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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 10

Speedup: 0.1×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{y}{-2}, z, t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma 0.125 x (fma (/ y -2.0) z t)))

C

double code(double x, double y, double z, double t) {
	return fma(0.125, x, fma((y / -2.0), z, t));
}

Julia

function code(x, y, z, t)
	return fma(0.125, x, fma(Float64(y / -2.0), z, t))
end

Wolfram

code[x_, y_, z_, t_] := N[(0.125 * x + N[(N[(y / -2.0), $MachinePrecision] * z + t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

   2. associate-+l+ 100.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x + \left(\left(-\frac{y \cdot z}{2}\right) + t\right)} \]

   3. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, \left(-\frac{y \cdot z}{2}\right) + t\right)} \]

   4. metadata-eval 100.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.125}, x, \left(-\frac{y \cdot z}{2}\right) + t\right) \]

   5. associate-/l* 99.9%

      \[\leadsto \mathsf{fma}\left(0.125, x, \left(-\color{blue}{\frac{y}{\frac{2}{z}}}\right) + t\right) \]

   6. distribute-frac-neg 99.9%

      \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{\frac{-y}{\frac{2}{z}}} + t\right) \]

   7. associate-/r/ 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{\frac{-y}{2} \cdot z} + t\right) \]

   8. fma-def 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \color{blue}{\mathsf{fma}\left(\frac{-y}{2}, z, t\right)}\right) \]

   9. neg-mul-1 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot y}}{2}, z, t\right)\right) \]

   10. *-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{\color{blue}{y \cdot -1}}{2}, z, t\right)\right) \]

   11. associate-/l* 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\color{blue}{\frac{y}{\frac{2}{-1}}}, z, t\right)\right) \]

   12. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{y}{\color{blue}{-2}}, z, t\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{y}{-2}, z, t\right)\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{y}{-2}, z, t\right)\right) \]

Alternative 2: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ t + \mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ t (fma y (* z -0.5) (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	return t + fma(y, (z * -0.5), (0.125 * x));
}

Julia

function code(x, y, z, t)
	return Float64(t + fma(y, Float64(z * -0.5), Float64(0.125 * x)))
end

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(y * N[(z * -0.5), $MachinePrecision] + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

   3. remove-double-neg 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

   4. fma-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   5. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

   6. remove-double-neg 100.0%

      \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

   7. associate-/l* 99.9%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

4. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{\left(-0.5 \cdot \left(y \cdot z\right) + 0.125 \cdot x\right)} + t \]
5. Step-by-step derivation

   1. *-commutative 100.0%

      \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot -0.5} + 0.125 \cdot x\right) + t \]

   2. associate-*l* 100.0%

      \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot -0.5\right)} + 0.125 \cdot x\right) + t \]

   3. metadata-eval 100.0%

      \[\leadsto \left(y \cdot \left(z \cdot \color{blue}{\left(-0.5\right)}\right) + 0.125 \cdot x\right) + t \]

   4. distribute-rgt-neg-in 100.0%

      \[\leadsto \left(y \cdot \color{blue}{\left(-z \cdot 0.5\right)} + 0.125 \cdot x\right) + t \]

   5. fma-udef 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, -z \cdot 0.5, 0.125 \cdot x\right)} + t \]

   6. distribute-rgt-neg-in 100.0%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(-0.5\right)}, 0.125 \cdot x\right) + t \]

   7. metadata-eval 100.0%

      \[\leadsto \mathsf{fma}\left(y, z \cdot \color{blue}{-0.5}, 0.125 \cdot x\right) + t \]

6. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right)} + t \]

7. Final simplification 100.0%

   \[\leadsto t + \mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right) \]

