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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 8

Speedup: 1.2×

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(z * N[(y / -2.0), $MachinePrecision] + N[(0.125 * x + 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. remove-double-neg 100.0%

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

   2. sub-neg 100.0%

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

   3. sub-neg 100.0%

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

   4. +-commutative 100.0%

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

   5. associate--l+ 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-*r/ 100.0%

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

   8. distribute-rgt-neg-in 100.0%

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

   9. fma-def 100.0%

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

   10. neg-mul-1 100.0%

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

   11. *-commutative 100.0%

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

   12. associate-*l/ 100.0%

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

   13. associate-/l* 100.0%

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

   14. metadata-eval 100.0%

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

   15. fma-neg 100.0%

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

   16. remove-double-neg 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot -0.5\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-59}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-104}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-207}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-107}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* y -0.5))))
   (if (<= y -1.9e+71)
     t_1
     (if (<= y -9.5e+32)
       (* 0.125 x)
       (if (<= y -6.5e-59)
         t
         (if (<= y -2.5e-104)
           (* 0.125 x)
           (if (<= y -3.6e-207)
             t
             (if (<= y -1.4e-302)
               (* 0.125 x)
               (if (<= y 4.7e-107) t t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y * -0.5);
	double tmp;
	if (y <= -1.9e+71) {
		tmp = t_1;
	} else if (y <= -9.5e+32) {
		tmp = 0.125 * x;
	} else if (y <= -6.5e-59) {
		tmp = t;
	} else if (y <= -2.5e-104) {
		tmp = 0.125 * x;
	} else if (y <= -3.6e-207) {
		tmp = t;
	} else if (y <= -1.4e-302) {
		tmp = 0.125 * x;
	} else if (y <= 4.7e-107) {
		tmp = t;
	} 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 = z * (y * (-0.5d0))
    if (y <= (-1.9d+71)) then
        tmp = t_1
    else if (y <= (-9.5d+32)) then
        tmp = 0.125d0 * x
    else if (y <= (-6.5d-59)) then
        tmp = t
    else if (y <= (-2.5d-104)) then
        tmp = 0.125d0 * x
    else if (y <= (-3.6d-207)) then
        tmp = t
    else if (y <= (-1.4d-302)) then
        tmp = 0.125d0 * x
    else if (y <= 4.7d-107) then
        tmp = t
    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 = z * (y * -0.5);
	double tmp;
	if (y <= -1.9e+71) {
		tmp = t_1;
	} else if (y <= -9.5e+32) {
		tmp = 0.125 * x;
	} else if (y <= -6.5e-59) {
		tmp = t;
	} else if (y <= -2.5e-104) {
		tmp = 0.125 * x;
	} else if (y <= -3.6e-207) {
		tmp = t;
	} else if (y <= -1.4e-302) {
		tmp = 0.125 * x;
	} else if (y <= 4.7e-107) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y * -0.5)
	tmp = 0
	if y <= -1.9e+71:
		tmp = t_1
	elif y <= -9.5e+32:
		tmp = 0.125 * x
	elif y <= -6.5e-59:
		tmp = t
	elif y <= -2.5e-104:
		tmp = 0.125 * x
	elif y <= -3.6e-207:
		tmp = t
	elif y <= -1.4e-302:
		tmp = 0.125 * x
	elif y <= 4.7e-107:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y * -0.5))
	tmp = 0.0
	if (y <= -1.9e+71)
		tmp = t_1;
	elseif (y <= -9.5e+32)
		tmp = Float64(0.125 * x);
	elseif (y <= -6.5e-59)
		tmp = t;
	elseif (y <= -2.5e-104)
		tmp = Float64(0.125 * x);
	elseif (y <= -3.6e-207)
		tmp = t;
	elseif (y <= -1.4e-302)
		tmp = Float64(0.125 * x);
	elseif (y <= 4.7e-107)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y * -0.5);
	tmp = 0.0;
	if (y <= -1.9e+71)
		tmp = t_1;
	elseif (y <= -9.5e+32)
		tmp = 0.125 * x;
	elseif (y <= -6.5e-59)
		tmp = t;
	elseif (y <= -2.5e-104)
		tmp = 0.125 * x;
	elseif (y <= -3.6e-207)
		tmp = t;
	elseif (y <= -1.4e-302)
		tmp = 0.125 * x;
	elseif (y <= 4.7e-107)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+71], t$95$1, If[LessEqual[y, -9.5e+32], N[(0.125 * x), $MachinePrecision], If[LessEqual[y, -6.5e-59], t, If[LessEqual[y, -2.5e-104], N[(0.125 * x), $MachinePrecision], If[LessEqual[y, -3.6e-207], t, If[LessEqual[y, -1.4e-302], N[(0.125 * x), $MachinePrecision], If[LessEqual[y, 4.7e-107], t, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e71 or 4.69999999999999998e-107 < y

