Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.8% → 91.5%

Time: 14.4s

Alternatives: 11

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t_1}}\right)}^{3} - y \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x}{t_1} - \frac{y \cdot z}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (pow (/ (cbrt x) (cbrt t_1)) 3.0) (* y (/ z t_1)))
     (if (<= t_2 5e+280) (- (/ x t_1) (/ (* y z) t_1)) (/ (- y (/ x z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = pow((cbrt(x) / cbrt(t_1)), 3.0) - (y * (z / t_1));
	} else if (t_2 <= 5e+280) {
		tmp = (x / t_1) - ((y * z) / t_1);
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = Math.pow((Math.cbrt(x) / Math.cbrt(t_1)), 3.0) - (y * (z / t_1));
	} else if (t_2 <= 5e+280) {
		tmp = (x / t_1) - ((y * z) / t_1);
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64((Float64(cbrt(x) / cbrt(t_1)) ^ 3.0) - Float64(y * Float64(z / t_1)));
	elseif (t_2 <= 5e+280)
		tmp = Float64(Float64(x / t_1) - Float64(Float64(y * z) / t_1));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[Power[N[(N[Power[x, 1/3], $MachinePrecision] / N[Power[t$95$1, 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision] - N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+280], N[(N[(x / t$95$1), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0

   1. Initial program 68.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 68.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-sub 68.2%

         \[\leadsto \color{blue}{\frac{x}{t - z \cdot a} - \frac{y \cdot z}{t - z \cdot a}} \]

      2. sub-neg 68.2%

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

      3. add-cube-cbrt 68.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{t - z \cdot a} + \left(-\frac{y \cdot z}{t - z \cdot a}\right) \]

      4. add-cube-cbrt 68.2%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}\right) \cdot \sqrt[3]{t - z \cdot a}}} + \left(-\frac{y \cdot z}{t - z \cdot a}\right) \]

      5. times-frac 68.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}} + \left(-\frac{y \cdot z}{t - z \cdot a}\right) \]

      6. fma-def 68.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}}, \frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}, -\frac{y \cdot z}{t - z \cdot a}\right)} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(\sqrt[3]{x}\right)}^{2}}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}}, \frac{\sqrt[3]{x}}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}}, -\frac{y}{\frac{\mathsf{fma}\left(a, -z, t\right)}{z}}\right)} \]
   7. Step-by-step derivation

      1. fma-neg 100.0%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}} - \frac{y}{\frac{\mathsf{fma}\left(a, -z, t\right)}{z}}} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x}}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}} \cdot \frac{{\left(\sqrt[3]{x}\right)}^{2}}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}}} - \frac{y}{\frac{\mathsf{fma}\left(a, -z, t\right)}{z}} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}\right)}^{3} - y \cdot \frac{z}{t - z \cdot a}} \]

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.0000000000000002e280

   1. Initial program 94.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 94.0%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 94.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z} + \frac{x}{t - a \cdot z}} \]

   if 5.0000000000000002e280 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 32.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 25.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y \cdot z}{a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 25.0%

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

      2. neg-mul-1 25.0%

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

      3. *-commutative 25.0%

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

      4. associate-/r* 26.4%

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

      5. sub-neg 26.4%

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

      6. distribute-neg-in 26.4%

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

      7. remove-double-neg 26.4%

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

   7. Simplified 26.4%

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

   8. Taylor expanded in x around 0 89.7%

      \[\leadsto \frac{\color{blue}{y + -1 \cdot \frac{x}{z}}}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg 89.7%

         \[\leadsto \frac{y + \color{blue}{\left(-\frac{x}{z}\right)}}{a} \]

      2. unsub-neg 89.7%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   10. Simplified 89.7%

