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

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

Alternatives: 10

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

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

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: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{-112} \lor \neg \left(y \cdot z \leq 10^{-33} \lor \neg \left(y \cdot z \leq 10^{-11}\right) \land y \cdot z \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -1e-112)
         (not
          (or (<= (* y z) 1e-33)
              (and (not (<= (* y z) 1e-11)) (<= (* y z) 2e+61)))))
   (- t (* (* y z) 0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1e-112) || !(((y * z) <= 1e-33) || (!((y * z) <= 1e-11) && ((y * z) <= 2e+61)))) {
		tmp = t - ((y * z) * 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 * z) <= (-1d-112)) .or. (.not. ((y * z) <= 1d-33) .or. (.not. ((y * z) <= 1d-11)) .and. ((y * z) <= 2d+61))) then
        tmp = t - ((y * z) * 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 * z) <= -1e-112) || !(((y * z) <= 1e-33) || (!((y * z) <= 1e-11) && ((y * z) <= 2e+61)))) {
		tmp = t - ((y * z) * 0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -1e-112) or not (((y * z) <= 1e-33) or (not ((y * z) <= 1e-11) and ((y * z) <= 2e+61))):
		tmp = t - ((y * z) * 0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -1e-112) || !((Float64(y * z) <= 1e-33) || (!(Float64(y * z) <= 1e-11) && (Float64(y * z) <= 2e+61))))
		tmp = Float64(t - Float64(Float64(y * z) * 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 * z) <= -1e-112) || ~((((y * z) <= 1e-33) || (~(((y * z) <= 1e-11)) && ((y * z) <= 2e+61)))))
		tmp = t - ((y * z) * 0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1e-112], N[Not[Or[LessEqual[N[(y * z), $MachinePrecision], 1e-33], And[N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e-11]], $MachinePrecision], LessEqual[N[(y * z), $MachinePrecision], 2e+61]]]], $MachinePrecision]], N[(t - N[(N[(y * z), $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) < -9.9999999999999995e-113 or 1.0000000000000001e-33 < (*.f64 y z) < 9.99999999999999939e-12 or 1.9999999999999999e61 < (*.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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 83.3%

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

   if -9.9999999999999995e-113 < (*.f64 y z) < 1.0000000000000001e-33 or 9.99999999999999939e-12 < (*.f64 y z) < 1.9999999999999999e61

   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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 y around 0 96.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{-112} \lor \neg \left(y \cdot z \leq 10^{-33} \lor \neg \left(y \cdot z \leq 10^{-11}\right) \land y \cdot z \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 3: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26500000000000 \lor \neg \left(z \leq 1.05 \cdot 10^{+94} \lor \neg \left(z \leq 2.1 \cdot 10^{+136}\right) \land \left(z \leq 6.6 \cdot 10^{+180} \lor \neg \left(z \leq 5 \cdot 10^{+232}\right) \land z \leq 9 \cdot 10^{+244}\right)\right):\\ \;\;\;\;\frac{y}{-2} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -26500000000000.0)
         (not
          (or (<= z 1.05e+94)
              (and (not (<= z 2.1e+136))
                   (or (<= z 6.6e+180)
                       (and (not (<= z 5e+232)) (<= z 9e+244)))))))
   (* (/ y -2.0) z)
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -26500000000000.0) || !((z <= 1.05e+94) || (!(z <= 2.1e+136) && ((z <= 6.6e+180) || (!(z <= 5e+232) && (z <= 9e+244)))))) {
		tmp = (y / -2.0) * 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 ((z <= (-26500000000000.0d0)) .or. (.not. (z <= 1.05d+94) .or. (.not. (z <= 2.1d+136)) .and. (z <= 6.6d+180) .or. (.not. (z <= 5d+232)) .and. (z <= 9d+244))) then
        tmp = (y / (-2.0d0)) * 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 ((z <= -26500000000000.0) || !((z <= 1.05e+94) || (!(z <= 2.1e+136) && ((z <= 6.6e+180) || (!(z <= 5e+232) && (z <= 9e+244)))))) {
		tmp = (y / -2.0) * z;
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -26500000000000.0) or not ((z <= 1.05e+94) or (not (z <= 2.1e+136) and ((z <= 6.6e+180) or (not (z <= 5e+232) and (z <= 9e+244))))):
		tmp = (y / -2.0) * z
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -26500000000000.0) || !((z <= 1.05e+94) || (!(z <= 2.1e+136) && ((z <= 6.6e+180) || (!(z <= 5e+232) && (z <= 9e+244))))))
		tmp = Float64(Float64(y / -2.0) * 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 ((z <= -26500000000000.0) || ~(((z <= 1.05e+94) || (~((z <= 2.1e+136)) && ((z <= 6.6e+180) || (~((z <= 5e+232)) && (z <= 9e+244)))))))
		tmp = (y / -2.0) * z;
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -26500000000000.0], N[Not[Or[LessEqual[z, 1.05e+94], And[N[Not[LessEqual[z, 2.1e+136]], $MachinePrecision], Or[LessEqual[z, 6.6e+180], And[N[Not[LessEqual[z, 5e+232]], $MachinePrecision], LessEqual[z, 9e+244]]]]]], $MachinePrecision]], N[(N[(y / -2.0), $MachinePrecision] * z), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e13 or 1.04999999999999995e94 < z < 2.0999999999999999e136 or 6.59999999999999978e180 < z < 4.99999999999999987e232 or 9.0000000000000005e244 < 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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 y around inf 66.0%

