Metrics for bug366 (missed optimization)

analyze2.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
100%	99.9%	0%	0.1%	0%	0%	0%	4

Compiler

Compiled 16 to 10 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

const: 0.0ms (0% of total)

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

backward-pass: 0.0ms (0% of total)

sample963.0ms (13.2%)

Results

722.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 409.0ms

ival-mult: 214.0ms (52.3% of total)

ival-add: 107.0ms (26.2% of total)

ival-sqrt: 78.0ms (19.1% of total)

const: 8.0ms (2% of total)

backward-pass: 3.0ms (0.7% of total)

Bogosity

preprocess41.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

612×	`sum5-define`
588×	`sum4-define`
560×	`fmsub-define`
520×	`fnmsub-define`
484×	`fnmadd-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	93
1	89	83
2	196	83
3	494	83
4	1374	83
5	2193	83
6	2415	83
7	2426	83
0	9	9
1	18	8
2	30	8
3	39	8
4	40	8
0	40	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))

Outputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))
(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))

Call 2

Inputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))
(sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z))))
(sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z))))
(sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z)))))
(neg (sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z)))))
(neg (sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z)))))
(neg (sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z))))))
(sqrt (+ (* y y) (+ (* x x) (* z z))))
(sqrt (+ (* z z) (+ (* y y) (* x x))))
(sqrt (+ (* x x) (+ (* z z) (* y y))))

Outputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))
(sqrt (sum3 (square x) (square y) (square z)))
(sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z))))
(sqrt (sum3 (square x) (square y) (square z)))
(sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z))))
(sqrt (sum3 (square x) (square y) (square z)))
(sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z)))))
(sqrt (sum3 (square x) (square y) (square z)))
(neg (sqrt (+ (* (neg x) (neg x)) (+ (* y y) (* z z)))))
(neg (sqrt (sum3 (square x) (square y) (square z))))
(neg (sqrt (+ (* x x) (+ (* (neg y) (neg y)) (* z z)))))
(neg (sqrt (sum3 (square x) (square y) (square z))))
(neg (sqrt (+ (* x x) (+ (* y y) (* (neg z) (neg z))))))
(neg (sqrt (sum3 (square x) (square y) (square z))))
(sqrt (+ (* y y) (+ (* x x) (* z z))))
(sqrt (sum3 (square x) (square y) (square z)))
(sqrt (+ (* z z) (+ (* y y) (* x x))))
(sqrt (sum3 (square x) (square y) (square z)))
(sqrt (+ (* x x) (+ (* z z) (* y y))))
(sqrt (sum3 (square x) (square y) (square z)))

Symmetry

(abs x)

(abs y)

(abs z)

(sort x y z)

explain126.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
164	-	1	(5.672963161618489e-215 9.465081932981403e-161 3.2624257132858394e-157)	`(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))`
0	-	0	-	`x`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 z z)`
0	-	0	-	`y`
0	-	0	-	`(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`z`
0	-	0	-	`(+.f64 (.f64 y y) (.f64 z z))`

Results

65.0ms

512×

valid

Compiler

Compiled 107 to 29 computations (72.9% saved)

Precisions

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

ival-mult: 13.0ms (58.9% of total)

ival-add: 5.0ms (22.7% of total)

ival-sqrt: 4.0ms (18.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.0%	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 15 to 9 computations (40% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 (.f64 y y) (.f64 z z))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))
✓	cost-diff	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))

Rules

24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
18×	`fma-lowering-fma.f32`
18×	`fma-define`
18×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	18	29
2	30	29
3	39	29
4	40	29
0	40	29

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))
(+ (* x x) (+ (* y y) (* z z)))
(* x x)
x
(+ (* y y) (* z z))
(* y y)
y
(* z z)
z

Outputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))
(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(+ (* x x) (+ (* y y) (* z z)))
(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))
(* x x)
(*.f64 x x)
x
(+ (* y y) (* z z))
(+.f64 (.f64 y y) (.f64 z z))
(* y y)
(*.f64 y y)
y
(* z z)
(*.f64 z z)
z

localize45.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 y y) (.f64 z z))
✓	accuracy	41.0%	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))

Results

35.0ms

256×

valid

Compiler

Compiled 46 to 10 computations (78.3% saved)

Precisions

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

ival-mult: 6.0ms (46.4% of total)

ival-add: 5.0ms (38.7% of total)

ival-sqrt: 2.0ms (15.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series11.0ms (0.1%)

Counts

5 → 120

Calls

Call 1

Inputs
#<alt (sqrt (+ (* x x) (+ (* y y) (* z z))))>
#<alt (+ (* x x) (+ (* y y) (* z z)))>
#<alt (* x x)>
#<alt (+ (* y y) (* z z))>
#<alt (* y y)>

Outputs
#<alt (sqrt (+ (pow y 2) (pow z 2)))>
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))>
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))))>
#<alt (+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))>
#<alt (sqrt (+ (pow x 2) (pow z 2)))>
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))>
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))))>
#<alt (+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))))>
#<alt (sqrt (+ (pow x 2) (pow y 2)))>
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))>
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))))>
#<alt (+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))>
#<alt (* -1 z)>
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (+ (pow x 2) (pow z 2))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow z 2)>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>

Calls

30 calls:

Time	Variable		Point	Expression
3.0ms	y	@	0	(sqrt (+ (* x x) (+ (* y y) (* z z))))
1.0ms	x	@	0	(sqrt (+ (* x x) (+ (* y y) (* z z))))
1.0ms	z	@	0	(sqrt (+ (* x x) (+ (* y y) (* z z))))
1.0ms	x	@	0	(+ (* x x) (+ (* y y) (* z z)))
1.0ms	x	@	inf	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

36×	`fma-define`
30×	`+-lowering-+.f64`
30×	`+-lowering-+.f32`
24×	`pow-to-exp`
24×	`exp-prod`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	24	24
2	48	24
3	72	24
4	110	24
5	123	24
6	132	24
0	132	24

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 26

Calls

Call 1

Inputs
(sqrt (+ (* x x) (+ (* y y) (* z z))))
(+ (* x x) (+ (* y y) (* z z)))
(* x x)
(+ (* y y) (* z z))
(* y y)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 z z))))))
(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))
(+.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 z z)))
(+.f64 (.f64 z z) (+.f64 (.f64 x x) (*.f64 y y)))
(+.f64 (+.f64 (.f64 y y) (.f64 z z)) (*.f64 x x))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(+.f64 (+.f64 (.f64 x x) (.f64 z z)) (*.f64 y y))
(exp.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))))
(fma.f64 z z (+.f64 (.f64 x x) (.f64 y y)))
(fma.f64 x x (+.f64 (.f64 y y) (.f64 z z)))
(fma.f64 y y (+.f64 (.f64 x x) (.f64 z z)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(+.f64 (.f64 y y) (.f64 z z))
(+.f64 (.f64 z z) (.f64 y y))
(fma.f64 z z (*.f64 y y))
(fma.f64 y y (*.f64 z z))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)))
(pow.f64 y #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(*.f64 y y)

simplify504.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

3616×	`-lowering-.f32`
3616×	`-lowering-.f64`
2312×	`+-lowering-+.f64`
2312×	`+-lowering-+.f32`
1858×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1791
1	535	1326
2	2059	1266
3	6120	1257
0	8097	1257

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(sqrt (+ (pow y 2) (pow z 2)))
(+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))))
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
x
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))
(sqrt (+ (pow x 2) (pow z 2)))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
y
(* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))))
(sqrt (+ (pow x 2) (pow y 2)))
(+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))))
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
(* -1 z)
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 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 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 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 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 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 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 x 2) (pow y 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 z 2)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(pow z 2)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow z 2)
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(pow y 2)
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(pow z 2)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(pow z 2)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)