       \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}\right)}^{3} - y \cdot \frac{z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-56}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 19.5:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+94} \lor \neg \left(z \leq 2.3 \cdot 10^{+130}\right) \land z \leq 4.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+127)
   (/ y a)
   (if (<= z -3.85e-22)
     (* y (/ (- z) t))
     (if (<= z -1.95e-56)
       (/ (- x) (* z a))
       (if (<= z 19.5)
         (/ x t)
         (if (or (<= z 2.1e+94) (and (not (<= z 2.3e+130)) (<= z 4.2e+185)))
           (/ (/ (- x) z) a)
           (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+127) {
		tmp = y / a;
	} else if (z <= -3.85e-22) {
		tmp = y * (-z / t);
	} else if (z <= -1.95e-56) {
		tmp = -x / (z * a);
	} else if (z <= 19.5) {
		tmp = x / t;
	} else if ((z <= 2.1e+94) || (!(z <= 2.3e+130) && (z <= 4.2e+185))) {
		tmp = (-x / z) / a;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.95d+127)) then
        tmp = y / a
    else if (z <= (-3.85d-22)) then
        tmp = y * (-z / t)
    else if (z <= (-1.95d-56)) then
        tmp = -x / (z * a)
    else if (z <= 19.5d0) then
        tmp = x / t
    else if ((z <= 2.1d+94) .or. (.not. (z <= 2.3d+130)) .and. (z <= 4.2d+185)) then
        tmp = (-x / z) / a
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+127) {
		tmp = y / a;
	} else if (z <= -3.85e-22) {
		tmp = y * (-z / t);
	} else if (z <= -1.95e-56) {
		tmp = -x / (z * a);
	} else if (z <= 19.5) {
		tmp = x / t;
	} else if ((z <= 2.1e+94) || (!(z <= 2.3e+130) && (z <= 4.2e+185))) {
		tmp = (-x / z) / a;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+127:
		tmp = y / a
	elif z <= -3.85e-22:
		tmp = y * (-z / t)
	elif z <= -1.95e-56:
		tmp = -x / (z * a)
	elif z <= 19.5:
		tmp = x / t
	elif (z <= 2.1e+94) or (not (z <= 2.3e+130) and (z <= 4.2e+185)):
		tmp = (-x / z) / a
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+127)
		tmp = Float64(y / a);
	elseif (z <= -3.85e-22)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= -1.95e-56)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 19.5)
		tmp = Float64(x / t);
	elseif ((z <= 2.1e+94) || (!(z <= 2.3e+130) && (z <= 4.2e+185)))
		tmp = Float64(Float64(Float64(-x) / z) / a);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+127)
		tmp = y / a;
	elseif (z <= -3.85e-22)
		tmp = y * (-z / t);
	elseif (z <= -1.95e-56)
		tmp = -x / (z * a);
	elseif (z <= 19.5)
		tmp = x / t;
	elseif ((z <= 2.1e+94) || (~((z <= 2.3e+130)) && (z <= 4.2e+185)))
		tmp = (-x / z) / a;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+127], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.85e-22], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-56], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 19.5], N[(x / t), $MachinePrecision], If[Or[LessEqual[z, 2.1e+94], And[N[Not[LessEqual[z, 2.3e+130]], $MachinePrecision], LessEqual[z, 4.2e+185]]], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.94999999999999991e127 or 2.09999999999999989e94 < z < 2.30000000000000021e130 or 4.2e185 < z

   1. Initial program 57.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 57.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -1.94999999999999991e127 < z < -3.8500000000000001e-22

   1. Initial program 93.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 93.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 70.0%

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

   6. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-*l/ 52.4%

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

      4. distribute-rgt-neg-in 52.4%

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

   8. Simplified 52.4%

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

   if -3.8500000000000001e-22 < z < -1.95e-56

   1. Initial program 100.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.7%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 67.7%

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

      2. neg-mul-1 67.7%

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

      3. *-commutative 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{a \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 54.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{a \cdot z}} \]

      2. neg-mul-1 54.1%

         \[\leadsto \frac{\color{blue}{-x}}{a \cdot z} \]

   10. Simplified 54.1%

       \[\leadsto \color{blue}{\frac{-x}{a \cdot z}} \]

   if -1.95e-56 < z < 19.5

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 64.9%

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

   if 19.5 < z < 2.09999999999999989e94 or 2.30000000000000021e130 < z < 4.2e185

   1. Initial program 86.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y \cdot z}{a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 66.3%

