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

Percentage Accurate: 85.7% → 91.6%

Time: 13.9s

Alternatives: 14

Speedup: 0.2×

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: 85.7% 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: 91.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -4e-284)
     t_1
     (if (<= t_1 0.0)
       (/ (/ (- (* y z) x) a) z)
       (if (<= t_1 1e+308) t_1 (/ (- y (/ x z)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-284) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_1 <= 1e+308) {
		tmp = t_1;
	} else {
		tmp = (y - (x / 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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    if (t_1 <= (-4d-284)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (((y * z) - x) / a) / z
    else if (t_1 <= 1d+308) then
        tmp = t_1
    else
        tmp = (y - (x / z)) / 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 - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-284) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_1 <= 1e+308) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -4e-284:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (((y * z) - x) / a) / z
	elif t_1 <= 1e+308:
		tmp = t_1
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= -4e-284)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) - x) / a) / z);
	elseif (t_1 <= 1e+308)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -4e-284)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (((y * z) - x) / a) / z;
	elseif (t_1 <= 1e+308)
		tmp = t_1;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-284], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], t$95$1, 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))) < -4.00000000000000015e-284 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1e308

   1. Initial program 98.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if -4.00000000000000015e-284 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 37.1%

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

      1. *-commutative 37.1%

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

   3. Simplified 37.1%

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

   5. Taylor expanded in t around 0 30.8%

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

      1. mul-1-neg 30.8%

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

      2. associate-/r* 96.6%

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

      3. distribute-neg-frac2 96.6%

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

   7. Simplified 96.6%

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

   if 1e308 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 48.3%

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

      1. *-commutative 48.3%

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

   3. Simplified 48.3%

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

   5. Taylor expanded in t around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. associate-/r* 41.4%

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

      3. distribute-neg-frac2 41.4%

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

   7. Simplified 41.4%

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

   8. Taylor expanded in x around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. associate-/r* 73.9%

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

   10. Simplified 73.9%

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

   11. Taylor expanded in y around 0 81.6%

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

       1. +-commutative 81.6%

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

       2. neg-mul-1 81.6%

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

       3. unsub-neg 81.6%

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

       4. associate-/l/ 81.6%

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

       5. div-sub 81.6%

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

   13. Simplified 81.6%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-284}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+308}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{-t}\\ t_2 := \frac{\frac{-x}{z}}{a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) (- t))) (t_2 (/ (/ (- x) z) a)))
   (if (<= z -1.35e+178)
     (/ y a)
     (if (<= z -4.2e+42)
       t_2
       (if (<= z -1.06e-88)
         (/ x t)
         (if (<= z -3.5e-159)
           t_1
           (if (<= z 9.6e-64)
             (/ x t)
             (if (<= z 1.4e+49)
               t_1
               (if (<= z 2.6e+113)
                 t_2
                 (if (<= z 4.5e+152) (* y (/ z (- t))) (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / -t;
	double t_2 = (-x / z) / a;
	double tmp;
	if (z <= -1.35e+178) {
		tmp = y / a;
	} else if (z <= -4.2e+42) {
		tmp = t_2;
