Metrics for Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

analyze66.0ms (0.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
50%	49.9%	49.9%	0.1%	0%	0%	0%	4
50%	49.9%	49.9%	0.1%	0%	0%	0%	5
50%	49.9%	49.9%	0.1%	0%	0%	0%	6
66.7%	49.9%	25%	0.1%	0%	25%	0%	7
66.7%	49.9%	25%	0.1%	0%	25%	0%	8
66.7%	49.9%	25%	0.1%	0%	25%	0%	9
80%	49.9%	12.5%	0.1%	0%	37.4%	0%	10
80%	49.9%	12.5%	0.1%	0%	37.4%	0%	11
80%	49.9%	12.5%	0.1%	0%	37.4%	0%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

Precisions

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

ival-mult: 7.0ms (33.9% of total)

ival-div: 5.0ms (24.2% of total)

ival-sqrt: 4.0ms (19.4% of total)

ival-add: 3.0ms (14.5% of total)

const: 1.0ms (4.8% of total)

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

sample1.5s (19.6%)

Results

968.0ms	8256×	0	valid
165.0ms	2162×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 592.0ms

ival-div: 202.0ms (34.1% of total)

ival-mult: 159.0ms (26.9% of total)

ival-add: 125.0ms (21.1% of total)

ival-sqrt: 84.0ms (14.2% of total)

const: 18.0ms (3% of total)

backward-pass: 4.0ms (0.7% of total)

Bogosity

preprocess72.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

2584×	`fnmadd-define`
1704×	`sum3-define`
1646×	`fmsub-define`
1538×	`fnmsub-define`
1244×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	86
1	118	72
2	368	72
3	818	72
4	1868	72
5	4169	72
6	6307	72
0	11	8
1	22	7
2	37	7
3	48	7
0	48	7

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

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

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

Call 2

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

Outputs
(* (/ 1 2) (+ x (* y (sqrt z))))
(* 1/2 (fma y (sqrt z) x))
(* (/ 1 2) (+ (neg x) (* y (sqrt z))))
(* 1/2 (fmsub y (sqrt z) x))
(* (/ 1 2) (+ x (* (neg y) (sqrt z))))
(* 1/2 (fnmadd y (sqrt z) x))
(* (/ 1 2) (+ x (* y (sqrt (neg z)))))
(* 1/2 (fma y (sqrt (neg z)) x))
(neg (* (/ 1 2) (+ (neg x) (* y (sqrt z)))))
(* 1/2 (fnmadd y (sqrt z) x))
(neg (* (/ 1 2) (+ x (* (neg y) (sqrt z)))))
(* 1/2 (fmsub y (sqrt z) x))
(neg (* (/ 1 2) (+ x (* y (sqrt (neg z))))))
(* 1/2 (fnmsub y (sqrt (neg z)) x))
(* (/ 1 2) (+ y (* x (sqrt z))))
(* 1/2 (fma x (sqrt z) y))
(* (/ 1 2) (+ z (* y (sqrt x))))
(* 1/2 (fma y (sqrt x) z))
(* (/ 1 2) (+ x (* z (sqrt y))))
(* 1/2 (fma z (sqrt y) x))

explain131.0ms (1.7%)

FPErrors

Click to see full error table

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

Results

94.0ms

512×

valid

Compiler

Compiled 81 to 32 computations (60.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 24.0ms (66.3% of total)

ival-div: 4.0ms (11.1% of total)

ival-sqrt: 4.0ms (11.1% of total)

ival-add: 3.0ms (8.3% of total)

const: 1.0ms (2.8% of total)

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

eval0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
20×	`fma-lowering-fma.f32`
20×	`fma-define`
20×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	17	22
2	34	22
3	44	22
0	44	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize74.0ms (1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	100.0%	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	accuracy	99.6%	(*.f64 y (sqrt.f64 z))

Results

42.0ms

256×

valid

Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions

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

ival-mult: 4.0ms (48.1% of total)

ival-sqrt: 3.0ms (36.1% of total)

ival-add: 1.0ms (12% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Counts

4 → 108

Calls

Call 1

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

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

Calls

27 calls:

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

rewrite285.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2916×	`-lowering-.f32`
2916×	`-lowering-.f64`
2390×	`/-lowering-/.f32`
2390×	`/-lowering-/.f64`
1382×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	31	18
2	243	18
3	2445	18
0	8453	18