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

      2. neg-mul-1 66.3%

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

      3. *-commutative 66.3%

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

      4. associate-/r* 70.6%

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

      5. sub-neg 70.6%

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

      6. distribute-neg-in 70.6%

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

      7. remove-double-neg 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in x around inf 52.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg 52.1%

         \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{a} \]

      2. distribute-neg-frac 52.1%

         \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{a} \]

   10. Simplified 52.1%

       \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-56}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 19.5:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+94} \lor \neg \left(z \leq 2.3 \cdot 10^{+130}\right) \land z \leq 4.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z a))))
   (if (<= z -2.1e+127)
     (/ y a)
     (if (<= z -8.8e-17)
       (* y (/ (- z) t))
       (if (<= z -3.1e-56)
         t_1
         (if (<= z 0.00036) (/ x t) (if (<= z 6e+93) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (z * a);
	double tmp;
	if (z <= -2.1e+127) {
		tmp = y / a;
	} else if (z <= -8.8e-17) {
		tmp = y * (-z / t);
	} else if (z <= -3.1e-56) {
		tmp = t_1;
	} else if (z <= 0.00036) {
		tmp = x / t;
	} else if (z <= 6e+93) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (z * a)
    if (z <= (-2.1d+127)) then
        tmp = y / a
    else if (z <= (-8.8d-17)) then
        tmp = y * (-z / t)
    else if (z <= (-3.1d-56)) then
        tmp = t_1
    else if (z <= 0.00036d0) then
        tmp = x / t
    else if (z <= 6d+93) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (z * a);
	double tmp;
	if (z <= -2.1e+127) {
		tmp = y / a;
	} else if (z <= -8.8e-17) {
		tmp = y * (-z / t);
	} else if (z <= -3.1e-56) {
		tmp = t_1;
	} else if (z <= 0.00036) {
		tmp = x / t;
	} else if (z <= 6e+93) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (z * a)
	tmp = 0
	if z <= -2.1e+127:
		tmp = y / a
	elif z <= -8.8e-17:
		tmp = y * (-z / t)
	elif z <= -3.1e-56:
		tmp = t_1
	elif z <= 0.00036:
		tmp = x / t
	elif z <= 6e+93:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(z * a))
	tmp = 0.0
	if (z <= -2.1e+127)
		tmp = Float64(y / a);
	elseif (z <= -8.8e-17)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= -3.1e-56)
		tmp = t_1;
	elseif (z <= 0.00036)
		tmp = Float64(x / t);
	elseif (z <= 6e+93)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (z * a);
	tmp = 0.0;
	if (z <= -2.1e+127)
		tmp = y / a;
	elseif (z <= -8.8e-17)
		tmp = y * (-z / t);
	elseif (z <= -3.1e-56)
		tmp = t_1;
	elseif (z <= 0.00036)
		tmp = x / t;
	elseif (z <= 6e+93)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+127], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.8e-17], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-56], t$95$1, If[LessEqual[z, 0.00036], N[(x / t), $MachinePrecision], If[LessEqual[z, 6e+93], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.09999999999999992e127 or 5.99999999999999957e93 < z

   1. Initial program 61.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 61.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.7%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -2.09999999999999992e127 < z < -8.8e-17

   1. Initial program 93.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 93.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 70.0%

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

   6. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-*l/ 52.4%

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

      4. distribute-rgt-neg-in 52.4%

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

   8. Simplified 52.4%

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

   if -8.8e-17 < z < -3.09999999999999987e-56 or 3.60000000000000023e-4 < z < 5.99999999999999957e93

   1. Initial program 91.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 91.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.3%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 69.3%

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

      2. neg-mul-1 69.3%

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

      3. *-commutative 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in x around inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{a \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 49.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{a \cdot z}} \]

      2. neg-mul-1 49.4%

         \[\leadsto \frac{\color{blue}{-x}}{a \cdot z} \]

