113.0ms (1.4%)

Memory

-24.9MiB live, 96.8MiB allocated

Counts

20 → 564

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
46.0ms	x	@	-inf	((/ 1 (/ y (- x z))) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) 1/2) (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (/ (- (+ (* 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)) (/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ y (- x z)))
8.0ms	z	@	-inf	((/ 1 (/ y (- x z))) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) 1/2) (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (/ (- (+ (* 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)) (/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ y (- x z)))
4.0ms	y	@	-inf	((/ 1 (/ y (- x z))) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) 1/2) (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (/ (- (+ (* 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)) (/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ y (- x z)))
3.0ms	y	@	inf	((/ 1 (/ y (- x z))) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) 1/2) (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (/ (- (+ (* 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)) (/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ y (- x z)))
3.0ms	y	@	0	((/ 1 (/ y (- x z))) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) 1/2) (+ (* (/ 1 (/ y (- x z))) (+ z x)) y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (/ (* z z) y) -1/2) (/ (* z z) y) (* z z) (/ (- (+ (* 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)) (/ 1 (/ y x)) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ 1 (/ y x)) x) y) 1/2) (+ (* (/ 1 (/ y x)) x) y) (/ y (- x z)))

simplify205.0ms (2.6%)

Memory

4.8MiB live, 166.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	703	8326
1	2320	7536
0	9079	7158

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 556

Calls

Call 1

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

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

rewrite173.0ms (2.2%)

Memory

14.0MiB live, 135.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	250
0	71	250
1	334	234
2	2873	234
0	8739	228

Stop Event

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

Counts

20 → 381

Calls

Call 1

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

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eval205.0ms (2.6%)

Memory: 7.9MiB live, 199.8MiB allocated
Compiler: Compiled 17 245 to 2 359 computations (86.3% saved)

prune89.0ms (1.1%)

Memory

13.5MiB live, 95.8MiB allocated

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	997	6	1 003
Fresh	3	2	5
Picked	4	1	5
Done	0	2	2
Total	1 004	11	1 015

Accuracy

100.0%

Counts

1 015 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	32.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
▶	32.7%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
	30.4%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 z z) (/.f64 #s(literal -1/2 binary64) y)))
▶	35.5%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))
✓	67.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	65.9%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ y (- x z)) (/.f64 (neg.f64 y) z))) (+.f64 z x) y) #s(literal 1/2 binary64)))
	66.3%	#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)))
▶	92.6%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)))
▶	67.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64)))
▶	85.5%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64)))
✓	34.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 219 to 194 computations (11.4% saved)

simplify195.0ms (2.5%)

Memory

-17.5MiB live, 217.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)))
cost-diff	0	(.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64)))
cost-diff	128	(fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (*.f64 y y)) #s(literal -1 binary64))
cost-diff	0	(*.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64)))
cost-diff	128	(+.f64 (/.f64 x (/.f64 y x)) y)
cost-diff	384	(/.f64 x (/.f64 y x))
cost-diff	0	(/.f64 z y)
cost-diff	0	(*.f64 (/.f64 z y) z)
cost-diff	0	(.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
cost-diff	0	(/.f64 x y)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
cost-diff	0	(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x)
cost-diff	0	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))
cost-diff	0	#s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x))
cost-diff	0	(fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y)
cost-diff	0	(.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.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 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	464
0	95	464
1	198	464
2	520	464
3	2079	460
4	7286	460
0	8139	444

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

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

localize146.0ms (1.9%)

Memory

28.2MiB live, 337.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ (* (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)))
accuracy	0.5287028437989916	(fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (*.f64 y y)) #s(literal -1 binary64))
accuracy	4.441974335473086	(.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))
accuracy	6.993991372252167	(/.f64 (-.f64 x z) (*.f64 y y))
accuracy	0	(+.f64 (/.f64 x (/.f64 y x)) y)
accuracy	0	(*.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64))
accuracy	0.1484375	(/.f64 x (/.f64 y x))
accuracy	20.562616096895457	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64)))
accuracy	0	(/.f64 z y)
accuracy	0	(.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))
accuracy	0.1328125	(*.f64 (/.f64 z y) z)
accuracy	43.02953059971684	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
accuracy	0.140625	(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x)
accuracy	41.24458031066708	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))
accuracy	0.01953125	(-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x)))
accuracy	0.07421875	(fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y)
accuracy	4.698863104062948	(.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)
accuracy	5.01610675318287	(/.f64 z (*.f64 y x))