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*r* 62.6%

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

   6. Simplified 62.6%

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

   if -1.9e71 < y < -9.50000000000000006e32 or -6.50000000000000017e-59 < y < -2.49999999999999989e-104 or -3.5999999999999997e-207 < y < -1.4e-302

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 55.5%

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

   if -9.50000000000000006e32 < y < -6.50000000000000017e-59 or -2.49999999999999989e-104 < y < -3.5999999999999997e-207 or -1.4e-302 < y < 4.69999999999999998e-107

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 43.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-59}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-104}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-207}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-107}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot 0.5\\ \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t - t_1\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+72}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* z y) 0.5)))
   (if (<= (* z y) -5e+166)
     (- t t_1)
     (if (<= (* z y) 5e+72) (+ t (* 0.125 x)) (- (* 0.125 x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * 0.5;
	double tmp;
	if ((z * y) <= -5e+166) {
		tmp = t - t_1;
	} else if ((z * y) <= 5e+72) {
		tmp = t + (0.125 * x);
	} else {
		tmp = (0.125 * x) - 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 = (z * y) * 0.5d0
    if ((z * y) <= (-5d+166)) then
        tmp = t - t_1
    else if ((z * y) <= 5d+72) then
        tmp = t + (0.125d0 * x)
    else
        tmp = (0.125d0 * x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) * 0.5;
	double tmp;
	if ((z * y) <= -5e+166) {
		tmp = t - t_1;
	} else if ((z * y) <= 5e+72) {
		tmp = t + (0.125 * x);
	} else {
		tmp = (0.125 * x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) * 0.5
	tmp = 0
	if (z * y) <= -5e+166:
		tmp = t - t_1
	elif (z * y) <= 5e+72:
		tmp = t + (0.125 * x)
	else:
		tmp = (0.125 * x) - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) * 0.5)
	tmp = 0.0
	if (Float64(z * y) <= -5e+166)
		tmp = Float64(t - t_1);
	elseif (Float64(z * y) <= 5e+72)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = Float64(Float64(0.125 * x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) * 0.5;
	tmp = 0.0;
	if ((z * y) <= -5e+166)
		tmp = t - t_1;
	elseif ((z * y) <= 5e+72)
		tmp = t + (0.125 * x);
	else
		tmp = (0.125 * x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -5e+166], N[(t - t$95$1), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 5e+72], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.0000000000000002e166

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 97.8%

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

   if -5.0000000000000002e166 < (*.f64 y z) < 4.99999999999999992e72

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 91.5%

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

   if 4.99999999999999992e72 < (*.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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 92.8%

      \[\leadsto \color{blue}{0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+72}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - \left(z \cdot y\right) \cdot 0.5\\ \end{array} \]