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

      1. metadata-eval 66.0%

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

      2. /-rgt-identity 66.0%

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

      3. associate-/r/ 65.9%

         \[\leadsto \frac{1}{-2} \cdot \color{blue}{\frac{y}{\frac{1}{z}}} \]

      4. times-frac 65.9%

         \[\leadsto \color{blue}{\frac{1 \cdot y}{-2 \cdot \frac{1}{z}}} \]

      5. *-lft-identity 65.9%

         \[\leadsto \frac{\color{blue}{y}}{-2 \cdot \frac{1}{z}} \]

      6. associate-/l/ 65.9%

         \[\leadsto \color{blue}{\frac{\frac{y}{\frac{1}{z}}}{-2}} \]

      7. associate-/r/ 66.0%

         \[\leadsto \frac{\color{blue}{\frac{y}{1} \cdot z}}{-2} \]

      8. /-rgt-identity 66.0%

         \[\leadsto \frac{\color{blue}{y} \cdot z}{-2} \]

      9. associate-*l/ 66.0%

         \[\leadsto \color{blue}{\frac{y}{-2} \cdot z} \]

      10. *-commutative 66.0%

          \[\leadsto \color{blue}{z \cdot \frac{y}{-2}} \]

   6. Simplified 66.0%

      \[\leadsto \color{blue}{z \cdot \frac{y}{-2}} \]

   if -2.65e13 < z < 1.04999999999999995e94 or 2.0999999999999999e136 < z < 6.59999999999999978e180 or 4.99999999999999987e232 < z < 9.0000000000000005e244