	} else if (z <= -1.06e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = t_1;
	} else if (z <= 9.6e-64) {
		tmp = x / t;
	} else if (z <= 1.4e+49) {
		tmp = t_1;
	} else if (z <= 2.6e+113) {
		tmp = t_2;
	} else if (z <= 4.5e+152) {
		tmp = y * (z / -t);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / -t
    t_2 = (-x / z) / a
    if (z <= (-1.35d+178)) then
        tmp = y / a
    else if (z <= (-4.2d+42)) then
        tmp = t_2
    else if (z <= (-1.06d-88)) then
        tmp = x / t
    else if (z <= (-3.5d-159)) then
        tmp = t_1
    else if (z <= 9.6d-64) then
        tmp = x / t
    else if (z <= 1.4d+49) then
        tmp = t_1
    else if (z <= 2.6d+113) then
        tmp = t_2
    else if (z <= 4.5d+152) then
        tmp = y * (z / -t)
    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 = (y * z) / -t;
	double t_2 = (-x / z) / a;
	double tmp;
	if (z <= -1.35e+178) {
		tmp = y / a;
	} else if (z <= -4.2e+42) {
		tmp = t_2;
	} else if (z <= -1.06e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = t_1;
	} else if (z <= 9.6e-64) {
		tmp = x / t;
	} else if (z <= 1.4e+49) {
		tmp = t_1;
	} else if (z <= 2.6e+113) {
		tmp = t_2;
	} else if (z <= 4.5e+152) {
		tmp = y * (z / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / -t
	t_2 = (-x / z) / a
	tmp = 0
	if z <= -1.35e+178:
		tmp = y / a
	elif z <= -4.2e+42:
		tmp = t_2
	elif z <= -1.06e-88:
		tmp = x / t
	elif z <= -3.5e-159:
		tmp = t_1
	elif z <= 9.6e-64:
		tmp = x / t
	elif z <= 1.4e+49:
		tmp = t_1
	elif z <= 2.6e+113:
		tmp = t_2
	elif z <= 4.5e+152:
		tmp = y * (z / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / Float64(-t))
	t_2 = Float64(Float64(Float64(-x) / z) / a)
	tmp = 0.0
	if (z <= -1.35e+178)
		tmp = Float64(y / a);
	elseif (z <= -4.2e+42)
		tmp = t_2;
	elseif (z <= -1.06e-88)
		tmp = Float64(x / t);
	elseif (z <= -3.5e-159)
		tmp = t_1;
	elseif (z <= 9.6e-64)
		tmp = Float64(x / t);
	elseif (z <= 1.4e+49)
		tmp = t_1;
	elseif (z <= 2.6e+113)
		tmp = t_2;
	elseif (z <= 4.5e+152)
		tmp = Float64(y * Float64(z / Float64(-t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / -t;
	t_2 = (-x / z) / a;
	tmp = 0.0;
	if (z <= -1.35e+178)
		tmp = y / a;
	elseif (z <= -4.2e+42)
		tmp = t_2;
	elseif (z <= -1.06e-88)
		tmp = x / t;
	elseif (z <= -3.5e-159)
		tmp = t_1;
	elseif (z <= 9.6e-64)
		tmp = x / t;
	elseif (z <= 1.4e+49)
		tmp = t_1;
	elseif (z <= 2.6e+113)
		tmp = t_2;
	elseif (z <= 4.5e+152)
		tmp = y * (z / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.35e+178], N[(y / a), $MachinePrecision], If[LessEqual[z, -4.2e+42], t$95$2, If[LessEqual[z, -1.06e-88], N[(x / t), $MachinePrecision], If[LessEqual[z, -3.5e-159], t$95$1, If[LessEqual[z, 9.6e-64], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.4e+49], t$95$1, If[LessEqual[z, 2.6e+113], t$95$2, If[LessEqual[z, 4.5e+152], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.35000000000000009e178 or 4.5000000000000001e152 < z

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

   3. Simplified 51.5%

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

   5. Taylor expanded in z around inf 70.5%

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

   if -1.35000000000000009e178 < z < -4.19999999999999991e42 or 1.3999999999999999e49 < z < 2.5999999999999999e113

   1. Initial program 81.0%

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

      1. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in t around 0 56.7%

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

      1. mul-1-neg 56.7%

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

      2. associate-/r* 59.5%

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

      3. distribute-neg-frac2 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in x around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. associate-/r* 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in y around 0 62.1%

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

       1. +-commutative 62.1%

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

       2. neg-mul-1 62.1%

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

       3. unsub-neg 62.1%

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

       4. associate-/l/ 72.7%

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

       5. div-sub 72.7%

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

   13. Simplified 72.7%

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

   14. Taylor expanded in y around 0 56.7%

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

       1. associate-*r/ 56.7%

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

       2. neg-mul-1 56.7%

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

   16. Simplified 56.7%

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

   if -4.19999999999999991e42 < z < -1.06e-88 or -3.50000000000000002e-159 < z < 9.59999999999999994e-64