Samples

113.0ms

256×

valid

Compiler

Compiled 318 to 58 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-mult: 35.0ms (42.9% of total)

ival-div: 15.0ms (18.4% of total)

ival-add: 14.0ms (17.2% of total)

ival-sub: 7.0ms (8.6% of total)

ival-neg: 4.0ms (4.9% of total)

ival-pow2: 3.0ms (3.7% of total)

ival-pow: 3.0ms (3.7% of total)

exact: 1.0ms (1.2% of total)

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

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

series105.0ms (1.3%)

Memory

-13.3MiB live, 141.6MiB allocated

Counts

25 → 792

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) (patch (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #<representation binary64>) () ())
#s(alt #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (patch #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x)) (patch #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x) (patch (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (/.f64 x y)) (patch (.f64 #s(literal 1/2 binary64) (/.f64 x y)) #<representation binary64>) () ())
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) (patch #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)) (patch (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 z y) z) (patch (.f64 (/.f64 z y) z) #<representation binary64>) () ())
#s(alt (/.f64 z y) (patch (/.f64 z y) #<representation binary64>) () ())
#s(alt (/.f64 x (/.f64 y x)) (patch (/.f64 x (/.f64 y x)) #<representation binary64>) () ())
#s(alt (+.f64 (/.f64 x (/.f64 y x)) y) (patch (+.f64 (/.f64 x (/.f64 y x)) y) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (*.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 (/.f64 x (/.f64 y x)) y) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (patch (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ ( (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) (patch #s(approx (+ (* (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #<representation binary64>) () ())
#s(alt (/.f64 z (.f64 y x)) (patch (/.f64 z (.f64 y x)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) (patch (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 x z) (.f64 y y)) (patch (/.f64 (-.f64 x z) (.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) (patch (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) #<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 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.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 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.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 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.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 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ ( x x) (* y y)) (* z z)) (* y 2)) (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (*.f64 y x))) x)) (+.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 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)) (patch (.f64 (fma.f64 #s(approx (/ (- x z) y) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x)) (+.f64 z x) y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#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 #s(approx (+ (* (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) (patch #s(approx (+ (* (/ (- x z) y) (+ z x)) y) (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y))) #<representation binary64>) () ())) ())
#s(alt (/ z (* x y)) (taylor -inf x) (#s(alt (/.f64 z (.f64 y x)) (patch (/.f64 z (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ z (* x y)) (taylor -inf x) (#s(alt (/.f64 z (.f64 y x)) (patch (/.f64 z (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ z (* x y)) (taylor -inf x) (#s(alt (/.f64 z (.f64 y x)) (patch (/.f64 z (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ z (* x y)) (taylor -inf x) (#s(alt (/.f64 z (.f64 y x)) (patch (/.f64 z (.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) (patch (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ z (* x y)) (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) (patch (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ z (* x y)) (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) (patch (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ z (* x y)) (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) (patch (.f64 (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ z (* x y))) (/ 1 y)) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ z (* x y))) (/ 1 y)) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ z (* x y))) (/ 1 y)) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 z (.