Alternative 3: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot z\right)\\ t_2 := t - t_1\\ t_3 := 0.125 \cdot x - t_1\\ \mathbf{if}\;y \cdot z \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \cdot z \leq -3.1 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \cdot z \leq -1 \cdot 10^{-27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \cdot z \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (* y z))) (t_2 (- t t_1)) (t_3 (- (* 0.125 x) t_1)))
   (if (<= (* y z) -8.5e+107)
     t_3
     (if (<= (* y z) -3.1e+49)
       t_2
       (if (<= (* y z) -1e-27)
         t_3
         (if (<= (* y z) 9.6e+84) (+ t (* 0.125 x)) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * (y * z);
	double t_2 = t - t_1;
	double t_3 = (0.125 * x) - t_1;
	double tmp;
	if ((y * z) <= -8.5e+107) {
		tmp = t_3;
	} else if ((y * z) <= -3.1e+49) {
		tmp = t_2;
	} else if ((y * z) <= -1e-27) {
		tmp = t_3;
	} else if ((y * z) <= 9.6e+84) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.5d0 * (y * z)
    t_2 = t - t_1
    t_3 = (0.125d0 * x) - t_1
    if ((y * z) <= (-8.5d+107)) then
        tmp = t_3
    else if ((y * z) <= (-3.1d+49)) then
        tmp = t_2
    else if ((y * z) <= (-1d-27)) then
        tmp = t_3
    else if ((y * z) <= 9.6d+84) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * (y * z);
	double t_2 = t - t_1;
	double t_3 = (0.125 * x) - t_1;
	double tmp;
	if ((y * z) <= -8.5e+107) {
		tmp = t_3;
	} else if ((y * z) <= -3.1e+49) {
		tmp = t_2;
	} else if ((y * z) <= -1e-27) {
		tmp = t_3;
	} else if ((y * z) <= 9.6e+84) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * (y * z)
	t_2 = t - t_1
	t_3 = (0.125 * x) - t_1
	tmp = 0
	if (y * z) <= -8.5e+107:
		tmp = t_3
	elif (y * z) <= -3.1e+49:
		tmp = t_2
	elif (y * z) <= -1e-27:
		tmp = t_3
	elif (y * z) <= 9.6e+84:
		tmp = t + (0.125 * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(y * z))
	t_2 = Float64(t - t_1)
	t_3 = Float64(Float64(0.125 * x) - t_1)
	tmp = 0.0
	if (Float64(y * z) <= -8.5e+107)
		tmp = t_3;
	elseif (Float64(y * z) <= -3.1e+49)
		tmp = t_2;
	elseif (Float64(y * z) <= -1e-27)
		tmp = t_3;
	elseif (Float64(y * z) <= 9.6e+84)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * (y * z);
	t_2 = t - t_1;
	t_3 = (0.125 * x) - t_1;
	tmp = 0.0;
	if ((y * z) <= -8.5e+107)
		tmp = t_3;
	elseif ((y * z) <= -3.1e+49)
		tmp = t_2;
	elseif ((y * z) <= -1e-27)
		tmp = t_3;
	elseif ((y * z) <= 9.6e+84)
		tmp = t + (0.125 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -8.5e+107], t$95$3, If[LessEqual[N[(y * z), $MachinePrecision], -3.1e+49], t$95$2, If[LessEqual[N[(y * z), $MachinePrecision], -1e-27], t$95$3, If[LessEqual[N[(y * z), $MachinePrecision], 9.6e+84], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -8.4999999999999999e107 or -3.09999999999999992e49 < (*.f64 y z) < -1e-27

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.9%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in t around 0 93.1%

      \[\leadsto \color{blue}{0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)} \]

   if -8.4999999999999999e107 < (*.f64 y z) < -3.09999999999999992e49 or 9.5999999999999999e84 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.8%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around 0 91.7%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]