   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 65.6%

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

   if -1.06e-88 < z < -3.50000000000000002e-159 or 9.59999999999999994e-64 < z < 1.3999999999999999e49

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. distribute-neg-frac2 73.9%

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

      3. sub-neg 73.9%

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

      4. +-commutative 73.9%

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

      5. distribute-neg-in 73.9%

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

      6. unsub-neg 73.9%

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

      7. *-commutative 73.9%

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

      8. remove-double-neg 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in z around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-/l* 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

   10. Simplified 59.1%

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

       1. distribute-neg-frac2 59.1%

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

       2. associate-*r/ 61.2%

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

   12. Applied egg-rr 61.2%

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

   if 2.5999999999999999e113 < z < 4.5000000000000001e152

   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 x around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-neg-frac2 72.3%

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

      3. sub-neg 72.3%

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

      4. +-commutative 72.3%

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

      5. distribute-neg-in 72.3%

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

      6. unsub-neg 72.3%

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

      7. *-commutative 72.3%

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

      8. remove-double-neg 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in z around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 85.4%

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

      3. distribute-rgt-neg-in 85.4%

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

   10. Simplified 85.4%

       \[\leadsto \color{blue}{y \cdot \left(-\frac{z}{t}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{-t}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) (- t))))
   (if (<= z -3.8e+182)
     (/ y a)
     (if (<= z -5.2e+42)
       (/ (/ (- x) z) a)
       (if (<= z -1.12e-88)
         (/ x t)
         (if (<= z -3.5e-159)
           t_1
           (if (<= z 6e-61)
             (/ x t)
             (if (<= z 5.5e+47)
               t_1
               (if (<= z 1.25e+118)
                 (* (/ x z) (/ -1.0 a))
                 (if (<= z 1.9e+152) (* y (/ z (- t))) (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / -t;
	double tmp;
	if (z <= -3.8e+182) {
		tmp = y / a;
	} else if (z <= -5.2e+42) {
		tmp = (-x / z) / a;
	} else if (z <= -1.12e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = t_1;
	} else if (z <= 6e-61) {
		tmp = x / t;
	} else if (z <= 5.5e+47) {
		tmp = t_1;
	} else if (z <= 1.25e+118) {
		tmp = (x / z) * (-1.0 / a);
	} else if (z <= 1.9e+152) {
		tmp = y * (z / -t);
	} 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 = (y * z) / -t
    if (z <= (-3.8d+182)) then
        tmp = y / a
    else if (z <= (-5.2d+42)) then
        tmp = (-x / z) / a
    else if (z <= (-1.12d-88)) then
        tmp = x / t
    else if (z <= (-3.5d-159)) then
        tmp = t_1
    else if (z <= 6d-61) then
        tmp = x / t
    else if (z <= 5.5d+47) then
        tmp = t_1
    else if (z <= 1.25d+118) then
        tmp = (x / z) * ((-1.0d0) / a)
    else if (z <= 1.9d+152) then
        tmp = y * (z / -t)
    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 = (y * z) / -t;
	double tmp;
	if (z <= -3.8e+182) {
		tmp = y / a;
	} else if (z <= -5.2e+42) {
		tmp = (-x / z) / a;
	} else if (z <= -1.12e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = t_1;
	} else if (z <= 6e-61) {
		tmp = x / t;
	} else if (z <= 5.5e+47) {
		tmp = t_1;
	} else if (z <= 1.25e+118) {
		tmp = (x / z) * (-1.0 / a);
	} else if (z <= 1.9e+152) {
		tmp = y * (z / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / -t
	tmp = 0
	if z <= -3.8e+182:
		tmp = y / a
	elif z <= -5.2e+42:
		tmp = (-x / z) / a
	elif z <= -1.12e-88:
		tmp = x / t
	elif z <= -3.5e-159:
		tmp = t_1
	elif z <= 6e-61:
		tmp = x / t
	elif z <= 5.5e+47:
		tmp = t_1
	elif z <= 1.25e+118:
		tmp = (x / z) * (-1.0 / a)
	elif z <= 1.9e+152:
		tmp = y * (z / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / Float64(-t))
	tmp = 0.0
	if (z <= -3.8e+182)
		tmp = Float64(y / a);
	elseif (z <= -5.2e+42)
		tmp = Float64(Float64(Float64(-x) / z) / a);
	elseif (z <= -1.12e-88)
		tmp = Float64(x / t);
	elseif (z <= -3.5e-159)
		tmp = t_1;
	elseif (z <= 6e-61)
		tmp = Float64(x / t);
	elseif (z <= 5.5e+47)
		tmp = t_1;
	elseif (z <= 1.25e+118)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / a));
	elseif (z <= 1.9e+152)
		tmp = Float64(y * Float64(z / Float64(-t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / -t;
	tmp = 0.0;
	if (z <= -3.8e+182)
		tmp = y / a;
	elseif (z <= -5.2e+42)
		tmp = (-x / z) / a;
	elseif (z <= -1.12e-88)
		tmp = x / t;
	elseif (z <= -3.5e-159)
		tmp = t_1;
	elseif (z <= 6e-61)
		tmp = x / t;
	elseif (z <= 5.5e+47)
		tmp = t_1;
	elseif (z <= 1.25e+118)
		tmp = (x / z) * (-1.0 / a);
	elseif (z <= 1.9e+152)
		tmp = y * (z / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision]}, If[LessEqual[z, -3.8e+182], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.2e+42], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, -1.12e-88], N[(x / t), $MachinePrecision], If[LessEqual[z, -3.5e-159], t$95$1, If[LessEqual[z, 6e-61], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.5e+47], t$95$1, If[LessEqual[z, 1.25e+118], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+152], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.80000000000000013e182 or 1.9e152 < z