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (/ x (pow y 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 x z) (.f64 y y)) (patch (/.f64 (-.f64 x z) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ z (* x (pow y 2))) (/ 1 (pow y 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x z) (.f64 y y)) (patch (/.f64 (-.f64 x z) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ z (* x (pow y 2))) (/ 1 (pow y 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x z) (.f64 y y)) (patch (/.f64 (-.f64 x z) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ z (* x (pow y 2))) (/ 1 (pow y 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 x z) (.f64 y y)) (patch (/.f64 (-.f64 x z) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) y) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) (patch (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (* y (+ (* -1 (/ z (pow y 2))) (/ z (pow y 2)))) x)) (/ 1 y))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) (patch (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* y (+ (* -1 (/ z (pow y 2))) (/ z (pow y 2)))) (/ (* y (- (/ (pow z 2) (pow y 2)) 1)) x)) x)) (/ 1 y))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) (patch (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* y (+ (* -1 (/ z (pow y 2))) (/ z (pow y 2)))) (/ (* y (- (/ (pow z 2) (pow y 2)) 1)) x)) x)) (/ 1 y))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) (patch (.f64 (fma.f64 (neg.f64 (+.f64 z x)) (/.f64 (-.f64 x z) (.f64 y y)) #s(literal -1 binary64)) (neg.f64 y)) #<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) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* 1/2 (/ x y)) x) (* 1/2 (/ x y)) (/ x y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (/ x (/ y x)) (+ (/ x (/ y x)) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (/ x (/ y x)) y) 1/2) (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ z (* y x)) (* (- (/ 1 y) (/ z (* y x))) x) (- (/ 1 y) (/ z (* y x))) (/ (- x z) (* y y)) (* (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (neg y)))
6.0ms	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) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* 1/2 (/ x y)) x) (* 1/2 (/ x y)) (/ x y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (/ x (/ y x)) (+ (/ x (/ y x)) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (/ x (/ y x)) y) 1/2) (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ z (* y x)) (* (- (/ 1 y) (/ z (* y x))) x) (- (/ 1 y) (/ z (* y x))) (/ (- x z) (* y y)) (* (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (neg y)))
5.0ms	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) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* 1/2 (/ x y)) x) (* 1/2 (/ x y)) (/ x y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (/ x (/ y x)) (+ (/ x (/ y x)) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (/ x (/ y x)) y) 1/2) (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ z (* y x)) (* (- (/ 1 y) (/ z (* y x))) x) (- (/ 1 y) (/ z (* y x))) (/ (- x z) (* y y)) (* (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (neg y)))
5.0ms	y	@	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) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* 1/2 (/ x y)) x) (* 1/2 (/ x y)) (/ x y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (/ x (/ y x)) (+ (/ x (/ y x)) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (/ x (/ y x)) y) 1/2) (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ z (* y x)) (* (- (/ 1 y) (/ z (* y x))) x) (- (/ 1 y) (/ z (* y x))) (/ (- x z) (* y y)) (* (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (neg y)))
4.0ms	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) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* 1/2 (/ x y)) x) (* 1/2 (/ x y)) (/ x y) (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (* (* (/ z y) z) -1/2) (* (/ z y) z) (/ z y) (/ x (/ y x)) (+ (/ x (/ y x)) y) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (/ x (/ y x)) y) 1/2) (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (* (+ (* (/ (- x z) y) (+ z x)) y) 1/2) (+ (* (/ (- x z) y) (+ z x)) y) (/ z (* y x)) (* (- (/ 1 y) (/ z (* y x))) x) (- (/ 1 y) (/ z (* y x))) (/ (- x z) (* y y)) (* (+ (* (neg (+ z x)) (/ (- x z) (* y y))) -1) (neg y)))

simplify210.0ms (2.7%)

Memory

-23.3MiB live, 311.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	708	12684
1	2377	10697
0	9490	10248

Stop Event

1×	iter limit
1×	node limit

Counts

792 → 783

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

rewrite287.0ms (3.7%)

Memory

15.7MiB live, 257.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	418
0	95	418
1	419	418
2	3794	406
0	8473	395

Stop Event

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

Counts

25 → 415

Calls

Call 1

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

Outputs
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eval252.0ms (3.2%)

Memory: 20.1MiB live, 284.0MiB allocated
Compiler: Compiled 23 565 to 2 926 computations (87.6% saved)

prune79.0ms (1%)