   if -1e-27 < (*.f64 y z) < 9.5999999999999999e84

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around inf 92.3%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq -3.1 \cdot 10^{+49}:\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq -1 \cdot 10^{-27}:\\ \;\;\;\;0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 56.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq 0:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{-108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (* y z))))
   (if (<= (* y z) -1.1e-23)
     t_1
     (if (<= (* y z) 0.0)
       (* 0.125 x)
       (if (<= (* y z) 5e-108) t (if (<= (* y z) 5.8e+84) (* 0.125 x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (y * z);
	double tmp;
	if ((y * z) <= -1.1e-23) {
		tmp = t_1;
	} else if ((y * z) <= 0.0) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 5e-108) {
		tmp = t;
	} else if ((y * z) <= 5.8e+84) {
		tmp = 0.125 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-0.5d0) * (y * z)
    if ((y * z) <= (-1.1d-23)) then
        tmp = t_1
    else if ((y * z) <= 0.0d0) then
        tmp = 0.125d0 * x
    else if ((y * z) <= 5d-108) then
        tmp = t
    else if ((y * z) <= 5.8d+84) then
        tmp = 0.125d0 * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (y * z);
	double tmp;
	if ((y * z) <= -1.1e-23) {
		tmp = t_1;
	} else if ((y * z) <= 0.0) {
		tmp = 0.125 * x;
	} else if ((y * z) <= 5e-108) {
		tmp = t;
	} else if ((y * z) <= 5.8e+84) {
		tmp = 0.125 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (y * z)
	tmp = 0
	if (y * z) <= -1.1e-23:
		tmp = t_1
	elif (y * z) <= 0.0:
		tmp = 0.125 * x
	elif (y * z) <= 5e-108:
		tmp = t
	elif (y * z) <= 5.8e+84:
		tmp = 0.125 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(y * z))
	tmp = 0.0
	if (Float64(y * z) <= -1.1e-23)
		tmp = t_1;
	elseif (Float64(y * z) <= 0.0)
		tmp = Float64(0.125 * x);
	elseif (Float64(y * z) <= 5e-108)
		tmp = t;
	elseif (Float64(y * z) <= 5.8e+84)
		tmp = Float64(0.125 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (y * z);
	tmp = 0.0;
	if ((y * z) <= -1.1e-23)
		tmp = t_1;
	elseif ((y * z) <= 0.0)
		tmp = 0.125 * x;
	elseif ((y * z) <= 5e-108)
		tmp = t;
	elseif ((y * z) <= 5.8e+84)
		tmp = 0.125 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -1.1e-23], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], 0.0], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e-108], t, If[LessEqual[N[(y * z), $MachinePrecision], 5.8e+84], N[(0.125 * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1.1e-23 or 5.79999999999999977e84 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.8%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \left(y \cdot z\right) + 0.125 \cdot x\right)} + t \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot -0.5} + 0.125 \cdot x\right) + t \]

      2. associate-*l* 100.0%

         \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot -0.5\right)} + 0.125 \cdot x\right) + t \]

      3. metadata-eval 100.0%

         \[\leadsto \left(y \cdot \left(z \cdot \color{blue}{\left(-0.5\right)}\right) + 0.125 \cdot x\right) + t \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(-z \cdot 0.5\right)} + 0.125 \cdot x\right) + t \]

      5. fma-udef 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -z \cdot 0.5, 0.125 \cdot x\right)} + t \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(-0.5\right)}, 0.125 \cdot x\right) + t \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(y, z \cdot \color{blue}{-0.5}, 0.125 \cdot x\right) + t \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right)} + t \]

   7. Taylor expanded in y around inf 69.3%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

   if -1.1e-23 < (*.f64 y z) < -0.0 or 5e-108 < (*.f64 y z) < 5.79999999999999977e84

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.9%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \left(y \cdot z\right) + 0.125 \cdot x\right)} + t \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot -0.5} + 0.125 \cdot x\right) + t \]

      2. associate-*l* 100.0%

         \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot -0.5\right)} + 0.125 \cdot x\right) + t \]

      3. metadata-eval 100.0%

         \[\leadsto \left(y \cdot \left(z \cdot \color{blue}{\left(-0.5\right)}\right) + 0.125 \cdot x\right) + t \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(-z \cdot 0.5\right)} + 0.125 \cdot x\right) + t \]

      5. fma-udef 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -z \cdot 0.5, 0.125 \cdot x\right)} + t \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(-0.5\right)}, 0.125 \cdot x\right) + t \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(y, z \cdot \color{blue}{-0.5}, 0.125 \cdot x\right) + t \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right)} + t \]

   7. Taylor expanded in x around inf 56.8%

      \[\leadsto \color{blue}{0.125 \cdot x} \]

   if -0.0 < (*.f64 y z) < 5e-108

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in t around inf 64.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 0:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{-108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.05 \cdot 10^{-23} \lor \neg \left(y \cdot z \leq 6.4 \cdot 10^{+88}\right):\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -1.05e-23) (not (<= (* y z) 6.4e+88)))
   (- t (* 0.5 (* y z)))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1.05e-23) || !((y * z) <= 6.4e+88)) {
		tmp = t - (0.5 * (y * z));
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y * z) <= (-1.05d-23)) .or. (.not. ((y * z) <= 6.4d+88))) then
        tmp = t - (0.5d0 * (y * z))
    else
        tmp = t + (0.125d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1.05e-23) || !((y * z) <= 6.4e+88)) {
		tmp = t - (0.5 * (y * z));
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -1.05e-23) or not ((y * z) <= 6.4e+88):
		tmp = t - (0.5 * (y * z))
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -1.05e-23) || !(Float64(y * z) <= 6.4e+88))
		tmp = Float64(t - Float64(0.5 * Float64(y * z)));
	else
		tmp = Float64(t + Float64(0.125 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -1.05e-23) || ~(((y * z) <= 6.4e+88)))
		tmp = t - (0.5 * (y * z));
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1.05e-23], N[Not[LessEqual[N[(y * z), $MachinePrecision], 6.4e+88]], $MachinePrecision]], N[(t - N[(0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.05e-23 or 6.3999999999999997e88 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.8%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around 0 83.6%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]

