Crypto.Random.Test:calculate from crypto-random-0.0.9

Average Accuracy: 90.3% → 99.9%

Time: 4.6s

Precision: binary64

Cost: 448

Math

\[x + \frac{y \cdot y}{z} \]

↓

\[x + \frac{y}{\frac{z}{y}} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (* y y) z)))

↓

(FPCore (x y z) :precision binary64 (+ x (/ y (/ z y))))

C

double code(double x, double y, double z) {
	return x + ((y * y) / z);
}

↓

double code(double x, double y, double z) {
	return x + (y / (z / y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y * y) / z)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y / (z / y))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * y) / z);
}

↓

public static double code(double x, double y, double z) {
	return x + (y / (z / y));
}

Python

def code(x, y, z):
	return x + ((y * y) / z)

↓

def code(x, y, z):
	return x + (y / (z / y))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * y) / z))
end

↓

function code(x, y, z)
	return Float64(x + Float64(y / Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * y) / z);
end

↓

function tmp = code(x, y, z)
	tmp = x + (y / (z / y));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(x + N[(y / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	90.3%
Target	99.9%
Herbie	99.9%

\[x + y \cdot \frac{y}{z} \]

Derivation

1. Initial program 90.3%

   \[x + \frac{y \cdot y}{z} \]

2. Simplified 99.9%

   \[\leadsto \color{blue}{x + \frac{y}{\frac{z}{y}}} \]
   Proof

   [Start] 90.3	\[ x + \frac{y \cdot y}{z} \]
   associate-/l* [=>] 99.9	\[ x + \color{blue}{\frac{y}{\frac{z}{y}}} \]

3. Final simplification 99.9%

   \[\leadsto x + \frac{y}{\frac{z}{y}} \]

Alternatives

Alternative 1
Accuracy	99.9%
Cost	448

\[x + y \cdot \frac{y}{z} \]

Alternative 2
Accuracy	66.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))