Memory

7.8MiB live, 165.8MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1 194	4	1 198
Fresh	2	1	3
Picked	3	2	5
Done	0	3	3
Total	1 199	10	1 209

Accuracy

100.0%

Counts

1 209 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	32.7%	(/.f64 #s(approx (- (+ (* x x) (* y y)) (* z z)) (.f64 x x)) (.f64 y #s(literal 2 binary64)))
	35.5%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 y x)))
	32.7%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (*.f64 (/.f64 z (/.f64 y z)) #s(literal -1/2 binary64)))
✓	32.7%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
	32.7%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) z))
	35.5%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))
✓	35.5%	#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))
✓	67.8%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 (fma.f64 (/.f64 x y) x y) #s(literal 1/2 binary64)))
	66.3%	#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)))
✓	34.7%	#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

Compiler

Compiled 524 to 232 computations (55.7% saved)

regimes77.0ms (1%)

Memory

4.4MiB live, 126.1MiB allocated

Counts

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

25.0ms	y
13.0ms	(*.f64 z z)
9.0ms	z
9.0ms	x
9.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

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)

regimes63.0ms (0.8%)

Memory

-4.9MiB live, 110.9MiB allocated

Counts

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

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)))

Calls

6 calls:

26.0ms	(*.f64 z z)
9.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))
8.0ms	x
6.0ms	y
6.0ms	z

Results

Accuracy	Segments	Branch
89.4%	2	`x`
86.6%	2	`y`
87.6%	2	`z`
95.7%	2	`(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))`
89.4%	2	`(*.f64 x x)`
87.6%	2	`(*.f64 z z)`

Compiler

Compiled 24 to 28 computations (-16.7% saved)

regimes7.0ms (0.1%)

Memory

-23.7MiB live, 15.2MiB allocated

Counts

13 → 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 (.f64 z z) y) #s(literal -1/2 binary64)))
#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))
#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))
#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 z z) (/.f64 #s(literal -1/2 binary64) y)))
#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) z))
#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64)))
#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)))
(.f64 #s(approx (+ ( (+ y z) (- y z)) (* x x)) (*.f64 x x)) (/.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 (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 (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (*.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) y) z) 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:

6.0ms

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

Results

Accuracy	Segments	Branch
95.7%	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)

regimes234.0ms (3%)

Memory

11.9MiB live, 48.1MiB allocated

Counts

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

Outputs

#s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (*.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))

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

Calls

6 calls:

215.0ms	z
4.0ms	y
4.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(*.f64 z z)

Results

Accuracy	Segments	Branch
54.2%	2	`y`
60.4%	5	`z`
58.6%	4	`(*.f64 z z)`
61.0%	3	`x`
61.0%	3	`(*.f64 x x)`
73.3%	3	`(/.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

6.6MiB live, 6.6MiB allocated

Counts

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

Outputs

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

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

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

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
71.9%	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)

regimes3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

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

Outputs

#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 #s(literal 1/2 binary64) y))

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

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
71.9%	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

5.5MiB live, 5.5MiB allocated

Counts

3 → 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 (*.f64 z z) y) #s(literal -1/2 binary64)))

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

Outputs

#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 #s(literal 1/2 binary64) y))

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

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
71.9%	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

4.6MiB live, 4.6MiB allocated

Counts

2 → 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 (.f64 z z) y) #s(literal -1/2 binary64)))

Outputs
#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 #s(literal 1/2 binary64) y))

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
61.0%	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)

regimes25.0ms (0.3%)

Memory

-44.4MiB live, 17.2MiB 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:

18.0ms	(*.f64 x x)
1.0ms	x
1.0ms	y
1.0ms	z
1.0ms	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
34.7%	1	`y`
34.7%	1	`(*.f64 z z)`
34.7%	1	`z`
34.7%	1	`x`
34.7%	1	`(*.f64 x x)`
34.7%	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