   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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 y around 0 80.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26500000000000 \lor \neg \left(z \leq 1.05 \cdot 10^{+94} \lor \neg \left(z \leq 2.1 \cdot 10^{+136}\right) \land \left(z \leq 6.6 \cdot 10^{+180} \lor \neg \left(z \leq 5 \cdot 10^{+232}\right) \land z \leq 9 \cdot 10^{+244}\right)\right):\\ \;\;\;\;\frac{y}{-2} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot 0.5\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+102} \lor \neg \left(x \leq 1.65 \cdot 10^{-63}\right):\\ \;\;\;\;0.125 \cdot x - t_1\\ \mathbf{else}:\\ \;\;\;\;t - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) 0.5)))
   (if (or (<= x -5.2e+102) (not (<= x 1.65e-63)))
     (- (* 0.125 x) t_1)
     (- t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * 0.5;
	double tmp;
	if ((x <= -5.2e+102) || !(x <= 1.65e-63)) {
		tmp = (0.125 * x) - t_1;
	} else {
		tmp = t - 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 = (y * z) * 0.5d0
    if ((x <= (-5.2d+102)) .or. (.not. (x <= 1.65d-63))) then
        tmp = (0.125d0 * x) - t_1
    else
        tmp = t - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * 0.5;
	double tmp;
	if ((x <= -5.2e+102) || !(x <= 1.65e-63)) {
		tmp = (0.125 * x) - t_1;
	} else {
		tmp = t - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * 0.5
	tmp = 0
	if (x <= -5.2e+102) or not (x <= 1.65e-63):
		tmp = (0.125 * x) - t_1
	else:
		tmp = t - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) * 0.5)
	tmp = 0.0
	if ((x <= -5.2e+102) || !(x <= 1.65e-63))
		tmp = Float64(Float64(0.125 * x) - t_1);
	else
		tmp = Float64(t - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) * 0.5;
	tmp = 0.0;
	if ((x <= -5.2e+102) || ~((x <= 1.65e-63)))
		tmp = (0.125 * x) - t_1;
	else
		tmp = t - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]}, If[Or[LessEqual[x, -5.2e+102], N[Not[LessEqual[x, 1.65e-63]], $MachinePrecision]], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.20000000000000013e102 or 1.64999999999999997e-63 < 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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 0 83.1%

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

   if -5.20000000000000013e102 < x < 1.64999999999999997e-63

   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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 90.5%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+102} \lor \neg \left(x \leq 1.65 \cdot 10^{-63}\right):\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]

Alternative 5: 49.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{-2} \cdot z\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-260}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-59}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y -2.0) z)))
   (if (<= y -4.3e+83)
     t_1
     (if (<= y -2.75e-260) t (if (<= y 1.7e-59) (* 0.125 x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / -2.0) * z;
	double tmp;
	if (y <= -4.3e+83) {
		tmp = t_1;
	} else if (y <= -2.75e-260) {
		tmp = t;
	} else if (y <= 1.7e-59) {
		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 = (y / (-2.0d0)) * z
    if (y <= (-4.3d+83)) then
        tmp = t_1
    else if (y <= (-2.75d-260)) then
        tmp = t
    else if (y <= 1.7d-59) 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 = (y / -2.0) * z;
	double tmp;
	if (y <= -4.3e+83) {
		tmp = t_1;
	} else if (y <= -2.75e-260) {
		tmp = t;
	} else if (y <= 1.7e-59) {
		tmp = 0.125 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / -2.0) * z
	tmp = 0
	if y <= -4.3e+83:
		tmp = t_1
	elif y <= -2.75e-260:
		tmp = t
	elif y <= 1.7e-59:
		tmp = 0.125 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / -2.0) * z)
	tmp = 0.0
	if (y <= -4.3e+83)
		tmp = t_1;
	elseif (y <= -2.75e-260)
		tmp = t;
	elseif (y <= 1.7e-59)
		tmp = Float64(0.125 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / -2.0) * z;
	tmp = 0.0;
	if (y <= -4.3e+83)
		tmp = t_1;
	elseif (y <= -2.75e-260)
		tmp = t;
	elseif (y <= 1.7e-59)
		tmp = 0.125 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / -2.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -4.3e+83], t$95$1, If[LessEqual[y, -2.75e-260], t, If[LessEqual[y, 1.7e-59], N[(0.125 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3e83 or 1.70000000000000009e-59 < 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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 y around inf 53.7%

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

      1. metadata-eval 53.7%

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

      2. /-rgt-identity 53.7%

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

      3. associate-/r/ 53.6%

         \[\leadsto \frac{1}{-2} \cdot \color{blue}{\frac{y}{\frac{1}{z}}} \]

      4. times-frac 53.6%

         \[\leadsto \color{blue}{\frac{1 \cdot y}{-2 \cdot \frac{1}{z}}} \]

      5. *-lft-identity 53.6%

         \[\leadsto \frac{\color{blue}{y}}{-2 \cdot \frac{1}{z}} \]