   10. Simplified 49.4%

       \[\leadsto \color{blue}{\frac{-x}{a \cdot z}} \]

   if -3.09999999999999987e-56 < z < 3.60000000000000023e-4

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 64.9%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+93}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 840000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= t -8.5e-9)
     (/ (- x (* y z)) t)
     (if (<= t -2.1e-22)
       t_1
       (if (<= t -1.15e-44)
         (/ x (- t (* z a)))
         (if (<= t 840000000000.0) t_1 (- (/ x t) (/ z (/ t y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (t <= -8.5e-9) {
		tmp = (x - (y * z)) / t;
	} else if (t <= -2.1e-22) {
		tmp = t_1;
	} else if (t <= -1.15e-44) {
		tmp = x / (t - (z * a));
	} else if (t <= 840000000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (t <= (-8.5d-9)) then
        tmp = (x - (y * z)) / t
    else if (t <= (-2.1d-22)) then
        tmp = t_1
    else if (t <= (-1.15d-44)) then
        tmp = x / (t - (z * a))
    else if (t <= 840000000000.0d0) then
        tmp = t_1
    else
        tmp = (x / t) - (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (t <= -8.5e-9) {
		tmp = (x - (y * z)) / t;
	} else if (t <= -2.1e-22) {
		tmp = t_1;
	} else if (t <= -1.15e-44) {
		tmp = x / (t - (z * a));
	} else if (t <= 840000000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if t <= -8.5e-9:
		tmp = (x - (y * z)) / t
	elif t <= -2.1e-22:
		tmp = t_1
	elif t <= -1.15e-44:
		tmp = x / (t - (z * a))
	elif t <= 840000000000.0:
		tmp = t_1
	else:
		tmp = (x / t) - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (t <= -8.5e-9)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (t <= -2.1e-22)
		tmp = t_1;
	elseif (t <= -1.15e-44)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 840000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (t <= -8.5e-9)
		tmp = (x - (y * z)) / t;
	elseif (t <= -2.1e-22)
		tmp = t_1;
	elseif (t <= -1.15e-44)
		tmp = x / (t - (z * a));
	elseif (t <= 840000000000.0)
		tmp = t_1;
	else
		tmp = (x / t) - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -8.5e-9], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -2.1e-22], t$95$1, If[LessEqual[t, -1.15e-44], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 840000000000.0], t$95$1, N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.5e-9

   1. Initial program 86.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.4%

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

   if -8.5e-9 < t < -2.10000000000000008e-22 or -1.14999999999999999e-44 < t < 8.4e11

   1. Initial program 84.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y \cdot z}{a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. *-commutative 68.8%

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

      4. associate-/r* 71.3%

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

      5. sub-neg 71.3%

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

      6. distribute-neg-in 71.3%

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

      7. remove-double-neg 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x around 0 81.9%

      \[\leadsto \frac{\color{blue}{y + -1 \cdot \frac{x}{z}}}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg 81.9%

         \[\leadsto \frac{y + \color{blue}{\left(-\frac{x}{z}\right)}}{a} \]

      2. unsub-neg 81.9%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   10. Simplified 81.9%

       \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   if -2.10000000000000008e-22 < t < -1.14999999999999999e-44

   1. Initial program 87.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 88.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]

   if 8.4e11 < t

   1. Initial program 86.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. div-sub 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-/l* 83.3%

         \[\leadsto \frac{x}{t} - \color{blue}{\frac{z}{\frac{t}{y}}} \]