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	5.147049485389357e-128

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.2957953605951864e-64	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.935348751676958e+148	4.384432607904655e+154
0.0ms	-1.2957953605951864e-64	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.935348751676958e+148	4.384432607904655e+154
0.0ms	-1.2957953605951864e-64	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.935348751676958e+148	4.384432607904655e+154
0.0ms	-1.2957953605951864e-64	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	5.935348751676958e+148	4.384432607904655e+154
0.0ms	-1.2957953605951864e-64	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.2957953605951864e-64	0.0

Compiler

Compiled 18 to 17 computations (5.6% saved)

simplify36.0ms (0.5%)

Memory

21.9MiB live, 61.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	741
1	105	741
2	112	741
3	115	741
4	116	741

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) (+.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))) #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 -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) 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 -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 z z) (/.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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) 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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) 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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #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 #s(literal 1/2 binary64) y)))
#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) (+.f64 z 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) (+.f64 z x) y)))
(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))) #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 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))) #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 -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) 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 -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) 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 -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) z) z)) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 z z) (/.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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (pow x 4) (pow (* (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 z z))) (if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) 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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) 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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) 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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x y)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 z z)) (.f64 #s(literal 2 binary64) y)) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 (/.f64 (.f64 z z) 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 100000000000000004897672657515052057957222700353074388874504237459016826359338475616123152924727646379311306468151027676205343291866258521710227619840 binary64)) #s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (.f64 #s(literal 1/2 binary64) y)) #s(approx (/ (- (pow x 4) (pow ( (+ y z) (- y z)) 2)) (* (* 2 y) (+ (* (+ x y) (- x y)) (* z z)))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))))
(if (<=.f64 (/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y #s(literal 2 binary64))) #s(literal -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #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 #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 -5928554968950589/59285549689505892056868344324448208820874232148807968788202283012051522375647232 binary64)) #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 #s(literal 1/2 binary64) y)))
#s(approx (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)) (*.f64 #s(literal 1/2 binary64) y))

soundness1.3s (16.3%)

Memory

-33.0MiB live, 1 166.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1020	9707
1	3496	8629
0	8864	8236
0	51	250
0	71	250
1	334	234
2	2873	234
0	8739	228
0	11	39
0	18	39
1	68	39
2	569	39
0	8301	36
0	67	418
0	95	418
1	419	418
2	3794	406
0	8473	395
0	703	8326
1	2320	7536
0	9079	7158
0	708	12684
1	2377	10697
0	9490	10248
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×	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
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 629 to 341 computations (45.8% saved)

preprocess106.0ms (1.4%)

Memory

29.1MiB live, 192.9MiB allocated

Remove

(negabs y)

(abs x)

(abs z)

Compiler

Compiled 902 to 286 computations (68.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze45.0ms (0.6%)

sample1.0s (12.8%)

explain140.0ms (1.8%)

preprocess207.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify160.0ms (2%)

localize31.0ms (0.4%)

series53.0ms (0.7%)

simplify125.0ms (1.6%)

rewrite238.0ms (3%)

eval124.0ms (1.6%)

prune25.0ms (0.3%)

simplify201.0ms (2.6%)

localize135.0ms (1.7%)

series147.0ms (1.9%)

simplify258.0ms (3.3%)

rewrite371.0ms (4.7%)

eval285.0ms (3.6%)

prune94.0ms (1.2%)

simplify141.0ms (1.8%)

localize160.0ms (2%)

series113.0ms (1.4%)

simplify205.0ms (2.6%)

rewrite173.0ms (2.2%)

eval205.0ms (2.6%)

prune89.0ms (1.1%)

simplify195.0ms (2.5%)

localize146.0ms (1.9%)

series105.0ms (1.3%)

simplify210.0ms (2.7%)

rewrite287.0ms (3.7%)

eval252.0ms (3.2%)

prune79.0ms (1%)

regimes77.0ms (1%)

regimes63.0ms (0.8%)

regimes7.0ms (0.1%)

regimes234.0ms (3%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes25.0ms (0.3%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify36.0ms (0.5%)

soundness1.3s (16.3%)

preprocess106.0ms (1.4%)

end0.0ms (0%)

Profiling