Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Average Accuracy: 100.0% → 100.0%

Time: 2.9s

Precision: binary64

Cost: 576

Math

\[\frac{x \cdot y}{2} - \frac{z}{8} \]

↓

\[\frac{x \cdot y}{2} - \frac{z}{8} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

↓

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

↓

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

↓

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

↓

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

↓

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x \cdot y}{2} - \frac{z}{8} \]

Alternatives

Alternative 1
Accuracy	72.8%
Cost	1115

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+20} \lor \neg \left(z \leq -1.65 \cdot 10^{-76}\right) \land \left(z \leq -3.2 \cdot 10^{-121} \lor \neg \left(z \leq -8.8 \cdot 10^{-151} \lor \neg \left(z \leq -4.2 \cdot 10^{-192}\right) \land z \leq 6.2 \cdot 10^{-19}\right)\right):\\ \;\;\;\;z \cdot -0.125\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 0.5\right)\\ \end{array} \]

Alternative 2
Accuracy	99.8%
Cost	576

\[\frac{x}{\frac{2}{y}} - \frac{z}{8} \]

Alternative 3
Accuracy	57.0%
Cost	192

\[z \cdot -0.125 \]

Reproduce

herbie shell --seed 2023153 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))