Outputs
(sqrt (+ (pow y 2) (pow z 2)))
(hypot.f64 y z)
(+ (sqrt (+ (pow y 2) (pow z 2))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))
(+.f64 (hypot.f64 y z) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 z z)))) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))))
(+.f64 (hypot.f64 y z) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z)))))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 z z))))))))
(+ (sqrt (+ (pow y 2) (pow z 2))) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(+.f64 (hypot.f64 y z) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 z z))))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 5 binary64)))) (.f64 (*.f64 x x) #s(literal 1/16 binary64)))))))))
x
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 y y) (.f64 z z))) x)))
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))
(.f64 x (+.f64 (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 y y) (.f64 z z))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(.f64 x (+.f64 (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 y y) (.f64 z z))) x) (+.f64 (/.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))))) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (*.f64 z z))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))
(-.f64 (.f64 (/.f64 (.f64 x (+.f64 (.f64 y y) (.f64 z z))) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(.f64 (+.f64 (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 y y) (.f64 z z))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))
(.f64 (+.f64 (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (.f64 y y) (.f64 z z))) x) (+.f64 (/.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (.f64 z z))))) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 z z)) (+.f64 (.f64 y y) (*.f64 z z))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(sqrt (+ (pow x 2) (pow z 2)))
(hypot.f64 z x)
(+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))
(+.f64 (hypot.f64 z x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 z z) (.f64 x x)))) (.f64 y (*.f64 y #s(literal 1/2 binary64)))))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))))
(+.f64 (hypot.f64 z x) (.f64 y (.f64 y (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 z z) (.f64 x x)) (.f64 (+.f64 (.f64 z z) (.f64 x x)) (+.f64 (.f64 z z) (.f64 x x)))))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 z z) (.f64 x x)))))))))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(+.f64 (hypot.f64 z x) (.f64 (.f64 y y) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 z z) (.f64 x x))))) (.f64 (.f64 y y) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 z z) (.f64 x x)) (.f64 (+.f64 (.f64 z z) (.f64 x x)) (+.f64 (.f64 z z) (.f64 x x))))))) (.f64 (.f64 y y) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (.f64 z z) (*.f64 x x)) #s(literal 5 binary64)))))))))))
y
(* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 z z) (.f64 x x))) (*.f64 y y))))
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 z z) (.f64 x x))) (.f64 y y)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (.f64 z z) (.f64 x x))) (/.f64 (+.f64 (.f64 z z) (*.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))))
(* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))
(.f64 y (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 z z) (.f64 x x))) (.f64 y y)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (.f64 z z) (.f64 x x))) (/.f64 (+.f64 (.f64 z z) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))) (/.f64 (.f64 (.f64 (+.f64 (.f64 z z) (.f64 x x)) (+.f64 (.f64 z z) (.f64 x x))) (.f64 #s(literal 1/16 binary64) (+.f64 (.f64 z z) (.f64 x x)))) (pow.f64 y #s(literal 6 binary64)))))
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))
(-.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 z z) (.f64 x x)) y) (/.f64 y y)) #s(literal -1/2 binary64)) y)
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))))
(.f64 y (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 z z) (.f64 x x))) (.f64 y y)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (.f64 z z) (.f64 x x))) (/.f64 (+.f64 (.f64 z z) (*.f64 x x)) (pow.f64 y #s(literal 4 binary64))))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (pow y 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (pow y 6))) (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))))
(.f64 (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 z z) (.f64 x x))) (.f64 y y)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (+.f64 (.f64 z z) (.f64 x x))) (/.f64 (+.f64 (.f64 z z) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))) (/.f64 (.f64 (.f64 (+.f64 (.f64 z z) (.f64 x x)) (+.f64 (.f64 z z) (.f64 x x))) (.f64 #s(literal 1/16 binary64) (+.f64 (.f64 z z) (.f64 x x)))) (pow.f64 y #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) y))
(sqrt (+ (pow x 2) (pow y 2)))
(hypot.f64 y x)
(+ (sqrt (+ (pow x 2) (pow y 2))) (* 1/2 (* (pow z 2) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))
(+.f64 (hypot.f64 y x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 x x)))) (.f64 z (*.f64 z #s(literal 1/2 binary64)))))
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* -1/8 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))))
(+.f64 (hypot.f64 y x) (.f64 (.f64 z z) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x x)))))) (.f64 (.f64 z z) #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 x x))))))))
(+ (sqrt (+ (pow x 2) (pow y 2))) (* (pow z 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow y 2))))) (* (pow z 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3)))) (* 1/16 (* (pow z 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))
(+.f64 (hypot.f64 y x) (.f64 (.f64 z z) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 x x))))) (.f64 (.f64 z z) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x x))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (.f64 y y) (.f64 x x)) #s(literal 5 binary64)))) (.f64 (*.f64 z z) #s(literal 1/16 binary64))))))))
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(.f64 z (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(.f64 z (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z)))) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (*.f64 x x))) (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
(.f64 z (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z)))) (+.f64 (.f64 (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x x))) (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x x))) (/.f64 (+.f64 (.f64 y y) (.f64 x x)) (pow.f64 z #s(literal 6 binary64))))))))
(* -1 z)
(-.f64 #s(literal 0 binary64) z)
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))) (-.f64 #s(literal 0 binary64) z))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
(-.f64 #s(literal 0 binary64) (.f64 z (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z)))) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (*.f64 x x))) (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64)))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))))
(.f64 (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z)))) (+.f64 (.f64 (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x x))) (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 (+.f64 (.f64 y y) (.f64 x x)) (+.f64 (.f64 y y) (.f64 x x))) (/.f64 (+.f64 (.f64 y y) (.f64 x x)) (pow.f64 z #s(literal 6 binary64))))))) (-.f64 #s(literal 0 binary64) z))
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) x) x))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) x) x))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) x) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) x) x))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) x) x))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) x) x))))
(+ (pow x 2) (pow z 2))
(+.f64 (.f64 z z) (.f64 x x))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (+.f64 (/.f64 (/.f64 (.f64 x x) y) y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 z z) y) y)))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (+.f64 (/.f64 (/.f64 (.f64 x x) y) y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 z z) y) y)))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (+.f64 (/.f64 (/.f64 (.f64 x x) y) y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 z z) y) y)))))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (+.f64 (/.f64 (/.f64 (.f64 x x) y) y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 z z) y) y)))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (+.f64 (/.f64 (/.f64 (.f64 x x) y) y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 z z) y) y)))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (+.f64 (/.f64 (/.f64 (.f64 x x) y) y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 z z) y) y)))))
(+ (pow x 2) (pow y 2))
(+.f64 (.f64 y y) (.f64 x x))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+.f64 (.f64 y y) (+.f64 (.f64 z z) (*.f64 x x)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (.f64 z z)) (/.f64 (.f64 y y) (.f64 z z)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (.f64 z z)) (/.f64 (.f64 y y) (.f64 z z)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (.f64 z z)) (/.f64 (.f64 y y) (.f64 z z)))))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (.f64 z z)) (/.f64 (.f64 y y) (.f64 z z)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (.f64 z z)) (/.f64 (.f64 y y) (.f64 z z)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (.f64 z z)) (/.f64 (.f64 y y) (.f64 z z)))))
(pow x 2)
(*.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)
(pow x 2)
(*.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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow z 2)
(*.f64 z z)
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) y) y)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) y) y)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) y) y)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) y) y)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) y) y)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 z z) y) y)))
(pow y 2)
(*.f64 y y)
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(+ (pow y 2) (pow z 2))
(+.f64 (.f64 y y) (.f64 z z))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y y) (.f64 z z))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y y) (.f64 z z))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y y) (.f64 z z))))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y y) (.f64 z z))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y y) (.f64 z z))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 y y) (.f64 z z))))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)

eval17.0ms (0.2%)