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 213

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))
(+.f64 (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x (.f64 y (sqrt.f64 z))))) (/.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)) (.f64 #s(literal 1/2 binary64) x))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)) (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)))
(fma.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)))
(fma.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) y (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (-.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (+.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x (.f64 y (sqrt.f64 z)))) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 y y) z) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (.f64 (*.f64 y y) z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (.f64 (.f64 y y) z))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (*.f64 x (sqrt.f64 z))))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) y)))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 (*.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x (.f64 y (sqrt.f64 z)))) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 y y) z) #s(literal 1/4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (.f64 (*.f64 y y) z))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))))))
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(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 y y) z) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (sqrt.f64 z) (*.f64 #s(literal 1/2 binary64) y)))))))
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(.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))) (/.f64 (+.f64 x (.f64 y (sqrt.f64 z))) (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))))))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) z)) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (.f64 y y) z) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (*.f64 x (sqrt.f64 z))))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 (.f64 y y) z))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y (sqrt.f64 z))))))
(.f64 #s(literal 1 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (*.f64 y y) z) #s(literal 3/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (*.f64 y y) z) #s(literal 3/2 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y (sqrt.f64 z)))) (-.f64 (.f64 x x) (.f64 (*.f64 y y) z)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 y (sqrt.f64 z)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 (*.f64 y y) z))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 (.f64 y y) z) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) z)) (-.f64 (.f64 x x) (.f64 (.f64 y y) z))) (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (.f64 y y) z) #s(literal 3/2 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (pow.f64 (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))) #s(literal 3 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))) (-.f64 (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (.f64 y y) z) #s(literal 3/2 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (pow.f64 (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (*.f64 x (sqrt.f64 z))))))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) z)) (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (.f64 y y) z) #s(literal 3/2 binary64)))) (+.f64 (.f64 x x) (.f64 y (+.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 y y) z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) z) (+.f64 (.f64 x x) (.f64 (.f64 y y) z))))))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 y y) z)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (*.f64 y y) z))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (pow.f64 (.f64 (.f64 y y) z) #s(literal 9/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 y y) z)))) (pow.f64 (.f64 x (.f64 x (.f64 (.f64 y y) z))) #s(literal 3/2 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 (.f64 y y) z) (.f64 (.f64 y y) z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 (.f64 y y) z) #s(literal 3/2 binary64)))))
(exp.f64 (log.f64 (*.f64 y (sqrt.f64 z))))
(exp.f64 (.f64 (log.f64 (.f64 y (sqrt.f64 z))) #s(literal 1 binary64)))
(pow.f64 (*.f64 y (sqrt.f64 z)) #s(literal 1 binary64))
(*.f64 y (sqrt.f64 z))
(*.f64 (sqrt.f64 z) y)
(*.f64 (sqrt.f64 z) (pow.f64 y #s(literal 1 binary64)))
(*.f64 (sqrt.f64 z) (exp.f64 (log.f64 y)))
(.f64 (pow.f64 z #s(literal 1/4 binary64)) (.f64 (pow.f64 z #s(literal 1/4 binary64)) y))
(.f64 (.f64 y (pow.f64 z #s(literal 1/4 binary64))) (pow.f64 z #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (pow.f64 z #s(literal 1/4 binary64)) y) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) (sqrt.f64 z))
(.f64 (pow.f64 (.f64 y (pow.f64 z #s(literal 1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (sqrt.f64 z))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
(exp.f64 (*.f64 (log.f64 (pow.f64 z #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 z z)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 z) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 z) #s(literal 1/4 binary64)) (.f64 (log.f64 z) #s(literal 1/4 binary64))))
(fabs.f64 (sqrt.f64 z))
(sqrt.f64 z)
(pow.f64 (sqrt.f64 z) #s(literal 1 binary64))
(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 z #s(literal 1/2 binary64))
(pow.f64 (*.f64 z z) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
(*.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 z #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 z #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 z #s(literal 1/4 binary64))))

simplify170.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

3400×	`-lowering-.f32`
3400×	`-lowering-.f64`
1344×	`/-lowering-/.f32`
1344×	`/-lowering-/.f64`
1232×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	622
1	264	578
2	891	578
3	2789	554
4	7950	554
0	8118	554

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

eval37.0ms (0.5%)

Compiler: Compiled 7917 to 763 computations (90.4% saved)

prune46.0ms (0.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	310	11	321
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	310	12	322

Accuracy

100.0%

Counts

322 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.6%	(/.f64 (.f64 (-.f64 (.f64 (.f64 y y) z) (.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
▶	99.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
	48.5%	(.f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) z)) (/.f64 #s(literal 1/2 binary64) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	48.8%	(.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
	25.4%	(.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (.f64 x x) (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (.f64 (.f64 y y) z))) (.f64 (-.f64 x (.f64 y (sqrt.f64 z))) #s(literal 1 binary64))) (.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (.f64 (*.f64 y y) z)))))
	99.7%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (pow.f64 z #s(literal 1/4 binary64)) (*.f64 (pow.f64 z #s(literal 1/4 binary64)) y))))
▶	93.3%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
▶	99.7%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
	70.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (pow.f64 (*.f64 z z) #s(literal 1/4 binary64)))))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
	51.7%	(.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z))))) (.f64 (+.f64 x (.f64 y (sqrt.f64 z))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 (.f64 y z) (.f64 x (sqrt.f64 z)))))))))
▶	53.3%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 455 to 260 computations (42.9% saved)