   7. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x}{t} - \frac{z}{\frac{t}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 840000000000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 11000000000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.2e-9)
   (/ (- x (* y z)) t)
   (if (<= t -7e-22)
     (- (/ y a) (/ x (* z a)))
     (if (<= t -7.5e-47)
       (/ x (- t (* z a)))
       (if (<= t 11000000000.0)
         (/ (- y (/ x z)) a)
         (- (/ x t) (/ z (/ t y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.2e-9) {
		tmp = (x - (y * z)) / t;
	} else if (t <= -7e-22) {
		tmp = (y / a) - (x / (z * a));
	} else if (t <= -7.5e-47) {
		tmp = x / (t - (z * a));
	} else if (t <= 11000000000.0) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8.2d-9)) then
        tmp = (x - (y * z)) / t
    else if (t <= (-7d-22)) then
        tmp = (y / a) - (x / (z * a))
    else if (t <= (-7.5d-47)) then
        tmp = x / (t - (z * a))
    else if (t <= 11000000000.0d0) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x / t) - (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.2e-9) {
		tmp = (x - (y * z)) / t;
	} else if (t <= -7e-22) {
		tmp = (y / a) - (x / (z * a));
	} else if (t <= -7.5e-47) {
		tmp = x / (t - (z * a));
	} else if (t <= 11000000000.0) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.2e-9:
		tmp = (x - (y * z)) / t
	elif t <= -7e-22:
		tmp = (y / a) - (x / (z * a))
	elif t <= -7.5e-47:
		tmp = x / (t - (z * a))
	elif t <= 11000000000.0:
		tmp = (y - (x / z)) / a
	else:
		tmp = (x / t) - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.2e-9)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (t <= -7e-22)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (t <= -7.5e-47)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 11000000000.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.2e-9)
		tmp = (x - (y * z)) / t;
	elseif (t <= -7e-22)
		tmp = (y / a) - (x / (z * a));
	elseif (t <= -7.5e-47)
		tmp = x / (t - (z * a));
	elseif (t <= 11000000000.0)
		tmp = (y - (x / z)) / a;
	else
		tmp = (x / t) - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.2e-9], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -7e-22], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-47], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 11000000000.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.2000000000000006e-9

   1. Initial program 86.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.4%

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

   if -8.2000000000000006e-9 < t < -7.00000000000000011e-22

   1. Initial program 79.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.2%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 75.2%

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

      2. neg-mul-1 75.2%

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

      3. *-commutative 75.2%

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

   7. Simplified 75.2%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{z \cdot \left(-a\right)}} \]
   8. Step-by-step derivation

      1. frac-2neg 75.2%

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

      2. div-inv 75.2%

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

      3. sub-neg 75.2%

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

      4. distribute-neg-in 75.2%

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

      5. *-commutative 75.2%

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

      6. distribute-lft-neg-in 75.2%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 36.9%

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

      9. sqr-neg 36.9%

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

      10. sqrt-unprod 36.9%

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

      11. add-sqr-sqrt 36.9%

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

      12. distribute-lft-neg-in 36.9%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 75.2%

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

      15. sqr-neg 75.2%

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

      16. sqrt-unprod 74.6%

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

      17. add-sqr-sqrt 75.2%

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

      18. distribute-rgt-neg-out 75.2%

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

      19. remove-double-neg 75.2%

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

   9. Applied egg-rr 75.2%

      \[\leadsto \color{blue}{\left(\left(-x\right) + z \cdot y\right) \cdot \frac{1}{z \cdot a}} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.2%

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

       2. *-rgt-identity 75.2%

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

       3. +-commutative 75.2%

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

       4. unsub-neg 75.2%

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

       5. *-commutative 75.2%

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

   11. Simplified 75.2%

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

   12. Taylor expanded in z around 0 95.2%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}} \]
   13. Step-by-step derivation

       1. +-commutative 95.2%

          \[\leadsto \color{blue}{\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}} \]

       2. mul-1-neg 95.2%

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

       3. associate-/l/ 94.9%

          \[\leadsto \frac{y}{a} + \left(-\color{blue}{\frac{\frac{x}{z}}{a}}\right) \]

       4. unsub-neg 94.9%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{z}}{a}} \]

       5. associate-/l/ 95.2%

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

   14. Simplified 95.2%

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

   if -7.00000000000000011e-22 < t < -7.49999999999999969e-47

   1. Initial program 87.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 88.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]

   if -7.49999999999999969e-47 < t < 1.1e10

   1. Initial program 84.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 84.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y \cdot z}{a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 68.6%