Compiler: Compiled 2723 to 276 computations (89.9% saved)

prune11.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	3	147

Accuracy

99.7%

Counts

147 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(hypot.f64 y z)
▶	79.2%	(.f64 z (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))
▶	97.9%	z

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify375.0ms (5.2%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(hypot.f64 y z)
✓	cost-diff	0	(+.f64 (.f64 y y) (.f64 x x))
✓	cost-diff	0	(.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z))))
✓	cost-diff	256	(.f64 z (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))

Rules

4656×	`-lowering-.f32`
4656×	`-lowering-.f64`
3272×	`+-lowering-+.f64`
3272×	`+-lowering-+.f32`
3218×	`distribute-lft-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	38	60
2	80	60
3	289	58
4	1033	57
5	2423	57
6	3825	57
7	6349	57
8	7012	57
9	7142	57
10	7230	57
11	7302	57
12	7356	57
0	9714	57

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
z
(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))
z
(+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z))))
1
(* (+ (* y y) (* x x)) (/ 1/2 (* z z)))
(+ (* y y) (* x x))
(* y y)
y
(* x x)
x
(/ 1/2 (* z z))
1/2
(* z z)
(sqrt (+ (* y y) (* z z)))
y
z

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

localize127.0ms (1.7%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(hypot.f64 y z)
✓	accuracy	100.0%	(+.f64 (.f64 y y) (.f64 x x))
✓	accuracy	100.0%	(.f64 z (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))
✓	accuracy	99.3%	(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
✓	accuracy	66.6%	(.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 z z)))

Results

110.0ms

256×

valid

Compiler

Compiled 81 to 15 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 11.0ms (40.9% of total)

compiled-spec: 7.0ms (26% of total)

ival-add: 4.0ms (14.9% of total)

ival-div: 2.0ms (7.4% of total)

ival-sqrt: 2.0ms (7.4% of total)

const: 1.0ms (3.7% of total)

backward-pass: 0.0ms (0% of total)

series23.0ms (0.3%)

Counts

6 → 168

Calls

Call 1

Inputs
#<alt (* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))>
#<alt (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z))))>
#<alt (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))>
#<alt (+ (* y y) (* x x))>
#<alt (sqrt (+ (* y y) (* z z)))>
#<alt (/ 1/2 (* z z))>

Outputs
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) z))>
#<alt (/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))>
#<alt (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2)))))>
#<alt (+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))>
#<alt (+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))>
#<alt (+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* 1/2 (/ (pow x 2) z))>
#<alt (* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))>
#<alt (* 1/2 (/ (pow x 2) z))>
#<alt (* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))>
#<alt (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))>
#<alt (+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* 1/2 (/ (pow x 2) (pow z 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* 1/2 (/ (pow x 2) (pow z 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) (pow z 2))>
#<alt (/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) (pow z 2))>
#<alt (/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) (pow z 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))>
#<alt (* 1/2 (/ (pow x 2) (pow z 2)))>
#<alt (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (* 1/2 (/ (pow x 2) (pow z 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* 1/2 (/ (pow x 2) (pow z 2)))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))>
#<alt (pow x 2)>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))>
#<alt (+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))>
#<alt y>
#<alt (+ y (* 1/2 (/ (pow z 2) y)))>
#<alt (+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))>
#<alt (+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))>
#<alt (* -1 z)>
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>
#<alt (/ 1/2 (pow z 2))>

Calls

42 calls:

Time	Variable		Point	Expression
12.0ms	y	@	inf	(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))
1.0ms	z	@	0	(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))
1.0ms	y	@	0	(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))
1.0ms	x	@	0	(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))
1.0ms	x	@	inf	(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))

rewrite282.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2648×	`-lowering-.f32`
2648×	`-lowering-.f64`
1586×	`+-lowering-+.f64`
1586×	`+-lowering-+.f32`
1544×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	51	46
2	169	46
3	883	43
4	5589	43
0	8147	43

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 808

Calls

Call 1

Inputs
(* z (+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z)))))
(+ 1 (* (+ (* y y) (* x x)) (/ 1/2 (* z z))))
(* (+ (* y y) (* x x)) (/ 1/2 (* z z)))
(+ (* y y) (* x x))
(sqrt (+ (* y y) (* z z)))
(/ 1/2 (* z z))

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

simplify319.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

5852×	`-lowering-.f32`
5852×	`-lowering-.f64`
1684×	`fma-define`
1526×	`/-lowering-/.f32`
1526×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2182
1	494	1717
2	1786	1593
3	7768	1593
0	8156	1593

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(* 1/2 (/ (+ (pow x 2) (pow y 2)) z))
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
z
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2)))))
(+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))
(+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))
(+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(* 1/2 (/ (pow x 2) z))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(* 1/2 (/ (pow x 2) z))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2))))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(* 1/2 (/ (pow x 2) (pow z 2)))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))
(* 1/2 (/ (pow x 2) (pow z 2)))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (+ (/ 1 (pow x 2)) (* 1/2 (/ 1 (pow z 2))))))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) (pow z 2))
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) (pow z 2))
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) (pow z 2))
1
(+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))
(+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))
(+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))
1
(+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))
(+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))
(+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))
(* 1/2 (/ (pow x 2) (pow z 2)))
(+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))
(+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))
(+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (* 1/2 (/ (pow x 2) (* (pow y 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))
(+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))
(+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2))))
(* 1/2 (/ (pow x 2) (pow z 2)))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* 1/2 (/ (pow x 2) (pow z 2)))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* (pow x 2) (+ (* 1/2 (/ (pow y 2) (* (pow x 2) (pow z 2)))) (* 1/2 (/ 1 (pow z 2)))))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))
(* 1/2 (/ (+ (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) (+ 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) (+ 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 x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (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) (+ 1 (/ (pow y 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))))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))
y
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))
y
(+ y (* 1/2 (/ (pow z 2) y)))
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))
(* -1 z)
(* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))
(/ 1/2 (pow z 2))

Outputs
(* 1/2 (/ (+ (pow x 2) (pow y 2)) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (*.f64 y y))) z)
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
(/ (+ (* 1/2 (+ (pow x 2) (pow y 2))) (pow z 2)) z)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(.f64 z (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(.f64 z (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(.f64 z (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
z
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(-.f64 #s(literal 0 binary64) (.f64 z (+.f64 #s(literal -1 binary64) (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) #s(literal -1/2 binary64)) (*.f64 z z)))))
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(-.f64 #s(literal 0 binary64) (.f64 z (+.f64 #s(literal -1 binary64) (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) #s(literal -1/2 binary64)) (*.f64 z z)))))
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(-.f64 #s(literal 0 binary64) (.f64 z (+.f64 #s(literal -1 binary64) (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) #s(literal -1/2 binary64)) (*.f64 z z)))))
(* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2)))))
(.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 z z))))
(+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(+ (* 1/2 (/ (pow y 2) z)) (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* 1/2 (/ (pow y 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* 1/2 (/ (pow y 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))) (pow y 2))))
(+.f64 z (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (.f64 x x) z) (.f64 z z)) (/.f64 (*.f64 y y) z))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) z)))
(+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(+ (* 1/2 (/ (pow x 2) z)) (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(* 1/2 (/ (pow x 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) z)
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(* 1/2 (/ (pow x 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) z)
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(* (pow x 2) (+ (* 1/2 (/ 1 z)) (/ (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))) (pow x 2))))
(+.f64 (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))) (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) z))
(+ 1 (* 1/2 (/ (pow x 2) (pow z 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 z z)))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))
(+ 1 (+ (* 1/2 (/ (pow x 2) (pow z 2))) (* 1/2 (/ (pow y 2) (pow z 2)))))
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(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))
(.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 z #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) z))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))
(.f64 (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 z #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 z #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))
(/ 1/2 (pow z 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 z z))

eval185.0ms (2.5%)