      6. associate-/l/ 53.6%

         \[\leadsto \color{blue}{\frac{\frac{y}{\frac{1}{z}}}{-2}} \]

      7. associate-/r/ 53.7%

         \[\leadsto \frac{\color{blue}{\frac{y}{1} \cdot z}}{-2} \]

      8. /-rgt-identity 53.7%

         \[\leadsto \frac{\color{blue}{y} \cdot z}{-2} \]

      9. associate-*l/ 53.7%

         \[\leadsto \color{blue}{\frac{y}{-2} \cdot z} \]

      10. *-commutative 53.7%

          \[\leadsto \color{blue}{z \cdot \frac{y}{-2}} \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{z \cdot \frac{y}{-2}} \]

   if -4.3e83 < y < -2.75000000000000012e-260

   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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 50.5%

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

   if -2.75000000000000012e-260 < y < 1.70000000000000009e-59

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. 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 50.8%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{-2} \cdot z\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-260}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-59}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-2} \cdot z\\ \end{array} \]

Alternative 6: 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. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

   4. 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 7: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t + ((0.125 * x) - ((y * z) / 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) - ((y * z) / 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 8: 48.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+88} \lor \neg \left(x \leq 2.65 \cdot 10^{-55}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1e+88) (not (<= x 2.65e-55))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e+88) || !(x <= 2.65e-55)) {
		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 <= (-1d+88)) .or. (.not. (x <= 2.65d-55))) 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 <= -1e+88) || !(x <= 2.65e-55)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1e+88) or not (x <= 2.65e-55):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1e+88) || !(x <= 2.65e-55))
		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 <= -1e+88) || ~((x <= 2.65e-55)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1e+88], N[Not[LessEqual[x, 2.65e-55]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999959e87 or 2.6500000000000001e-55 < 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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 61.7%

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

   if -9.99999999999999959e87 < x < 2.6500000000000001e-55

   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. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. 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 t around inf 47.9%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+88} \lor \neg \left(x \leq 2.65 \cdot 10^{-55}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 2.3% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 0.0)

C

double code(double x, double y, double z, double t) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0;
}

Python

def code(x, y, z, t):
	return 0.0

Julia

function code(x, y, z, t)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_] := 0.0

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. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

   4. 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 y around inf 35.1%

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

   1. metadata-eval 35.1%

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

   2. /-rgt-identity 35.1%

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

   3. associate-/r/ 35.0%

      \[\leadsto \frac{1}{-2} \cdot \color{blue}{\frac{y}{\frac{1}{z}}} \]

   4. times-frac 35.0%

      \[\leadsto \color{blue}{\frac{1 \cdot y}{-2 \cdot \frac{1}{z}}} \]

   5. *-lft-identity 35.0%

      \[\leadsto \frac{\color{blue}{y}}{-2 \cdot \frac{1}{z}} \]

   6. associate-/l/ 35.0%

      \[\leadsto \color{blue}{\frac{\frac{y}{\frac{1}{z}}}{-2}} \]

   7. associate-/r/ 35.1%

      \[\leadsto \frac{\color{blue}{\frac{y}{1} \cdot z}}{-2} \]

   8. /-rgt-identity 35.1%

      \[\leadsto \frac{\color{blue}{y} \cdot z}{-2} \]

   9. associate-*l/ 35.1%

      \[\leadsto \color{blue}{\frac{y}{-2} \cdot z} \]

   10. *-commutative 35.1%

       \[\leadsto \color{blue}{z \cdot \frac{y}{-2}} \]

6. Simplified 35.1%

   \[\leadsto \color{blue}{z \cdot \frac{y}{-2}} \]

7. Taylor expanded in z around 0 35.1%

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

9. Simplified 2.4%

   \[\leadsto \color{blue}{0} \]

10. Final simplification 2.4%

    \[\leadsto 0 \]

Alternative 10: 32.8% 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. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

   4. 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 35.0%

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

5. Final simplification 35.0%

   \[\leadsto t \]

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 2023320 
(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))