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

      2. neg-mul-1 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-/r* 71.1%

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

      5. sub-neg 71.1%

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

      6. distribute-neg-in 71.1%

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

      7. remove-double-neg 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in x around 0 81.4%

      \[\leadsto \frac{\color{blue}{y + -1 \cdot \frac{x}{z}}}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg 81.4%

         \[\leadsto \frac{y + \color{blue}{\left(-\frac{x}{z}\right)}}{a} \]

      2. unsub-neg 81.4%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   10. Simplified 81.4%

       \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   if 1.1e10 < t

   1. Initial program 86.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. div-sub 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-/l* 83.3%

         \[\leadsto \frac{x}{t} - \color{blue}{\frac{z}{\frac{t}{y}}} \]

   7. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x}{t} - \frac{z}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 11000000000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 12500000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (/ (- x (* y z)) t)))
   (if (<= t -8.2e-9)
     t_2
     (if (<= t -5.5e-21)
       t_1
       (if (<= t -5.1e-46)
         (/ x (- t (* z a)))
         (if (<= t 12500000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (t <= -8.2e-9) {
		tmp = t_2;
	} else if (t <= -5.5e-21) {
		tmp = t_1;
	} else if (t <= -5.1e-46) {
		tmp = x / (t - (z * a));
	} else if (t <= 12500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    t_2 = (x - (y * z)) / t
    if (t <= (-8.2d-9)) then
        tmp = t_2
    else if (t <= (-5.5d-21)) then
        tmp = t_1
    else if (t <= (-5.1d-46)) then
        tmp = x / (t - (z * a))
    else if (t <= 12500000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (t <= -8.2e-9) {
		tmp = t_2;
	} else if (t <= -5.5e-21) {
		tmp = t_1;
	} else if (t <= -5.1e-46) {
		tmp = x / (t - (z * a));
	} else if (t <= 12500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = (x - (y * z)) / t
	tmp = 0
	if t <= -8.2e-9:
		tmp = t_2
	elif t <= -5.5e-21:
		tmp = t_1
	elif t <= -5.1e-46:
		tmp = x / (t - (z * a))
	elif t <= 12500000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (t <= -8.2e-9)
		tmp = t_2;
	elseif (t <= -5.5e-21)
		tmp = t_1;
	elseif (t <= -5.1e-46)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 12500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = (x - (y * z)) / t;
	tmp = 0.0;
	if (t <= -8.2e-9)
		tmp = t_2;
	elseif (t <= -5.5e-21)
		tmp = t_1;
	elseif (t <= -5.1e-46)
		tmp = x / (t - (z * a));
	elseif (t <= 12500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -8.2e-9], t$95$2, If[LessEqual[t, -5.5e-21], t$95$1, If[LessEqual[t, -5.1e-46], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 12500000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2000000000000006e-9 or 1.25e10 < t

   1. Initial program 86.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.4%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.1%

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

   if -8.2000000000000006e-9 < t < -5.49999999999999977e-21 or -5.0999999999999997e-46 < t < 1.25e10

   1. Initial program 84.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y \cdot z}{a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. *-commutative 68.8%

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

      4. associate-/r* 71.3%

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

      5. sub-neg 71.3%

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

      6. distribute-neg-in 71.3%

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

      7. remove-double-neg 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x around 0 81.9%

      \[\leadsto \frac{\color{blue}{y + -1 \cdot \frac{x}{z}}}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg 81.9%

         \[\leadsto \frac{y + \color{blue}{\left(-\frac{x}{z}\right)}}{a} \]

      2. unsub-neg 81.9%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   10. Simplified 81.9%

       \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   if -5.49999999999999977e-21 < t < -5.0999999999999997e-46