Compiler: Compiled 29574 to 3227 computations (89.1% saved)

prune143.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	971	5	976
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	972	7	979

Accuracy

99.7%

Counts

979 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(hypot.f64 y z)
▶	40.5%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
▶	81.9%	(-.f64 z (/.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 z #s(literal -1/2 binary64))))
▶	81.9%	(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
▶	80.8%	(+.f64 z (.f64 y (.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 y y) z) z)) z)))))
▶	81.9%	(.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) z)))
✓	97.9%	z

Compiler

Compiled 182 to 117 computations (35.7% saved)

simplify174.0ms (2.4%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 y y) z) z)) z))
✓	cost-diff	128	(.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (*.f64 y y) z) z)) z)))
✓	cost-diff	128	(.f64 y (.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 y y) z) z)) z))))
✓	cost-diff	128	(+.f64 z (.f64 y (.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 y y) z) z)) z)))))
✓	cost-diff	0	(+.f64 (.f64 x x) (.f64 y y))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (*.f64 y y)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
✓	cost-diff	0	(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z))
✓	cost-diff	256	(.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) z)))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 y y))
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
✓	cost-diff	0	(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(+.f64 (.f64 y y) (.f64 x x))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 z #s(literal -1/2 binary64)))
✓	cost-diff	0	(-.f64 z (/.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 z #s(literal -1/2 binary64))))

Rules

2204×	`-lowering-.f32`
2204×	`-lowering-.f64`
1444×	`fma-define`
1228×	`fma-lowering-fma.f32`
1228×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	237
1	87	230
2	217	219
3	694	218
4	1875	214
5	3172	214
6	5673	214
0	8129	214

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize203.0ms (2.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (*.f64 y y) z) z)) z)))
✓	accuracy	99.5%	(/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 y y) z) z)) z)
✓	accuracy	98.7%	(/.f64 (/.f64 (*.f64 y y) z) z)
✓	accuracy	78.9%	(/.f64 (*.f64 y y) z)
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 y y))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (*.f64 y y)))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z))
✓	accuracy	40.9%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 y y))
✓	accuracy	100.0%	(.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) z)))
✓	accuracy	98.7%	(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) z)
✓	accuracy	78.9%	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
✓	accuracy	100.0%	(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 y y))
✓	accuracy	78.9%	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 y y) (.f64 x x))
✓	accuracy	78.9%	(/.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 z #s(literal -1/2 binary64)))

Results

130.0ms

256×

valid

Compiler

Compiled 298 to 34 computations (88.6% saved)

Precisions

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

ival-div: 17.0ms (39.4% of total)

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

ival-add: 9.0ms (20.9% of total)

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

const: 1.0ms (2.3% of total)

backward-pass: 0.0ms (0% of total)

series76.0ms (1%)

Counts

22 → 540

Calls

Call 1

Inputs
#<alt (- z (/ (+ (* y y) (* x x)) (/ z -1/2)))>
#<alt (/ (+ (* y y) (* x x)) (/ z -1/2))>
#<alt (+ (* y y) (* x x))>
#<alt (* y y)>
#<alt (+ z (/ (* 1/2 (* y y)) z))>
#<alt (/ (* 1/2 (* y y)) z)>
#<alt (* 1/2 (* y y))>
#<alt (* z (+ 1 (/ (/ (* 1/2 (* y y)) z) z)))>
#<alt (+ 1 (/ (/ (* 1/2 (* y y)) z) z))>
#<alt (/ (/ (* 1/2 (* y y)) z) z)>
#<alt (/ (+ (* 1/2 (+ (* x x) (* y y))) (* z z)) z)>
#<alt (+ (* 1/2 (+ (* x x) (* y y))) (* z z))>
#<alt (* 1/2 (+ (* x x) (* y y)))>
#<alt (+ (* x x) (* y y))>
#<alt (+ z (* y (* y (+ (/ 1/2 z) (/ (* -1/8 (/ (/ (* y y) z) z)) z)))))>
#<alt (* y (* y (+ (/ 1/2 z) (/ (* -1/8 (/ (/ (* y y) z) z)) z))))>
#<alt (* y (+ (/ 1/2 z) (/ (* -1/8 (/ (/ (* y y) z) z)) z)))>
#<alt (+ (/ 1/2 z) (/ (* -1/8 (/ (/ (* y y) z) z)) z))>
#<alt (* x x)>
#<alt (/ (* y y) z)>
#<alt (/ (/ (* y y) z) z)>
#<alt (/ (* -1/8 (/ (/ (* y y) z) z)) z)>