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

   3. Simplified 51.5%

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

   5. Taylor expanded in z around inf 70.5%

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

   if -3.80000000000000013e182 < z < -5.1999999999999998e42

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate-/r* 59.0%

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

      3. distribute-neg-frac2 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in x around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. associate-/r* 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in y around 0 66.4%

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

       1. +-commutative 66.4%

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

       2. neg-mul-1 66.4%

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

       3. unsub-neg 66.4%

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

       4. associate-/l/ 73.7%

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

       5. div-sub 73.7%

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

   13. Simplified 73.7%

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

   14. Taylor expanded in y around 0 51.6%

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

       1. associate-*r/ 51.6%

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

       2. neg-mul-1 51.6%

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

   16. Simplified 51.6%

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

   if -5.1999999999999998e42 < z < -1.12e-88 or -3.50000000000000002e-159 < z < 6.00000000000000024e-61

   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 65.6%

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

   if -1.12e-88 < z < -3.50000000000000002e-159 or 6.00000000000000024e-61 < z < 5.4999999999999998e47

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. distribute-neg-frac2 73.9%

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

      3. sub-neg 73.9%

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

      4. +-commutative 73.9%

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

      5. distribute-neg-in 73.9%

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

      6. unsub-neg 73.9%

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

      7. *-commutative 73.9%

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

      8. remove-double-neg 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in z around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-/l* 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

   10. Simplified 59.1%

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

       1. distribute-neg-frac2 59.1%

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

       2. associate-*r/ 61.2%

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

   12. Applied egg-rr 61.2%

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

   if 5.4999999999999998e47 < z < 1.24999999999999993e118

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 51.8%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

      3. *-commutative 51.8%

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

   10. Simplified 51.8%

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

       1. neg-mul-1 51.8%

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

       2. *-commutative 51.8%

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

       3. times-frac 69.9%

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

   12. Applied egg-rr 69.9%

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

   if 1.24999999999999993e118 < z < 1.9e152

   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 x around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-neg-frac2 72.3%

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

      3. sub-neg 72.3%

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

      4. +-commutative 72.3%

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

      5. distribute-neg-in 72.3%

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

      6. unsub-neg 72.3%

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

      7. *-commutative 72.3%

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

      8. remove-double-neg 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in z around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 85.4%