simplify129.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 y y) z)
✓	cost-diff	0	(-.f64 (.f64 (.f64 y y) z) (*.f64 x x))
✓	cost-diff	0	(.f64 (-.f64 (.f64 (.f64 y y) z) (.f64 x x)) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (.f64 (-.f64 (.f64 (.f64 y y) z) (.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z))
✓	cost-diff	0	(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
✓	cost-diff	0	(*.f64 y (sqrt.f64 z))
✓	cost-diff	0	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
✓	cost-diff	128	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	6528	(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	6528	(*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	cost-diff	6528	(+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	cost-diff	6528	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))

Rules

1952×	`-lowering-.f32`
1952×	`-lowering-.f64`
1900×	`sum3-define`
1208×	`sum4-define`
1126×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	187
1	77	160
2	164	150
3	324	150
4	547	150
5	899	150
6	1981	150
7	5528	150
0	8100	150

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize201.0ms (2.6%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 y (sqrt.f64 z))
✓	accuracy	95.5%	(-.f64 (.f64 (.f64 y y) z) (*.f64 x x))
✓	accuracy	91.2%	(.f64 (.f64 y y) z)
✓	accuracy	55.3%	(/.f64 (.f64 (-.f64 (.f64 (.f64 y y) z) (.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
✓	accuracy	100.0%	(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
✓	accuracy	87.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z))
✓	accuracy	100.0%	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
✓	accuracy	99.6%	(*.f64 y (sqrt.f64 z))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
✓	accuracy	100.0%	(+.f64 x (*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	accuracy	99.6%	(*.f64 y (pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	accuracy	99.2%	(pow.f64 (pow.f64 z #s(literal 1/4 binary64)) #s(literal 2 binary64))

Results

155.0ms

256×

valid

Compiler

Compiled 195 to 32 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 18.0ms (35.7% of total)

ival-pow: 15.0ms (29.7% of total)

ival-div: 7.0ms (13.9% of total)

ival-add: 4.0ms (7.9% of total)

ival-sqrt: 4.0ms (7.9% of total)

ival-sub: 2.0ms (4% of total)

const: 1.0ms (2% of total)

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

series34.0ms (0.4%)

Counts

17 → 492

Calls

Call 1

Inputs
#<alt (* 1/2 (+ x (* y (pow (pow z 1/4) 2))))>
#<alt (+ x (* y (pow (pow z 1/4) 2)))>
#<alt (* y (pow (pow z 1/4) 2))>
#<alt (pow (pow z 1/4) 2)>
#<alt (* 1/2 x)>
#<alt (/ 1/2 (/ 1 (+ x (* y (sqrt z)))))>
#<alt (/ 1 (+ x (* y (sqrt z))))>
#<alt (+ x (* y (sqrt z)))>
#<alt (* y (sqrt z))>
#<alt (* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))>
#<alt (+ x (* (sqrt (/ 1 z)) (* y z)))>
#<alt (* (sqrt (/ 1 z)) (* y z))>
#<alt (sqrt (/ 1 z))>
#<alt (/ (* (- (* (* y y) z) (* x x)) 1/2) (- (* y (sqrt z)) x))>
#<alt (* (- (* (* y y) z) (* x x)) 1/2)>
#<alt (- (* (* y y) z) (* x x))>
#<alt (* (* y y) z)>

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

Calls

123 calls:

Time	Variable		Point	Expression
4.0ms	z	@	-inf	(* 1/2 (+ x (* (sqrt (/ 1 z)) (* y z))))
3.0ms	x	@	0	(/ (* (- (* (* y y) z) (* x x)) 1/2) (- (* y (sqrt z)) x))
2.0ms	y	@	-inf	(* (* y y) z)
1.0ms	y	@	0	(/ 1 (+ x (* y (sqrt z))))
1.0ms	z	@	-inf	(/ (* (- (* (* y y) z) (* x x)) 1/2) (- (* y (sqrt z)) x))

rewrite483.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3826×	`-lowering-.f32`
3826×	`-lowering-.f64`
3086×	`/-lowering-/.f32`
3086×	`/-lowering-/.f64`
1588×	`frac-times`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	95
1	186	86
2	1190	86
0	9077	86