   if -1.05e-23 < (*.f64 y z) < 6.3999999999999997e88

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around inf 91.7%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.05 \cdot 10^{-23} \lor \neg \left(y \cdot z \leq 6.4 \cdot 10^{+88}\right):\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 6: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -7.2 \cdot 10^{+213} \lor \neg \left(y \cdot z \leq 2.05 \cdot 10^{+118}\right):\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -7.2e+213) (not (<= (* y z) 2.05e+118)))
   (* -0.5 (* y z))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -7.2e+213) || !((y * z) <= 2.05e+118)) {
		tmp = -0.5 * (y * z);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y * z) <= (-7.2d+213)) .or. (.not. ((y * z) <= 2.05d+118))) then
        tmp = (-0.5d0) * (y * z)
    else
        tmp = t + (0.125d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -7.2e+213) || !((y * z) <= 2.05e+118)) {
		tmp = -0.5 * (y * z);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -7.2e+213) or not ((y * z) <= 2.05e+118):
		tmp = -0.5 * (y * z)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -7.2e+213) || !(Float64(y * z) <= 2.05e+118))
		tmp = Float64(-0.5 * Float64(y * z));
	else
		tmp = Float64(t + Float64(0.125 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -7.2e+213) || ~(((y * z) <= 2.05e+118)))
		tmp = -0.5 * (y * z);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -7.2e+213], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2.05e+118]], $MachinePrecision]], N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -7.2000000000000002e213 or 2.0499999999999999e118 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.8%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \left(y \cdot z\right) + 0.125 \cdot x\right)} + t \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot -0.5} + 0.125 \cdot x\right) + t \]

      2. associate-*l* 100.0%

         \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot -0.5\right)} + 0.125 \cdot x\right) + t \]

      3. metadata-eval 100.0%

         \[\leadsto \left(y \cdot \left(z \cdot \color{blue}{\left(-0.5\right)}\right) + 0.125 \cdot x\right) + t \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(-z \cdot 0.5\right)} + 0.125 \cdot x\right) + t \]

      5. fma-udef 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -z \cdot 0.5, 0.125 \cdot x\right)} + t \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(-0.5\right)}, 0.125 \cdot x\right) + t \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(y, z \cdot \color{blue}{-0.5}, 0.125 \cdot x\right) + t \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right)} + t \]

   7. Taylor expanded in y around inf 90.6%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

   if -7.2000000000000002e213 < (*.f64 y z) < 2.0499999999999999e118

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.9%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around inf 81.2%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -7.2 \cdot 10^{+213} \lor \neg \left(y \cdot z \leq 2.05 \cdot 10^{+118}\right):\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ t + \left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ t (- (* 0.125 x) (/ y (/ 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	return t + ((0.125 * x) - (y / (2.0 / z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + ((0.125d0 * x) - (y / (2.0d0 / z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t + ((0.125 * x) - (y / (2.0 / z)));
}

Python

def code(x, y, z, t):
	return t + ((0.125 * x) - (y / (2.0 / z)))

Julia

function code(x, y, z, t)
	return Float64(t + Float64(Float64(0.125 * x) - Float64(y / Float64(2.0 / z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t + ((0.125 * x) - (y / (2.0 / z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(N[(0.125 * x), $MachinePrecision] - N[(y / N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

   3. remove-double-neg 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

   4. fma-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   5. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

   6. remove-double-neg 100.0%

      \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

   7. associate-/l* 99.9%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

4. Final simplification 99.9%

   \[\leadsto t + \left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) \]

Alternative 8: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(t + 0.125 \cdot x\right) - y \cdot \left(z \cdot 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (+ t (* 0.125 x)) (* y (* z 0.5))))

C

double code(double x, double y, double z, double t) {
	return (t + (0.125 * x)) - (y * (z * 0.5));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (t + (0.125d0 * x)) - (y * (z * 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (t + (0.125 * x)) - (y * (z * 0.5));
}