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

      3. distribute-rgt-neg-in 85.4%

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

   10. Simplified 85.4%

       \[\leadsto \color{blue}{y \cdot \left(-\frac{z}{t}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{-t}\\ t_2 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) (- t))) (t_2 (/ x (- t (* z a)))))
   (if (<= z -2e+78)
     (/ y a)
     (if (<= z -1.06e-88)
       t_2
       (if (<= z -3.4e-159)
         t_1
         (if (<= z 1.06e-58)
           t_2
           (if (<= z 3.5e+47)
             t_1
             (if (<= z 5.5e+114)
               (* (/ x z) (/ -1.0 a))
               (if (<= z 1.6e+152) (* y (/ z (- t))) (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / -t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -2e+78) {
		tmp = y / a;
	} else if (z <= -1.06e-88) {
		tmp = t_2;
	} else if (z <= -3.4e-159) {
		tmp = t_1;
	} else if (z <= 1.06e-58) {
		tmp = t_2;
	} else if (z <= 3.5e+47) {
		tmp = t_1;
	} else if (z <= 5.5e+114) {
		tmp = (x / z) * (-1.0 / a);
	} else if (z <= 1.6e+152) {
		tmp = y * (z / -t);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / -t
    t_2 = x / (t - (z * a))
    if (z <= (-2d+78)) then
        tmp = y / a
    else if (z <= (-1.06d-88)) then
        tmp = t_2
    else if (z <= (-3.4d-159)) then
        tmp = t_1
    else if (z <= 1.06d-58) then
        tmp = t_2
    else if (z <= 3.5d+47) then
        tmp = t_1
    else if (z <= 5.5d+114) then
        tmp = (x / z) * ((-1.0d0) / a)
    else if (z <= 1.6d+152) then
        tmp = y * (z / -t)
    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 = (y * z) / -t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -2e+78) {
		tmp = y / a;
	} else if (z <= -1.06e-88) {
		tmp = t_2;
	} else if (z <= -3.4e-159) {
		tmp = t_1;
	} else if (z <= 1.06e-58) {
		tmp = t_2;
	} else if (z <= 3.5e+47) {
		tmp = t_1;
	} else if (z <= 5.5e+114) {
		tmp = (x / z) * (-1.0 / a);
	} else if (z <= 1.6e+152) {
		tmp = y * (z / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / -t
	t_2 = x / (t - (z * a))
	tmp = 0
	if z <= -2e+78:
		tmp = y / a
	elif z <= -1.06e-88:
		tmp = t_2
	elif z <= -3.4e-159:
		tmp = t_1
	elif z <= 1.06e-58:
		tmp = t_2
	elif z <= 3.5e+47:
		tmp = t_1
	elif z <= 5.5e+114:
		tmp = (x / z) * (-1.0 / a)
	elif z <= 1.6e+152:
		tmp = y * (z / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / Float64(-t))
	t_2 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -2e+78)
		tmp = Float64(y / a);
	elseif (z <= -1.06e-88)
		tmp = t_2;
	elseif (z <= -3.4e-159)
		tmp = t_1;
	elseif (z <= 1.06e-58)
		tmp = t_2;
	elseif (z <= 3.5e+47)
		tmp = t_1;
	elseif (z <= 5.5e+114)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / a));
	elseif (z <= 1.6e+152)
		tmp = Float64(y * Float64(z / Float64(-t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / -t;
	t_2 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -2e+78)
		tmp = y / a;
	elseif (z <= -1.06e-88)
		tmp = t_2;
	elseif (z <= -3.4e-159)
		tmp = t_1;
	elseif (z <= 1.06e-58)
		tmp = t_2;
	elseif (z <= 3.5e+47)
		tmp = t_1;
	elseif (z <= 5.5e+114)
		tmp = (x / z) * (-1.0 / a);
	elseif (z <= 1.6e+152)
		tmp = y * (z / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+78], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.06e-88], t$95$2, If[LessEqual[z, -3.4e-159], t$95$1, If[LessEqual[z, 1.06e-58], t$95$2, If[LessEqual[z, 3.5e+47], t$95$1, If[LessEqual[z, 5.5e+114], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+152], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.00000000000000002e78 or 1.60000000000000003e152 < z

