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

Average Accuracy: 90.8% → 99.9%

Time: 6.1s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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 * (y / z));
}

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 * (y / z))
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 * (y / z));
}

Python

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

↓

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

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(y / z)))
end

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = x + (y * (y / z));
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[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	90.8%
Target	99.9%
Herbie	99.9%

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

Derivation

1. Initial program 90.8%

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

2. Simplified 99.9%

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

   [Start] 90.8	\[ x + \frac{y \cdot y}{z} \]
   associate-*l/ [<=] 99.9	\[ x + \color{blue}{\frac{y}{z} \cdot y} \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	75.9%
Cost	1115

\[\begin{array}{l} \mathbf{if}\;y \leq -180000 \lor \neg \left(y \leq 1.6 \cdot 10^{-61} \lor \neg \left(y \leq 3.5 \cdot 10^{+32}\right) \land \left(y \leq 2 \cdot 10^{+75} \lor \neg \left(y \leq 5.2 \cdot 10^{+111}\right) \land y \leq 1.25 \cdot 10^{+130}\right)\right):\\ \;\;\;\;y \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	83.2%
Cost	1096

\[\begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ \mathbf{if}\;t_0 \leq -6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \mathbf{elif}\;t_0 \leq 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3
Accuracy	67.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(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)))