Python

def code(x, y, z, t):
	return (t + (0.125 * x)) - (y * (z * 0.5))

Julia

function code(x, y, z, t)
	return Float64(Float64(t + Float64(0.125 * x)) - Float64(y * Float64(z * 0.5)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (t + (0.125 * x)) - (y * (z * 0.5));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision] - N[(y * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

   3. remove-double-neg 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

   4. fma-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   5. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

   6. remove-double-neg 100.0%

      \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

   7. associate-/l* 99.9%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]
4. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{t + \left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right)} \]

   2. associate-/l* 100.0%

      \[\leadsto t + \left(0.125 \cdot x - \color{blue}{\frac{y \cdot z}{2}}\right) \]

   3. associate-+r- 100.0%

      \[\leadsto \color{blue}{\left(t + 0.125 \cdot x\right) - \frac{y \cdot z}{2}} \]

   4. div-inv 100.0%

      \[\leadsto \left(t + 0.125 \cdot x\right) - \color{blue}{\left(y \cdot z\right) \cdot \frac{1}{2}} \]

   5. associate-*l* 100.0%

      \[\leadsto \left(t + 0.125 \cdot x\right) - \color{blue}{y \cdot \left(z \cdot \frac{1}{2}\right)} \]

   6. metadata-eval 100.0%

      \[\leadsto \left(t + 0.125 \cdot x\right) - y \cdot \left(z \cdot \color{blue}{0.5}\right) \]

5. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(t + 0.125 \cdot x\right) - y \cdot \left(z \cdot 0.5\right)} \]

6. Final simplification 100.0%

   \[\leadsto \left(t + 0.125 \cdot x\right) - y \cdot \left(z \cdot 0.5\right) \]

Alternative 9: 49.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-34} \lor \neg \left(x \leq 140000\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.8e-34) (not (<= x 140000.0))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.8e-34) || !(x <= 140000.0)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6.8d-34)) .or. (.not. (x <= 140000.0d0))) then
        tmp = 0.125d0 * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.8e-34) || !(x <= 140000.0)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.8e-34) or not (x <= 140000.0):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.8e-34) || !(x <= 140000.0))
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.8e-34) || ~((x <= 140000.0)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.8e-34], N[Not[LessEqual[x, 140000.0]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000001e-34 or 1.4e5 < x

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.9%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \left(y \cdot z\right) + 0.125 \cdot x\right)} + t \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot z\right) \cdot -0.5} + 0.125 \cdot x\right) + t \]

      2. associate-*l* 100.0%

         \[\leadsto \left(\color{blue}{y \cdot \left(z \cdot -0.5\right)} + 0.125 \cdot x\right) + t \]

      3. metadata-eval 100.0%

         \[\leadsto \left(y \cdot \left(z \cdot \color{blue}{\left(-0.5\right)}\right) + 0.125 \cdot x\right) + t \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(-z \cdot 0.5\right)} + 0.125 \cdot x\right) + t \]

      5. fma-udef 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -z \cdot 0.5, 0.125 \cdot x\right)} + t \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{z \cdot \left(-0.5\right)}, 0.125 \cdot x\right) + t \]

      7. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(y, z \cdot \color{blue}{-0.5}, 0.125 \cdot x\right) + t \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot -0.5, 0.125 \cdot x\right)} + t \]

   7. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{0.125 \cdot x} \]

   if -6.8000000000000001e-34 < x < 1.4e5

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

      3. remove-double-neg 100.0%

         \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

      4. fma-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

      7. associate-/l* 99.9%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

   4. Taylor expanded in t around inf 45.3%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-34} \lor \neg \left(x \leq 140000\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 33.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, -\frac{y \cdot z}{2}\right)} + t \]

   3. remove-double-neg 100.0%

      \[\leadsto \mathsf{fma}\left(\frac{1}{8}, \color{blue}{-\left(-x\right)}, -\frac{y \cdot z}{2}\right) + t \]

   4. fma-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   5. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]

   6. remove-double-neg 100.0%

      \[\leadsto \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]

   7. associate-/l* 99.9%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{\frac{2}{z}}\right) + t} \]

4. Taylor expanded in t around inf 29.7%

   \[\leadsto \color{blue}{t} \]

5. Final simplification 29.7%

   \[\leadsto t \]

Developer target: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / 8.0d0) + t) - ((z / 2.0d0) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))