Outputs
#<alt (* 1/2 (/ (+ (pow x 2) (pow y 2)) z))>
#<alt (/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)>
#<alt (/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)>
#<alt (/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))>
#<alt (- z (* -1/2 (/ (pow x 2) z)))>
#<alt (- (+ z (* 1/2 (/ (pow y 2) z))) (* -1/2 (/ (pow x 2) z)))>
#<alt (- (+ z (* 1/2 (/ (pow y 2) z))) (* -1/2 (/ (pow x 2) z)))>
#<alt (- (+ z (* 1/2 (/ (pow y 2) z))) (* -1/2 (/ (pow x 2) z)))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))>
#<alt (* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))>
#<alt (* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))>
#<alt (* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))>
#<alt (* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))>
#<alt (- z (* -1/2 (/ (pow y 2) z)))>
#<alt (- (+ z (* 1/2 (/ (pow x 2) z))) (* -1/2 (/ (pow y 2) z)))>
#<alt (- (+ z (* 1/2 (/ (pow x 2) z))) (* -1/2 (/ (pow y 2) z)))>
#<alt (- (+ z (* 1/2 (/ (pow x 2) z))) (* -1/2 (/ (pow y 2) z)))>
#<alt (* 1/2 (/ (pow x 2) z))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))>
#<alt (* 1/2 (/ (pow x 2) z))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))>
#<alt (* -1/2 (/ (pow x 2) z))>
#<alt (+ (* -1/2 (/ (pow x 2) z)) (* -1/2 (/ (pow y 2) z)))>
#<alt (+ (* -1/2 (/ (pow x 2) z)) (* -1/2 (/ (pow y 2) z)))>
#<alt (+ (* -1/2 (/ (pow x 2) z)) (* -1/2 (/ (pow y 2) z)))>
#<alt (* -1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* -1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* -1/2 (/ (pow y 2) z))>
#<alt (+ (* -1/2 (/ (pow x 2) z)) (* -1/2 (/ (pow y 2) z)))>
#<alt (+ (* -1/2 (/ (pow x 2) z)) (* -1/2 (/ (pow y 2) z)))>
#<alt (+ (* -1/2 (/ (pow x 2) z)) (* -1/2 (/ (pow y 2) z)))>
#<alt (* -1/2 (/ (pow x 2) z))>
#<alt (* (pow x 2) (- (* -1/2 (/ (pow y 2) (* (pow x 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow x 2) (- (* -1/2 (/ (pow y 2) (* (pow x 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow x 2) (- (* -1/2 (/ (pow y 2) (* (pow x 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* -1/2 (/ (pow x 2) z))>
#<alt (* (pow x 2) (- (* -1/2 (/ (pow y 2) (* (pow x 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow x 2) (- (* -1/2 (/ (pow y 2) (* (pow x 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* (pow x 2) (- (* -1/2 (/ (pow y 2) (* (pow x 2) z))) (* 1/2 (/ 1 z))))>
#<alt (* -1/2 (/ (+ (pow x 2) (pow y 2)) z))>
#<alt (* -1/2 (/ (+ (pow x 2) (pow y 2)) z))>
#<alt (* -1/2 (/ (+ (pow x 2) (pow y 2)) z))>
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#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)>
#<alt (/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)>
#<alt (/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))>
#<alt (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))>
#<alt (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))>
#<alt (* 1/2 (/ y z))>
#<alt (* y (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))>
#<alt (* y (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))>
#<alt (* y (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))>
#<alt (* -1/8 (/ (pow y 3) (pow z 3)))>
#<alt (* (pow y 3) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 3) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 3) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 3) (pow z 3)))>
#<alt (* -1 (* (pow y 3) (- (* 1/8 (/ 1 (pow z 3))) (* 1/2 (/ 1 (* (pow y 2) z))))))>
#<alt (* -1 (* (pow y 3) (- (* 1/8 (/ 1 (pow z 3))) (* 1/2 (/ 1 (* (pow y 2) z))))))>
#<alt (* -1 (* (pow y 3) (- (* 1/8 (/ 1 (pow z 3))) (* 1/2 (/ 1 (* (pow y 2) z))))))>
#<alt (* -1/8 (/ (pow y 3) (pow z 3)))>
#<alt (/ (+ (* -1/8 (pow y 3)) (* 1/2 (* y (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 3)) (* 1/2 (* y (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 3)) (* 1/2 (* y (pow z 2)))) (pow z 3))>
#<alt (* 1/2 (/ y z))>
#<alt (/ (+ (* -1/8 (/ (pow y 3) (pow z 2))) (* 1/2 y)) z)>
#<alt (/ (+ (* -1/8 (/ (pow y 3) (pow z 2))) (* 1/2 y)) z)>
#<alt (/ (+ (* -1/8 (/ (pow y 3) (pow z 2))) (* 1/2 y)) z)>
#<alt (* 1/2 (/ y z))>
#<alt (* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 3) (pow z 2)))) z))>
#<alt (* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 3) (pow z 2)))) z))>
#<alt (* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 3) (pow z 2)))) z))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (pow z 2))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (pow z 2))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 2)) (* 1/2 (pow z 2))) (pow z 3))>
#<alt (/ 1/2 z)>
#<alt (/ (+ 1/2 (* -1/8 (/ (pow y 2) (pow z 2)))) z)>
#<alt (/ (+ 1/2 (* -1/8 (/ (pow y 2) (pow z 2)))) z)>
#<alt (/ (+ 1/2 (* -1/8 (/ (pow y 2) (pow z 2)))) z)>
#<alt (/ 1/2 z)>
#<alt (* -1 (/ (- (* 1/8 (/ (pow y 2) (pow z 2))) 1/2) z))>
#<alt (* -1 (/ (- (* 1/8 (/ (pow y 2) (pow z 2))) 1/2) z))>
#<alt (* -1 (/ (- (* 1/8 (/ (pow y 2) (pow z 2))) 1/2) z))>
#<alt (/ 1/2 z)>
#<alt (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))>
#<alt (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))>
#<alt (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 3)))>

Calls

135 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	(+ 1 (/ (/ (* 1/2 (* y y)) z) z))
3.0ms	z	@	0	(+ z (/ (* 1/2 (* y y)) z))
1.0ms	y	@	inf	(* y (* y (+ (/ 1/2 z) (/ (* -1/8 (/ (/ (* y y) z) z)) z))))
1.0ms	y	@	inf	(* z (+ 1 (/ (/ (* 1/2 (* y y)) z) z)))
1.0ms	y	@	inf	(+ z (* y (* y (+ (/ 1/2 z) (/ (* -1/8 (/ (/ (* y y) z) z)) z)))))

rewrite258.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3546×	`-lowering-.f32`
3546×	`-lowering-.f64`
2674×	`/-lowering-/.f32`
2674×	`/-lowering-/.f64`
1762×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	183
1	146	176
2	795	160
3	6618	160
0	8020	160

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 929

Calls

Call 1

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

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

simplify317.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

3744×	`-lowering-.f32`
3744×	`-lowering-.f64`
2550×	`fma-lowering-fma.f32`
2550×	`fma-lowering-fma.f64`
2058×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	5645
1	605	4596
2	1883	4402
3	6603	4402
0	8215	4402

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 540

Calls

Call 1

Inputs
(* 1/2 (/ (+ (pow x 2) (pow y 2)) z))
(/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)
(/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)
(/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
z
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))) 1)))
(- z (* -1/2 (/ (pow x 2) z)))
(- (+ z (* 1/2 (/ (pow y 2) z))) (* -1/2 (/ (pow x 2) z)))
(- (+ z (* 1/2 (/ (pow y 2) z))) (* -1/2 (/ (pow x 2) z)))
(- (+ z (* 1/2 (/ (pow y 2) z))) (* -1/2 (/ (pow x 2) z)))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))
(* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))
(* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))
(* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))
(* (pow y 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))) (* -1/2 (/ (pow x 2) (* (pow y 2) z)))))
(- z (* -1/2 (/ (pow y 2) z)))
(- (+ z (* 1/2 (/ (pow x 2) z))) (* -1/2 (/ (pow y 2) z)))
(- (+ z (* 1/2 (/ (pow x 2) z))) (* -1/2 (/ (pow y 2) z)))
(- (+ z (* 1/2 (/ (pow x 2) z))) (* -1/2 (/ (pow y 2) z)))
(* 1/2 (/ (pow x 2) z))
(* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))
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(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(* 1/2 (/ (pow y 2) z))
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(* 1/2 (/ y z))
(* y (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(* y (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(* y (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(* -1/8 (/ (pow y 3) (pow z 3)))
(* (pow y 3) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 3) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 3) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* -1/8 (/ (pow y 3) (pow z 3)))
(* -1 (* (pow y 3) (- (* 1/8 (/ 1 (pow z 3))) (* 1/2 (/ 1 (* (pow y 2) z))))))
(* -1 (* (pow y 3) (- (* 1/8 (/ 1 (pow z 3))) (* 1/2 (/ 1 (* (pow y 2) z))))))
(* -1 (* (pow y 3) (- (* 1/8 (/ 1 (pow z 3))) (* 1/2 (/ 1 (* (pow y 2) z))))))
(* -1/8 (/ (pow y 3) (pow z 3)))
(/ (+ (* -1/8 (pow y 3)) (* 1/2 (* y (pow z 2)))) (pow z 3))
(/ (+ (* -1/8 (pow y 3)) (* 1/2 (* y (pow z 2)))) (pow z 3))
(/ (+ (* -1/8 (pow y 3)) (* 1/2 (* y (pow z 2)))) (pow z 3))
(* 1/2 (/ y z))
(/ (+ (* -1/8 (/ (pow y 3) (pow z 2))) (* 1/2 y)) z)
(/ (+ (* -1/8 (/ (pow y 3) (pow z 2))) (* 1/2 y)) z)
(/ (+ (* -1/8 (/ (pow y 3) (pow z 2))) (* 1/2 y)) z)
(* 1/2 (/ y z))
(* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 3) (pow z 2)))) z))
(* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 3) (pow z 2)))) z))
(* -1 (/ (+ (* -1/2 y) (* 1/8 (/ (pow y 3) (pow z 2)))) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (pow z 2))) (pow z 3))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (pow z 2))) (pow z 3))
(/ (+ (* -1/8 (pow y 2)) (* 1/2 (pow z 2))) (pow z 3))
(/ 1/2 z)
(/ (+ 1/2 (* -1/8 (/ (pow y 2) (pow z 2)))) z)
(/ (+ 1/2 (* -1/8 (/ (pow y 2) (pow z 2)))) z)
(/ (+ 1/2 (* -1/8 (/ (pow y 2) (pow z 2)))) z)
(/ 1/2 z)
(* -1 (/ (- (* 1/8 (/ (pow y 2) (pow z 2))) 1/2) z))
(* -1 (/ (- (* 1/8 (/ (pow y 2) (pow z 2))) 1/2) z))
(* -1 (/ (- (* 1/8 (/ (pow y 2) (pow z 2))) 1/2) z))
(/ 1/2 z)
(+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))
(+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))
(+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))
(* -1/8 (/ (pow y 2) (pow z 3)))
(* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
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(* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 2) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(* -1/8 (/ (pow y 2) (pow z 3)))
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(* -1/8 (/ (pow y 2) (pow z 3)))
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(* -1/8 (/ (pow y 2) (pow z 3)))
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(* -1/8 (/ (pow y 2) (pow z 3)))
(* -1/8 (/ (pow y 2) (pow z 3)))
(* -1/8 (/ (pow y 2) (pow z 3)))