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1450

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))) (*.f64 #s(literal 1/2 binary64) x))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (sqrt.f64 z)) x))) (.f64 #s(literal -1/2 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))))
(fma.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))))
(fma.f64 y (.f64 (sqrt.f64 z) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (sqrt.f64 z) (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 y (sqrt.f64 z)) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (pow.f64 z #s(literal -1/2 binary64)) (.f64 (.f64 y z) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 y z) (.f64 (pow.f64 z #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 y (pow.f64 z #s(literal -1/2 binary64))) (.f64 z #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 z #s(literal -1/2 binary64))) (.f64 y z) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y (pow.f64 z #s(literal -1/2 binary64)))) z (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 z) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)) y (.f64 #s(literal 1/2 binary64) x))
(neg.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z)))))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(neg.f64 (/.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) #s(literal -1/2 binary64)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
(/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
(/.f64 #s(literal 1/2 binary64) (.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal 1/2 binary64) (.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (-.f64 (*.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (-.f64 (*.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64)) (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (-.f64 (*.f64 y (sqrt.f64 z)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))) #s(literal 1 binary64))))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 #s(literal -1/2 binary64) (.f64 (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x))))
(/.f64 #s(literal -1/2 binary64) (.f64 (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x))))
(/.f64 #s(literal -1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (sqrt.f64 z)) x)) (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal -1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (sqrt.f64 z)) x)) (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (*.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 y (sqrt.f64 z)) x)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y (.f64 y z)) (-.f64 #s(literal 0 binary64) (.f64 x x))))) (-.f64 (.f64 y (sqrt.f64 z)) x)))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x)))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 y (.f64 y z)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 (.f64 y (sqrt.f64 z)) x)))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) #s(literal -1/2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 y (sqrt.f64 z)) x))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (*.f64 y (sqrt.f64 z)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z))) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y (.f64 y z)) (-.f64 #s(literal 0 binary64) (.f64 x x)))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) (-.f64 (.f64 y (.f64 y z)) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) #s(literal 1 binary64)) (-.f64 (.f64 y (sqrt.f64 z)) x))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y (sqrt.f64 z)))) #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (/.f64 (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z)))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64))))))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 y (*.f64 y z))))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64))) #s(literal 1/2 binary64)) (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z)))))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) #s(literal 1/2 binary64)) (-.f64 x (*.f64 y (sqrt.f64 z))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (sqrt.f64 z)) x))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (*.f64 x x)))))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (sqrt.f64 z)) x))) (+.f64 (.f64 y (.f64 y z)) (*.f64 x x)))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (+.f64 x (.f64 y (sqrt.f64 z)))) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (/.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 y (.f64 y z)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (/.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y (.f64 y z)) (-.f64 #s(literal 0 binary64) (.f64 x x))))) (/.f64 (-.f64 (.f64 y (sqrt.f64 z)) x) #s(literal 1/2 binary64))))
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(/.f64 (.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)))) (-.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) (.f64 x (.f64 x x)))) (.f64 (neg.f64 (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z))))) (+.f64 (.f64 y (.f64 y z)) (-.f64 (.f64 x x) (.f64 (.f64 y (sqrt.f64 z)) (-.f64 #s(literal 0 binary64) x))))))
(/.f64 (.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)))) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (.f64 (neg.f64 (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z))))) (+.f64 x (*.f64 y (sqrt.f64 z)))))
(/.f64 (.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)))) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (.f64 (neg.f64 (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z))))) (-.f64 (*.f64 y (sqrt.f64 z)) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) (.f64 x (.f64 x x))))) (.f64 (neg.f64 (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z))))) (neg.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x (+.f64 x (*.f64 y (sqrt.f64 z))))))))