Alternative 4: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+166} \lor \neg \left(z \cdot y \leq 10^{+60}\right):\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z y) -5e+166) (not (<= (* z y) 1e+60)))
   (- t (* (* z y) 0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -5e+166) || !((z * y) <= 1e+60)) {
		tmp = t - ((z * y) * 0.5);
	} 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 (((z * y) <= (-5d+166)) .or. (.not. ((z * y) <= 1d+60))) then
        tmp = t - ((z * y) * 0.5d0)
    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 (((z * y) <= -5e+166) || !((z * y) <= 1e+60)) {
		tmp = t - ((z * y) * 0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * y) <= -5e+166) or not ((z * y) <= 1e+60):
		tmp = t - ((z * y) * 0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * y) <= -5e+166) || !(Float64(z * y) <= 1e+60))
		tmp = Float64(t - Float64(Float64(z * y) * 0.5));
	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 (((z * y) <= -5e+166) || ~(((z * y) <= 1e+60)))
		tmp = t - ((z * y) * 0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * y), $MachinePrecision], -5e+166], N[Not[LessEqual[N[(z * y), $MachinePrecision], 1e+60]], $MachinePrecision]], N[(t - N[(N[(z * y), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.0000000000000002e166 or 9.9999999999999995e59 < (*.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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 93.2%

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

   if -5.0000000000000002e166 < (*.f64 y z) < 9.9999999999999995e59

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 91.4%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{+166} \lor \neg \left(z \cdot y \leq 10^{+60}\right):\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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) - (z * (y / 2.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(N[(0.125 * x), $MachinePrecision] - N[(z * N[(y / 2.0), $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. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

   4. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

   5. sub-neg 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

   6. +-commutative 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

   7. associate--r+ 100.0%

      \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   8. neg-sub0 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. distribute-rgt-neg-in 100.0%

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

   11. metadata-eval 100.0%

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

   12. remove-double-neg 100.0%

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

   13. associate-*l/ 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 6: 71.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+122} \lor \neg \left(y \leq 1.35 \cdot 10^{-58}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e+122) (not (<= y 1.35e-58)))
   (* z (* y -0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e+122) || !(y <= 1.35e-58)) {
		tmp = z * (y * -0.5);
	} 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 <= (-1.25d+122)) .or. (.not. (y <= 1.35d-58))) then
        tmp = z * (y * (-0.5d0))
    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 <= -1.25e+122) || !(y <= 1.35e-58)) {
		tmp = z * (y * -0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e+122) or not (y <= 1.35e-58):
		tmp = z * (y * -0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e+122) || !(y <= 1.35e-58))
		tmp = Float64(z * Float64(y * -0.5));
	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 <= -1.25e+122) || ~((y <= 1.35e-58)))
		tmp = z * (y * -0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e+122], N[Not[LessEqual[y, 1.35e-58]], $MachinePrecision]], N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999997e122 or 1.3499999999999999e-58 < y

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-*r* 65.6%

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

   6. Simplified 65.6%

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

   if -1.24999999999999997e122 < y < 1.3499999999999999e-58

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 82.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+122} \lor \neg \left(y \leq 1.35 \cdot 10^{-58}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 7: 49.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+109}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.4e+49) t (if (<= t 3.5e+109) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e+49) {
		tmp = t;
	} else if (t <= 3.5e+109) {
		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 (t <= (-3.4d+49)) then
        tmp = t
    else if (t <= 3.5d+109) 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 (t <= -3.4e+49) {
		tmp = t;
	} else if (t <= 3.5e+109) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.4e+49:
		tmp = t
	elif t <= 3.5e+109:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.4e+49)
		tmp = t;
	elseif (t <= 3.5e+109)
		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 (t <= -3.4e+49)
		tmp = t;
	elseif (t <= 3.5e+109)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.4e+49], t, If[LessEqual[t, 3.5e+109], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e49 or 3.49999999999999983e109 < t

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 61.9%

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

   if -3.4000000000000001e49 < t < 3.49999999999999983e109

   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. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

      4. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

      5. sub-neg 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

      6. +-commutative 100.0%

         \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

      7. associate--r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. remove-double-neg 100.0%

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

      13. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 44.3%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+109}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 34.5% 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. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]

   4. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]

   5. sub-neg 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]

   6. +-commutative 100.0%

      \[\leadsto \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]

   7. associate--r+ 100.0%

      \[\leadsto \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]

   8. neg-sub0 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. distribute-rgt-neg-in 100.0%

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

   11. metadata-eval 100.0%

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

   12. remove-double-neg 100.0%

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

   13. associate-*l/ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in t around inf 31.9%

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

5. Final simplification 31.9%

   \[\leadsto t \]

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 2023200 
(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))