Outputs
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(/ (- (pow z 2) (* -1/2 (+ (pow x 2) (pow y 2)))) z)
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z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
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z
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(* 1/2 (/ (pow x 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) z)
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(.f64 (.f64 x x) (+.f64 (/.f64 z (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 y y) x) x)) (/.f64 #s(literal 1/2 binary64) z))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))
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(* (pow x 2) (- (+ (* 1/2 (/ 1 z)) (/ z (pow x 2))) (* -1/2 (/ (pow y 2) (* (pow x 2) z)))))
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(* (pow y 2) (- (* -1/2 (/ (pow x 2) (* (pow y 2) z))) (* 1/2 (/ 1 z))))
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(* -1/2 (/ (pow y 2) z))
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(pow x 2)
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(/.f64 (*.f64 y y) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(/ (pow y 2) (pow z 2))
(/.f64 (/.f64 (*.f64 y y) z) z)
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))
(* -1/8 (/ (pow y 2) (pow z 3)))
(.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (/.f64 (.f64 y y) z) z) z))

eval211.0ms (2.9%)

Compiler: Compiled 30519 to 4302 computations (85.9% saved)

prune164.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1738	7	1745
Fresh	0	0	0
Picked	5	0	5
Done	0	2	2
Total	1743	9	1752

Accuracy

99.7%

Counts

1752 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(hypot.f64 y z)
▶	40.5%	(/.f64 (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y))) z)
▶	39.7%	(/.f64 (*.f64 z z) z)
	80.6%	(+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/2 binary64)) z) (+.f64 (/.f64 (*.f64 y y) (/.f64 z (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y)))))) z))
▶	99.4%	(+.f64 (*.f64 (/.f64 y (/.f64 z y)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y)))))) z)
▶	99.1%	(+.f64 z (/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y)))
▶	99.1%	(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 y (*.f64 (/.f64 z y) z)))) z)
	97.8%	(.f64 z (+.f64 #s(literal 1 binary64) (.f64 y (.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) z) z)))))
✓	97.9%	z

Compiler

Compiled 246 to 153 computations (37.8% saved)

simplify202.0ms (2.8%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 y (*.f64 (/.f64 z y) z))
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (/.f64 y (.f64 (/.f64 z y) z)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 y (.f64 (/.f64 z y) z))))
✓	cost-diff	256	(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 y (*.f64 (/.f64 z y) z)))) z)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 y y))
✓	cost-diff	0	(*.f64 z z)
✓	cost-diff	0	(+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y)))
✓	cost-diff	128	(/.f64 (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y))) z)
✓	cost-diff	0	(/.f64 z y)
✓	cost-diff	0	(*.f64 y #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y))
✓	cost-diff	0	(+.f64 z (/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y)))
✓	cost-diff	0	(*.f64 z z)
✓	cost-diff	256	(/.f64 (*.f64 z z) z)
✓	cost-diff	0	(/.f64 z y)
✓	cost-diff	0	(/.f64 y (/.f64 z y))
✓	cost-diff	0	(*.f64 (/.f64 y (/.f64 z y)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y))))))
✓	cost-diff	0	(+.f64 (*.f64 (/.f64 y (/.f64 z y)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y)))))) z)

Rules

3396×	`-lowering-.f32`
3396×	`-lowering-.f64`
1784×	`/-lowering-/.f32`
1784×	`/-lowering-/.f64`
1718×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	174
1	73	151
2	194	141
3	608	138
4	2212	138
5	4943	138
6	7788	138
0	8600	138

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize180.0ms (2.5%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (/.f64 y (.f64 (/.f64 z y) z)))
✓	accuracy	100.0%	(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 y (*.f64 (/.f64 z y) z)))) z)
✓	accuracy	99.8%	(*.f64 (/.f64 z y) z)
✓	accuracy	86.0%	(/.f64 y (*.f64 (/.f64 z y) z))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 y y))
✓	accuracy	100.0%	(+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y)))
✓	accuracy	40.9%	(/.f64 (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y))) z)
✓	accuracy	100.0%	(/.f64 z y)
✓	accuracy	100.0%	(+.f64 z (/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y)))
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	40.9%	(/.f64 (*.f64 z z) z)
✓	accuracy	100.0%	(*.f64 (/.f64 y (/.f64 z y)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y))))))
✓	accuracy	99.7%	(/.f64 y (/.f64 z y))
✓	accuracy	99.2%	(/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y))))
✓	accuracy	98.7%	(/.f64 z (/.f64 y (/.f64 z y)))

Results

131.0ms

256×

valid

Compiler

Compiled 199 to 29 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-div: 15.0ms (42.7% of total)

ival-mult: 13.0ms (37% of total)

ival-add: 5.0ms (14.2% of total)

ival-sub: 1.0ms (2.8% of total)

const: 1.0ms (2.8% of total)

backward-pass: 0.0ms (0% of total)

series26.0ms (0.4%)

Counts

20 → 420

Calls

Call 1

Inputs
#<alt (+ (* (/ y (/ z y)) (+ 1/2 (/ -1/8 (/ z (/ y (/ z y)))))) z)>
#<alt (* (/ y (/ z y)) (+ 1/2 (/ -1/8 (/ z (/ y (/ z y))))))>
#<alt (/ y (/ z y))>
#<alt (/ z y)>
#<alt (/ (* z z) z)>
#<alt (* z z)>
#<alt (+ z (/ (* y 1/2) (/ z y)))>
#<alt (/ (* y 1/2) (/ z y))>
#<alt (* y 1/2)>
#<alt (/ (+ (* z z) (* 1/2 (* y y))) z)>
#<alt (+ (* z z) (* 1/2 (* y y)))>
#<alt (* 1/2 (* y y))>
#<alt (* (- 1 (* -1/2 (/ y (* (/ z y) z)))) z)>
#<alt (- 1 (* -1/2 (/ y (* (/ z y) z))))>
#<alt (* -1/2 (/ y (* (/ z y) z)))>
#<alt (/ y (* (/ z y) z))>
#<alt (/ z (/ y (/ z y)))>
#<alt (/ -1/8 (/ z (/ y (/ z y))))>
#<alt (* y y)>
#<alt (* (/ z y) z)>