(/.f64 (.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (.f64 (neg.f64 (-.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 x (.f64 y (sqrt.f64 z))))) (-.f64 #s(literal 0 binary64) (+.f64 x (*.f64 y (sqrt.f64 z))))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) #s(literal 1 binary64)) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x (+.f64 x (.f64 y (sqrt.f64 z))))) (-.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) (.f64 x (.f64 x x))))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) #s(literal 1 binary64)) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (/.f64 (+.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 y (.f64 y z)) (.f64 x x)))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (-.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) (.f64 x (.f64 x x)))) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (+.f64 (.f64 y (.f64 y z)) (.f64 x (+.f64 x (.f64 y (sqrt.f64 z)))))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (-.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) (.f64 x (.f64 x x)))) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (+.f64 (.f64 y (.f64 y z)) (-.f64 (.f64 x x) (.f64 (*.f64 y (sqrt.f64 z)) (-.f64 #s(literal 0 binary64) x))))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (+.f64 x (.f64 y (sqrt.f64 z)))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (-.f64 (.f64 y (sqrt.f64 z)) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (neg.f64 (-.f64 (pow.f64 (.f64 y (.f64 y z)) #s(literal 3/2 binary64)) (.f64 x (.f64 x x))))) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (neg.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x (+.f64 x (.f64 y (sqrt.f64 z))))))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z)))) (neg.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (.f64 (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))) (-.f64 #s(literal 0 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (*.f64 x x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (neg.f64 (+.f64 (.f64 y (.f64 y z)) (*.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (-.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))))) (neg.f64 (-.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))
(/.f64 (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (-.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 y (.f64 y z)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))))
(/.f64 (+.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (pow.f64 (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (-.f64 (.f64 (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))))
(/.f64 (+.f64 (neg.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z))))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 y (*.f64 y z))))))
(/.f64 (+.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))))) (+.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (-.f64 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (.f64 x x))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (-.f64 (.f64 y (.f64 y z)) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (pow.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (+.f64 (.f64 (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))) (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 y (.f64 y z)) (-.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))))) (.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (*.f64 x x)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))) (/.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (.f64 (/.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 y (.f64 y z)) (*.f64 x x)))))))
(pow.f64 (/.f64 (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x)))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 y (.f64 y z)) (.f64 x x)) (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (+.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (*.f64 y (sqrt.f64 z)) x))
(.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y z) (.f64 (.f64 y z) (.f64 y z)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))))
(.f64 (-.f64 (.f64 y (.f64 (.f64 y z) (.f64 y (.f64 y z)))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y z)) (.f64 x x))))
(exp.f64 (.f64 (log.f64 (.f64 y (sqrt.f64 z))) #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 y z) (*.f64 y z)) z)
(/.f64 (.f64 (.f64 y z) (.f64 (.f64 y z) #s(literal 1 binary64))) z)
(/.f64 (.f64 (.f64 y z) (.f64 #s(literal 1 binary64) (.f64 y z))) z)
(/.f64 (.f64 (.f64 (.f64 y z) #s(literal 1 binary64)) (.f64 y z)) z)
(/.f64 (.f64 (.f64 (.f64 y z) #s(literal 1 binary64)) (.f64 (*.f64 y z) #s(literal 1 binary64))) z)
(/.f64 (.f64 (.f64 (.f64 y z) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (*.f64 y z))) z)
(/.f64 (.f64 (.f64 #s(literal 1 binary64) (.f64 y z)) (.f64 y z)) z)
(/.f64 (.f64 (.f64 #s(literal 1 binary64) (.f64 y z)) (.f64 (*.f64 y z) #s(literal 1 binary64))) z)
(/.f64 (.f64 (.f64 #s(literal 1 binary64) (.f64 y z)) (.f64 #s(literal 1 binary64) (*.f64 y z))) z)
(pow.f64 (*.f64 y (sqrt.f64 z)) #s(literal 2 binary64))
(.f64 y (.f64 y z))
(.f64 y (.f64 (sqrt.f64 z) (*.f64 y (sqrt.f64 z))))
(.f64 z (.f64 y y))
(.f64 (sqrt.f64 z) (.f64 y (*.f64 y (sqrt.f64 z))))
(.f64 (sqrt.f64 z) (pow.f64 (.f64 (pow.f64 z #s(literal 1/4 binary64)) y) #s(literal 2 binary64)))
(.f64 (.f64 y (sqrt.f64 z)) (*.f64 y (sqrt.f64 z)))
(.f64 (/.f64 #s(literal 1 binary64) z) (.f64 (.f64 y z) (.f64 y z)))
(.f64 (pow.f64 z #s(literal -1/2 binary64)) (.f64 (.f64 y z) (.f64 y (sqrt.f64 z))))
(.f64 (.f64 y z) y)
(.f64 (.f64 y z) (/.f64 (.f64 #s(literal 1 binary64) (.f64 y z)) z))
(.f64 (.f64 y y) z)
(.f64 (.f64 y y) (pow.f64 (*.f64 z (pow.f64 z #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 y (pow.f64 z #s(literal -1/2 binary64))) (.f64 z (.f64 y (sqrt.f64 z))))
(.f64 (.f64 z z) (/.f64 (.f64 (.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 1 binary64) y)) z))
(.f64 (.f64 (.f64 y z) (.f64 y z)) (/.f64 #s(literal 1 binary64) z))
(.f64 (/.f64 (.f64 (.f64 #s(literal 1 binary64) y) (.f64 #s(literal 1 binary64) y)) z) (*.f64 z z))
(.f64 (/.f64 (.f64 (.f64 y z) #s(literal 1 binary64)) z) (.f64 y z))
(.f64 (.f64 (.f64 y (sqrt.f64 z)) (.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)))
(.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 1 binary64) y)) z) z)
(.f64 (.f64 (*.f64 y (sqrt.f64 z)) y) (sqrt.f64 z))
(.f64 (.f64 (*.f64 y (sqrt.f64 z)) (sqrt.f64 z)) y)
(.f64 (pow.f64 (.f64 y (pow.f64 z #s(literal 1/4 binary64))) #s(literal 2 binary64)) (sqrt.f64 z))