   1. Initial program 87.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 88.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 12500000000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+127)
   (/ y a)
   (if (<= z -7.5e-238)
     (/ (- x (* y z)) t)
     (if (<= z 4.2e+185) (/ x (- t (* z a))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+127) {
		tmp = y / a;
	} else if (z <= -7.5e-238) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 4.2e+185) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d+127)) then
        tmp = y / a
    else if (z <= (-7.5d-238)) then
        tmp = (x - (y * z)) / t
    else if (z <= 4.2d+185) then
        tmp = x / (t - (z * a))
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+127) {
		tmp = y / a;
	} else if (z <= -7.5e-238) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 4.2e+185) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+127:
		tmp = y / a
	elif z <= -7.5e-238:
		tmp = (x - (y * z)) / t
	elif z <= 4.2e+185:
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+127)
		tmp = Float64(y / a);
	elseif (z <= -7.5e-238)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 4.2e+185)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+127)
		tmp = y / a;
	elseif (z <= -7.5e-238)
		tmp = (x - (y * z)) / t;
	elseif (z <= 4.2e+185)
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+127], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.5e-238], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.2e+185], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000002e127 or 4.2e185 < z

   1. Initial program 57.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 57.9%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 57.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 69.8%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -2.5000000000000002e127 < z < -7.50000000000000061e-238

   1. Initial program 98.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 71.2%

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

   if -7.50000000000000061e-238 < z < 4.2e185

   1. Initial program 91.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 91.4%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 71.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+150} \lor \neg \left(z \leq 3.7 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e+150) (not (<= z 3.7e+105)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e+150) || !(z <= 3.7e+105)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.02d+150)) .or. (.not. (z <= 3.7d+105))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e+150) || !(z <= 3.7e+105)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.02e+150) or not (z <= 3.7e+105):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.02e+150) || !(z <= 3.7e+105))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.02e+150) || ~((z <= 3.7e+105)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.02e+150], N[Not[LessEqual[z, 3.7e+105]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0199999999999999e150 or 3.69999999999999985e105 < z

   1. Initial program 59.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 59.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 47.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x - y \cdot z}{a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 47.0%

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

      2. neg-mul-1 47.0%

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

      3. *-commutative 47.0%

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

      4. associate-/r* 61.8%

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

      5. sub-neg 61.8%

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

      6. distribute-neg-in 61.8%

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

      7. remove-double-neg 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in x around 0 86.2%

      \[\leadsto \frac{\color{blue}{y + -1 \cdot \frac{x}{z}}}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg 86.2%

         \[\leadsto \frac{y + \color{blue}{\left(-\frac{x}{z}\right)}}{a} \]

      2. unsub-neg 86.2%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   10. Simplified 86.2%

       \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   if -1.0199999999999999e150 < z < 3.69999999999999985e105

   1. Initial program 97.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+150} \lor \neg \left(z \leq 3.7 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+98} \lor \neg \left(z \leq 4.2 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+98) (not (<= z 4.2e+185))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+98) || !(z <= 4.2e+185)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+98)) .or. (.not. (z <= 4.2d+185))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+98) || !(z <= 4.2e+185)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+98) or not (z <= 4.2e+185):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+98) || !(z <= 4.2e+185))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+98) || ~((z <= 4.2e+185)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+98], N[Not[LessEqual[z, 4.2e+185]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e98 or 4.2e185 < z

   1. Initial program 59.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 59.1%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 68.5%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -1.95e98 < z < 4.2e185

   1. Initial program 93.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 93.9%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 68.7%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+98} \lor \neg \left(z \leq 4.2 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+104} \lor \neg \left(z \leq 54\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.06e+104) (not (<= z 54.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e+104) || !(z <= 54.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.06d+104)) .or. (.not. (z <= 54.0d0))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e+104) || !(z <= 54.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.06e+104) or not (z <= 54.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.06e+104) || !(z <= 54.0))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.06e+104) || ~((z <= 54.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.06e+104], N[Not[LessEqual[z, 54.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05999999999999994e104 or 54 < z

   1. Initial program 68.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 68.4%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 51.5%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -1.05999999999999994e104 < z < 54

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 60.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+104} \lor \neg \left(z \leq 54\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(x / t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 85.5%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 85.5%

      \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

3. Simplified 85.5%

   \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 39.4%

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

6. Final simplification 39.4%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))