Outputs
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))>
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* (pow z 2) (+ (* 1/2 (pow y 2)) (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* (pow z 2) (+ (* 1/2 (pow y 2)) (pow z 2)))) (pow z 3))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/8 (/ (pow y 4) (pow z 4)))) 1)))>
#<alt (* -1 (* z (- (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/8 (/ (pow y 4) (pow z 4)))) 1)))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))>
#<alt (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))>
#<alt (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))>
#<alt (* -1/8 (/ (pow y 4) (pow z 3)))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)>
#<alt (/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)>
#<alt (/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))>
#<alt (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))>
#<alt (* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ (pow y 2) z)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt (/ z y)>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt z>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (pow y 2))>
#<alt (+ (* 1/2 (pow y 2)) (pow z 2))>
#<alt (+ (* 1/2 (pow y 2)) (pow z 2))>
#<alt (+ (* 1/2 (pow y 2)) (pow z 2))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (pow z 2)>
#<alt (+ (* 1/2 (pow y 2)) (pow z 2))>
#<alt (+ (* 1/2 (pow y 2)) (pow z 2))>
#<alt (+ (* 1/2 (pow y 2)) (pow z 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))>
#<alt (* 1/2 (pow y 2))>
#<alt (* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt (* 1/2 (pow y 2))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))>
#<alt (* 1/2 (/ (pow y 2) (pow z 2)))>
#<alt (/ (- (pow z 2) (* -1/2 (pow y 2))) (pow z 2))>
#<alt (/ (- (pow z 2) (* -1/2 (pow y 2))) (pow z 2))>
#<alt (/ (- (pow z 2) (* -1/2 (pow y 2))) (pow z 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/2 (/ (pow y 2) (pow z 2)))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow y 2) (pow z 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (/ (pow z 2) (pow y 2))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (* -1/8 (/ (pow y 2) (pow z 2)))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>
#<alt (/ (pow z 2) y)>

Calls

105 calls:

Time	Variable		Point	Expression
5.0ms	z	@	0	(/ z y)
2.0ms	z	@	inf	(/ z (/ y (/ z y)))
2.0ms	y	@	0	(+ (* (/ y (/ z y)) (+ 1/2 (/ -1/8 (/ z (/ y (/ z y)))))) z)
1.0ms	z	@	inf	(+ (* (/ y (/ z y)) (+ 1/2 (/ -1/8 (/ z (/ y (/ z y)))))) z)
0.0ms	z	@	inf	(/ z y)

rewrite380.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4358×	`-lowering-.f32`
4358×	`-lowering-.f64`
3144×	`/-lowering-/.f32`
3144×	`/-lowering-/.f64`
1200×	`frac-add`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	146
1	124	119
2	758	110
3	7967	110
0	8081	110

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1083

Calls

Call 1

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

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

simplify291.0ms (4%)

Algorithm

1×	egg-herbie

Rules

4140×	`-lowering-.f32`
4140×	`-lowering-.f64`
1246×	`/-lowering-/.f32`
1246×	`/-lowering-/.f64`
1082×	`distribute-lft-neg-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	3109
1	268	2519
2	763	2394
3	2796	2381
4	5772	2371
0	8521	2371

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/ (+ (* -1/8 (pow y 4)) (* (pow z 2) (+ (* 1/2 (pow y 2)) (pow z 2)))) (pow z 3))
(/ (+ (* -1/8 (pow y 4)) (* (pow z 2) (+ (* 1/2 (pow y 2)) (pow z 2)))) (pow z 3))
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/8 (/ (pow y 4) (pow z 4)))) 1)))
(* -1 (* z (- (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/8 (/ (pow y 4) (pow z 4)))) 1)))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(* 1/2 (/ (pow y 2) z))
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(* 1/2 (/ (pow y 2) z))
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ (pow y 2) z)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
z
z
z
z
z
z
z
z
z
z
z
z
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(* 1/2 (/ (pow y 2) z))
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 (/ (pow y 2) z))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 (/ (pow y 2) z))
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (pow y 2))
(+ (* 1/2 (pow y 2)) (pow z 2))
(+ (* 1/2 (pow y 2)) (pow z 2))
(+ (* 1/2 (pow y 2)) (pow z 2))
(pow z 2)
(* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(pow z 2)
(* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(pow z 2)
(+ (* 1/2 (pow y 2)) (pow z 2))
(+ (* 1/2 (pow y 2)) (pow z 2))
(+ (* 1/2 (pow y 2)) (pow z 2))
(* 1/2 (pow y 2))
(* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))
(* 1/2 (pow y 2))
(* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1/2 (/ (pow z 2) (pow y 2))))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
(* 1/2 (pow y 2))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
1
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))
(* (pow y 2) (+ (/ 1 (pow y 2)) (* 1/2 (/ 1 (pow z 2)))))
(* 1/2 (/ (pow y 2) (pow z 2)))
(/ (- (pow z 2) (* -1/2 (pow y 2))) (pow z 2))
(/ (- (pow z 2) (* -1/2 (pow y 2))) (pow z 2))
(/ (- (pow z 2) (* -1/2 (pow y 2))) (pow z 2))
1
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
1
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(* -1/2 (/ (pow y 2) (pow z 2)))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow y 2) (pow z 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(/ (pow z 2) (pow y 2))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)
(/ (pow z 2) y)

Outputs
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(+.f64 z (.f64 (/.f64 (.f64 y y) z) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z)))))
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(+.f64 z (.f64 (/.f64 (.f64 y y) z) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (*.f64 z z)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))) (/.f64 z (pow.f64 y #s(literal 4 binary64)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))) (/.f64 z (pow.f64 y #s(literal 4 binary64)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (*.f64 z z)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))) (/.f64 z (pow.f64 y #s(literal 4 binary64)))))
(* (pow y 4) (- (+ (/ 1/2 (* (pow y 2) z)) (/ z (pow y 4))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))) (/.f64 z (pow.f64 y #s(literal 4 binary64)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (*.f64 z z)))
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(/ (+ (* -1/8 (pow y 4)) (* (pow z 2) (+ (* 1/2 (pow y 2)) (pow z 2)))) (pow z 3))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (.f64 z (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (.f64 y y)))))) (.f64 z (.f64 z z)))
(/ (+ (* -1/8 (pow y 4)) (* (pow z 2) (+ (* 1/2 (pow y 2)) (pow z 2)))) (pow z 3))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (.f64 z (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (.f64 y y)))))) (.f64 z (.f64 z z)))
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (.f64 z (*.f64 z z)))))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (.f64 z (*.f64 z z)))))))
z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
(* -1 (* z (- (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/8 (/ (pow y 4) (pow z 4)))) 1)))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (.f64 z (*.f64 z z)))))))
(* -1 (* z (- (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/8 (/ (pow y 4) (pow z 4)))) 1)))
(+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z) (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (.f64 z (*.f64 z z)))))))
(* 1/2 (/ (pow y 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(.f64 (/.f64 (.f64 y y) z) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(.f64 (/.f64 (.f64 y y) z) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z))))
(.f64 (/.f64 (.f64 y y) z) (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (*.f64 z z)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (*.f64 z z)))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* (pow y 4) (- (* 1/2 (/ 1 (* (pow y 2) z))) (* 1/8 (/ 1 (pow z 3)))))
(.f64 (pow.f64 y #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z (.f64 y y))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))))
(* -1/8 (/ (pow y 4) (pow z 3)))
(/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z (*.f64 z z)))
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(/ (+ (* -1/8 (pow y 4)) (* 1/2 (* (pow y 2) (pow z 2)))) (pow z 3))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(* 1/2 (/ (pow y 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(/ (+ (* -1/8 (/ (pow y 4) (pow z 2))) (* 1/2 (pow y 2))) z)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(* 1/2 (/ (pow y 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(* -1 (/ (+ (* -1/2 (pow y 2)) (* 1/8 (/ (pow y 4) (pow z 2)))) z))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 z z))) z)
(/ (pow y 2) z)
(/.f64 (*.f64 y y) z)
(/ (pow y 2) z)
(/.f64 (*.f64 y y) z)
(/ (pow y 2) z)
(/.f64 (*.f64 y y) z)
(/ (pow y 2) z)
(/.f64 (*.f64 y y) z)
(/ (pow y 2) z)
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(/ (pow y 2) z)
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(/ (pow y 2) z)
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(/ (pow y 2) z)
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(/ z y)
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(/ z y)
(/.f64 z y)
z
z
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z
z
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z
z
z
z
z
(pow z 2)
(*.f64 z z)
(pow z 2)
(*.f64 z z)
(pow z 2)
(*.f64 z z)
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(*.f64 z z)
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(* 1/2 (/ (pow y 2) z))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
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z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
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(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
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(* -1/2 (/ (pow y 2) (pow z 2)))
(/.f64 (/.f64 (.f64 (.f64 y y) #s(literal -1/2 binary64)) z) z)
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow y 2) (pow z 2))
(.f64 y (/.f64 y (.f64 z z)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(/ (pow z 2) (pow y 2))
(.f64 z (/.f64 z (.f64 y y)))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(* -1/8 (/ (pow y 2) (pow z 2)))
(/.f64 (.f64 (.f64 y y) #s(literal -1/8 binary64)) (*.f64 z z))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)