simplify362.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

4412×	`-lowering-.f32`
4412×	`-lowering-.f64`
1590×	`/-lowering-/.f32`
1590×	`/-lowering-/.f64`
1186×	`neg-lowering-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	4449
1	1285	3845
2	4599	3718
0	8389	3718

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

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

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

eval543.0ms (7%)

Compiler: Compiled 62665 to 3016 computations (95.2% saved)

prune141.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1993	6	1999
Fresh	5	1	6
Picked	4	1	5
Done	0	1	1
Total	2002	9	2011

Accuracy

100.0%

Counts

2011 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
▶	48.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
▶	53.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
▶	48.8%	(.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
▶	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z)))))
	93.3%	(.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (.f64 y z) (sqrt.f64 z))))
	94.6%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (*.f64 y (pow.f64 z #s(literal -1/2 binary64))) z)))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	53.3%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 187 to 141 computations (24.6% saved)

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) z)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
✓	cost-diff	0	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
✓	cost-diff	0	(sqrt.f64 z)
✓	cost-diff	0	(*.f64 y (sqrt.f64 z))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))
✓	cost-diff	128	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
✓	cost-diff	0	(sqrt.f64 z)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))
✓	cost-diff	0	(.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	256	(.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64))
✓	cost-diff	384	(/.f64 (.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z)))
✓	cost-diff	384	(+.f64 x (/.f64 (.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z))))
✓	cost-diff	384	(.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z)))))

Rules

304×	`-lowering-.f32`
304×	`-lowering-.f64`
222×	`times-frac`
218×	`/-lowering-/.f32`
218×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	108
1	60	102
2	145	101
3	279	101
4	431	101
5	532	101
6	600	101
7	614	101
8	619	101
0	619	101

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize179.0ms (2.3%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) z)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	99.6%	(*.f64 y (sqrt.f64 z))
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z))))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 z)))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 z))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	99.6%	(.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	100.0%	(+.f64 x (/.f64 (.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z))))
✓	accuracy	99.7%	(/.f64 (.f64 (.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z)))
✓	accuracy	99.5%	(*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) z))

Results

128.0ms

256×

valid

Compiler

Compiled 145 to 24 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-div: 13.0ms (41.9% of total)

ival-mult: 12.0ms (38.7% of total)

ival-sqrt: 4.0ms (12.9% of total)

ival-add: 1.0ms (3.2% of total)

const: 1.0ms (3.2% of total)

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

series21.0ms (0.3%)

Counts

17 → 336

Calls

Call 1

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

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

Calls

84 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	(/ 1/2 (/ 1 x))
1.0ms	z	@	-inf	(* 1/2 (+ x (/ (* (* 1 y) 1) (* (sqrt z) (/ 1 z)))))
1.0ms	y	@	0	(/ 1 (* y (sqrt z)))
1.0ms	z	@	-inf	(/ 1 (* y (sqrt z)))
1.0ms	z	@	0	(/ 1 (* y (sqrt z)))

rewrite370.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4840×	`-lowering-.f32`
4840×	`-lowering-.f64`
2538×	`/-lowering-/.f32`
2538×	`/-lowering-/.f64`
1070×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	78
1	132	66
2	841	64
0	9023	64

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1064

Calls

Call 1

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

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

simplify206.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

3670×	`-lowering-.f32`
3670×	`-lowering-.f64`
1478×	`/-lowering-/.f32`
1478×	`/-lowering-/.f64`
1412×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	1690
1	292	1570
2	944	1570
3	2964	1546
0	8623	1546

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

Outputs
(* 1/2 (* y (sqrt z)))
(.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (+ x (* y (sqrt z))))
(.f64 #s(literal 1/2 binary64) (+.f64 (.f64 y (sqrt.f64 z)) x))
(* 1/2 (* y (sqrt z)))
(.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* 1/2 (* y (sqrt z)))
(.f64 #s(literal 1/2 binary64) (.f64 y (sqrt.f64 z)))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* -1 (* z (+ (* -1/2 (* y (sqrt (/ 1 z)))) (* -1/2 (/ x z)))))
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 y z))))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* x (+ 1 (* (/ y x) (sqrt z))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* x (+ 1 (* (/ y x) (sqrt z))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (+ (sqrt z) (/ x y)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (+ (sqrt z) (/ x y)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (+ (sqrt z) (/ x y)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+ x (* y (sqrt z)))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
(* -1 (* z (+ (* -1 (* y (sqrt (/ 1 z)))) (* -1 (/ x z)))))
(+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 y z)))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
(*.f64 y (sqrt.f64 z))
(* y (sqrt z))
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eval272.0ms (3.5%)

Compiler: Compiled 21332 to 3103 computations (85.5% saved)

prune159.0ms (2.1%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1593	4	1597
Fresh	2	0	2
Picked	3	2	5
Done	0	2	2
Total	1598	8	1606