eval261.0ms (3.6%)

Compiler: Compiled 33474 to 4743 computations (85.8% saved)

prune269.0ms (3.7%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	1762	2	1764
Fresh	1	1	2
Picked	0	5	5
Done	0	2	2
Total	1763	10	1773

Accuracy

99.7%

Counts

1773 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(hypot.f64 y z)
✓	40.5%	(/.f64 (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y))) z)
✓	39.7%	(/.f64 (*.f64 z z) z)
	99.4%	(+.f64 (/.f64 (/.f64 y (/.f64 z y)) (/.f64 (/.f64 z (/.f64 y (/.f64 z y))) #s(literal -1/8 binary64))) (+.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 z y) y))))
✓	99.4%	(+.f64 (*.f64 (/.f64 y (/.f64 z y)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y)))))) z)
✓	99.1%	(+.f64 z (/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y)))
✓	99.1%	(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 y (*.f64 (/.f64 z y) z)))) z)
	97.8%	(.f64 z (+.f64 #s(literal 1 binary64) (.f64 y (.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) z) z)))))
	89.6%	(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 z y) y))))) #s(literal -1 binary64)))
✓	97.9%	z

Compiler

Compiled 390 to 174 computations (55.4% saved)

regimes57.0ms (0.8%)

Counts

18 → 1

Calls

Call 1

Inputs
z
(/.f64 (*.f64 z z) z)
(+.f64 z (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) z))
(+.f64 z (/.f64 (*.f64 y #s(literal 1/2 binary64)) (/.f64 z y)))
(/.f64 (+.f64 (.f64 z z) (.f64 #s(literal 1/2 binary64) (*.f64 y y))) z)
(.f64 z (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) z) z)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 y (*.f64 (/.f64 z y) z)))) z)
(-.f64 z (/.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 z #s(literal -1/2 binary64))))
(.f64 z (+.f64 #s(literal 1 binary64) (.f64 y (.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) z) z)))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) (.f64 y y))) (.f64 z z)) z)
(.f64 z (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 z z)))))
(+.f64 (*.f64 (/.f64 y (/.f64 z y)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y)))))) z)
(+.f64 z (.f64 y (.f64 y (+.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 y y) z) z)) z)))))
(+.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/2 binary64)) z) (+.f64 (/.f64 (*.f64 y y) (/.f64 z (/.f64 #s(literal -1/8 binary64) (/.f64 z (/.f64 y (/.f64 z y)))))) z))
(+.f64 (/.f64 (/.f64 y (/.f64 z y)) (/.f64 (/.f64 z (/.f64 y (/.f64 z y))) #s(literal -1/8 binary64))) (+.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 z y) y))))
(hypot.f64 y z)
(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 z y) y))))) #s(literal -1 binary64)))

Outputs
(hypot.f64 y z)

Calls

9 calls:

9.0ms	x
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))
7.0ms	(+.f64 (.f64 y y) (.f64 z z))
6.0ms	y
6.0ms	z

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`y`
99.7%	1	`z`
99.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z))))`
99.7%	1	`(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 z z)))`
99.7%	1	`(*.f64 x x)`
99.7%	1	`(+.f64 (.f64 y y) (.f64 z z))`
99.7%	1	`(*.f64 y y)`
99.7%	1	`(*.f64 z z)`

Compiler

Compiled 69 to 44 computations (36.2% saved)

regimes27.0ms (0.4%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

5 calls:

8.0ms	x
5.0ms	y
5.0ms	z
4.0ms	(*.f64 y y)
4.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`y`
99.4%	1	`z`
99.4%	1	`(*.f64 x x)`
99.4%	1	`(*.f64 y y)`

Compiler

Compiled 24 to 17 computations (29.2% saved)

regimes19.0ms (0.3%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`y`
99.1%	1	`z`
99.1%	1	`(*.f64 x x)`
99.1%	1	`(*.f64 y y)`

Compiler

Compiled 24 to 17 computations (29.2% saved)

regimes13.0ms (0.2%)

Accuracy

Total -37.3b remaining (-2835.9%)

Threshold costs -37.3b (-2835.9%)

Counts

3 → 1

Calls

Call 1

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

Outputs
z

Calls

4 calls:

7.0ms	(*.f64 y y)
2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`y`
97.9%	1	`z`
97.9%	1	`(*.f64 y y)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	20	32

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness850.0ms (11.7%)

Rules

5852×	`-lowering-.f32`
5852×	`-lowering-.f64`
3616×	`-lowering-.f32`
3616×	`-lowering-.f64`
3546×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2182
1	494	1717
2	1786	1593
3	7768	1593
0	8156	1593
0	33	183
1	146	176
2	795	160
3	6618	160
0	8020	160
0	183	1791
1	535	1326
2	2059	1266
3	6120	1257
0	8097	1257

Stop Event

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

Compiler

Compiled 87 to 53 computations (39.1% saved)

preprocess70.0ms (1%)

Compiler: Compiled 212 to 124 computations (41.5% saved)

analyze2.0ms (0%)

sample963.0ms (13.2%)

preprocess41.0ms (0.6%)

explain126.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.2%)

localize45.0ms (0.6%)

series11.0ms (0.1%)

rewrite47.0ms (0.6%)

simplify504.0ms (6.9%)

eval17.0ms (0.2%)

prune11.0ms (0.2%)

simplify375.0ms (5.2%)

localize127.0ms (1.7%)

series23.0ms (0.3%)

rewrite282.0ms (3.9%)

simplify319.0ms (4.4%)

eval185.0ms (2.5%)

prune143.0ms (2%)

simplify174.0ms (2.4%)

localize203.0ms (2.8%)

series76.0ms (1%)

rewrite258.0ms (3.5%)

simplify317.0ms (4.3%)

eval211.0ms (2.9%)

prune164.0ms (2.3%)

simplify202.0ms (2.8%)

localize180.0ms (2.5%)

series26.0ms (0.4%)

rewrite380.0ms (5.2%)

simplify291.0ms (4%)

eval261.0ms (3.6%)

prune269.0ms (3.7%)

regimes57.0ms (0.8%)

regimes27.0ms (0.4%)

regimes19.0ms (0.3%)

regimes13.0ms (0.2%)

simplify7.0ms (0.1%)

soundness850.0ms (11.7%)

preprocess70.0ms (1%)

end0.0ms (0%)

Profiling