Accuracy

100.0%

Counts

1606 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
▶	48.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
▶	48.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sqrt.f64 z) z) y))
✓	53.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
✓	48.8%	(.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
▶	94.7%	(*.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 z (/.f64 (sqrt.f64 z) y))))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	53.3%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 78 to 60 computations (23.1% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Program
✓	cost-diff	(pow.f64 z #s(literal -1/2 binary64))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
✓	cost-diff	(pow.f64 z #s(literal -1/2 binary64))
✓	cost-diff	(/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
✓	cost-diff	(sqrt.f64 z)
✓	cost-diff	(/.f64 (sqrt.f64 z) z)
✓	cost-diff	(/.f64 (/.f64 (sqrt.f64 z) z) y)
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sqrt.f64 z) z) y))
✓	cost-diff	(/.f64 (sqrt.f64 z) y)
✓	cost-diff	(/.f64 z (/.f64 (sqrt.f64 z) y))
✓	cost-diff	(+.f64 x (/.f64 z (/.f64 (sqrt.f64 z) y)))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 z (/.f64 (sqrt.f64 z) y))))

Rules

88×	`-lowering-.f32`
88×	`-lowering-.f64`
48×	`/-lowering-/.f32`
48×	`/-lowering-/.f64`
46×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	93
1	37	91
2	62	91
3	96	91
4	122	91
5	126	91
6	127	91
0	127	91

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize142.0ms (1.8%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(pow.f64 z #s(literal -1/2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(pow.f64 z #s(literal -1/2 binary64))
✓	accuracy	99.6%	(/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	99.6%	(/.f64 (/.f64 (sqrt.f64 z) z) y)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sqrt.f64 z) z) y))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 z) z)
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	100.0%	(+.f64 x (/.f64 z (/.f64 (sqrt.f64 z) y)))
✓	accuracy	99.7%	(/.f64 (sqrt.f64 z) y)
✓	accuracy	92.3%	(/.f64 z (/.f64 (sqrt.f64 z) y))

Results

118.0ms

256×

valid

Compiler

Compiled 97 to 19 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-div: 14.0ms (45.7% of total)

ival-pow: 7.0ms (22.9% of total)

ival-mult: 4.0ms (13.1% of total)

ival-sqrt: 4.0ms (13.1% of total)

ival-add: 1.0ms (3.3% of total)

const: 1.0ms (3.3% of total)

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

series7.0ms (0.1%)

Counts

13 → 288

Calls

Call 1

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

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

Calls

72 calls:

Time	Variable		Point	Expression
0.0ms	z	@	-inf	(pow z -1/2)
0.0ms	z	@	-inf	(/ (/ (sqrt z) z) y)
0.0ms	z	@	inf	(pow z -1/2)
0.0ms	z	@	-inf	(/ 1/2 (/ (/ (sqrt z) z) y))
0.0ms	y	@	-inf	(/ (sqrt z) y)

rewrite303.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4182×	`-lowering-.f32`
4182×	`-lowering-.f64`
2998×	`/-lowering-/.f32`
2998×	`/-lowering-/.f64`
1218×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	77
1	106	75
2	753	55
3	7705	55
0	8414	55

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 995

Calls

Call 1

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

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

simplify207.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

3684×	`-lowering-.f32`
3684×	`-lowering-.f64`
1524×	`fnmadd-define`
1220×	`fma-define`
1048×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1606
1	290	1462
2	904	1462
3	2970	1438
0	8624	1438

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

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

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

eval181.0ms (2.3%)

Compiler: Compiled 17980 to 1858 computations (89.7% saved)

prune151.0ms (1.9%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1397	2	1399
Fresh	0	0	0
Picked	2	2	4
Done	0	4	4
Total	1399	8	1407

Accuracy

100.0%

Counts

1407 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	48.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64)))
	48.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 (sqrt.f64 z) z))
	48.7%	(/.f64 (sqrt.f64 z) (/.f64 #s(literal 2 binary64) y))
✓	48.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
✓	53.1%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
✓	48.8%	(.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z)))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	53.3%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 388 to 157 computations (59.5% saved)

regimes54.0ms (0.7%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

7 calls:

8.0ms	(*.f64 y (sqrt.f64 z))
8.0ms	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
8.0ms	x
7.0ms	(sqrt.f64 z)
7.0ms	z

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`z`
99.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
99.8%	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
99.8%	1	`(*.f64 y (sqrt.f64 z))`
99.8%	1	`(sqrt.f64 z)`

Compiler

Compiled 46 to 34 computations (26.1% saved)

regimes11.0ms (0.1%)

Counts

6 → 3

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
3.0ms	(sqrt.f64 z)
2.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
75.4%	3	`x`
75.2%	3	`y`
69.7%	2	`z`
69.7%	2	`(sqrt.f64 z)`

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes3.0ms (0%)

Counts

5 → 3

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
75.4%	3	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes199.0ms (2.6%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))

Outputs
(*.f64 #s(literal 1/2 binary64) x)

Calls

3 calls:

195.0ms	y
1.0ms	z
1.0ms	x

Results

Accuracy	Segments	Branch
53.3%	1	`z`
53.3%	1	`y`
53.3%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch30.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	1.131701851912874e-140	1.998272342391208e-138
15.0ms	-5.200189771812396e-93	-7.062764657807921e-102

Results

18.0ms

256×

valid

Compiler

Compiled 307 to 255 computations (16.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 4.0ms (43.5% of total)

ival-div: 2.0ms (21.8% of total)

ival-sqrt: 2.0ms (21.8% of total)

ival-add: 1.0ms (10.9% of total)

const: 0.0ms (0% of total)

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

bsearch196.0ms (2.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
179.0ms	1.131701851912874e-140	1.998272342391208e-138
15.0ms	-5.200189771812396e-93	-7.062764657807921e-102

Results

185.0ms

256×

valid

Compiler

Compiled 291 to 239 computations (17.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 4.0ms (43.4% of total)

ival-div: 2.0ms (21.7% of total)

ival-sqrt: 2.0ms (21.7% of total)

ival-add: 1.0ms (10.8% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
4×	`if-if-or-not_binary32`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	34	48

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
(if (<=.f64 x #s(literal -5871356456934583/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) (.f64 #s(literal 1/2 binary64) x) (if (<=.f64 x #s(literal 817038295730877/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x)))
(if (<=.f64 x #s(literal -5871356456934583/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) (.f64 #s(literal 1/2 binary64) x) (if (<=.f64 x #s(literal 817038295730877/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128 binary64)) (.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) (.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal 1/2 binary64) x)

Outputs
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
(if (<=.f64 x #s(literal -5871356456934583/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) (.f64 #s(literal 1/2 binary64) x) (if (<=.f64 x #s(literal 817038295730877/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) y) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) x)))
(if (<=.f64 x #s(literal -5871356456934583/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) (.f64 #s(literal 1/2 binary64) x) (if (<=.f64 x #s(literal 817038295730877/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128 binary64)) (.f64 y (.f64 #s(literal 1/2 binary64) (sqrt.f64 z))) (.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal 1/2 binary64) x)

soundness660.0ms (8.5%)

Rules

4840×	`-lowering-.f32`
4840×	`-lowering-.f64`
3400×	`-lowering-.f32`
3400×	`-lowering-.f64`
2538×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	622
1	264	578
2	891	578
3	2789	554
4	7950	554
0	8118	554
0	23	78
1	132	66
2	841	64
0	9023	64
0	11	8
1	22	7
2	37	7
3	48	7
0	48	7

Stop Event

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

Compiler

Compiled 167 to 108 computations (35.3% saved)

preprocess33.0ms (0.4%)

Compiler: Compiled 136 to 66 computations (51.5% saved)

Iter	Nodes	Cost
0	23	108
1	60	102
2	145	101
3	279	101
4	431	101
5	532	101
6	600	101
7	614	101
8	619	101
0	619	101

Iter	Nodes	Cost
0	23	108
1	60	102
2	145	101
3	279	101
4	431	101
5	532	101
6	600	101
7	614	101
8	619	101
0	619	101

analyze66.0ms (0.9%)

sample1.5s (19.6%)

preprocess72.0ms (0.9%)

explain131.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize74.0ms (1%)

series8.0ms (0.1%)

rewrite285.0ms (3.7%)

simplify170.0ms (2.2%)

eval37.0ms (0.5%)

prune46.0ms (0.6%)

simplify129.0ms (1.7%)

localize201.0ms (2.6%)

series34.0ms (0.4%)

rewrite483.0ms (6.2%)

simplify362.0ms (4.7%)

eval543.0ms (7%)

prune141.0ms (1.8%)

simplify27.0ms (0.4%)

localize179.0ms (2.3%)

series21.0ms (0.3%)

rewrite370.0ms (4.8%)

simplify206.0ms (2.7%)

eval272.0ms (3.5%)

prune159.0ms (2.1%)

simplify10.0ms (0.1%)

localize142.0ms (1.8%)

series7.0ms (0.1%)

rewrite303.0ms (3.9%)

simplify207.0ms (2.7%)

eval181.0ms (2.3%)

prune151.0ms (1.9%)

regimes54.0ms (0.7%)

regimes11.0ms (0.1%)

regimes3.0ms (0%)

regimes199.0ms (2.6%)

bsearch30.0ms (0.4%)

bsearch196.0ms (2.5%)

simplify9.0ms (0.1%)

soundness660.0ms (8.5%)

preprocess33.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	23	108
1	60	102
2	145	101
3	279	101
4	431	101
5	532	101
6	600	101
7	614	101
8	619	101
0	619	101