   1. Initial program 59.5%

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

      1. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in z around inf 62.0%

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

   if -2.00000000000000002e78 < z < -1.06e-88 or -3.39999999999999984e-159 < z < 1.0600000000000001e-58

   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 x around inf 80.9%

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

      1. *-commutative 80.9%

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

   7. Simplified 80.9%

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

   if -1.06e-88 < z < -3.39999999999999984e-159 or 1.0600000000000001e-58 < z < 3.50000000000000015e47

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-neg-frac2 74.4%

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

      3. sub-neg 74.4%

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

      4. +-commutative 74.4%

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

      5. distribute-neg-in 74.4%

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

      6. unsub-neg 74.4%

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

      7. *-commutative 74.4%

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

      8. remove-double-neg 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-/l* 57.9%

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

      3. distribute-rgt-neg-in 57.9%

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

   10. Simplified 57.9%

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

       1. distribute-neg-frac2 57.9%

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

       2. associate-*r/ 60.0%

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

   12. Applied egg-rr 60.0%

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

   if 3.50000000000000015e47 < z < 5.5000000000000001e114

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 51.8%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

      3. *-commutative 51.8%

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

   10. Simplified 51.8%

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

       1. neg-mul-1 51.8%

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

       2. *-commutative 51.8%

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

       3. times-frac 69.9%

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

   12. Applied egg-rr 69.9%

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

   if 5.5000000000000001e114 < z < 1.60000000000000003e152

   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 x around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-neg-frac2 72.3%

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

      3. sub-neg 72.3%

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

      4. +-commutative 72.3%

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

      5. distribute-neg-in 72.3%

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

      6. unsub-neg 72.3%

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

      7. *-commutative 72.3%

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

      8. remove-double-neg 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in z around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 85.4%

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

      3. distribute-rgt-neg-in 85.4%

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

   10. Simplified 85.4%

       \[\leadsto \color{blue}{y \cdot \left(-\frac{z}{t}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= z -1.35e+178)
     (/ y a)
     (if (<= z -2.1e+45)
       (/ (/ (- x) z) a)
       (if (<= z 2.05e-201)
         t_1
         (if (<= z 8.5e-60)
           (/ x (- t (* z a)))
           (if (<= z 1.6e+152) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (z <= -1.35e+178) {
		tmp = y / a;
	} else if (z <= -2.1e+45) {
		tmp = (-x / z) / a;
	} else if (z <= 2.05e-201) {
		tmp = t_1;
	} else if (z <= 8.5e-60) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.6e+152) {
		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 - (y * z)) / t
    if (z <= (-1.35d+178)) then
        tmp = y / a
    else if (z <= (-2.1d+45)) then
        tmp = (-x / z) / a
    else if (z <= 2.05d-201) then
        tmp = t_1
    else if (z <= 8.5d-60) then
        tmp = x / (t - (z * a))
    else if (z <= 1.6d+152) 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 - (y * z)) / t;
	double tmp;
	if (z <= -1.35e+178) {
		tmp = y / a;
	} else if (z <= -2.1e+45) {
		tmp = (-x / z) / a;
	} else if (z <= 2.05e-201) {
		tmp = t_1;
	} else if (z <= 8.5e-60) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.6e+152) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if z <= -1.35e+178:
		tmp = y / a
	elif z <= -2.1e+45:
		tmp = (-x / z) / a
	elif z <= 2.05e-201:
		tmp = t_1
	elif z <= 8.5e-60:
		tmp = x / (t - (z * a))
	elif z <= 1.6e+152:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (z <= -1.35e+178)
		tmp = Float64(y / a);
	elseif (z <= -2.1e+45)
		tmp = Float64(Float64(Float64(-x) / z) / a);
	elseif (z <= 2.05e-201)
		tmp = t_1;
	elseif (z <= 8.5e-60)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.6e+152)
		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 - (y * z)) / t;
	tmp = 0.0;
	if (z <= -1.35e+178)
		tmp = y / a;
	elseif (z <= -2.1e+45)
		tmp = (-x / z) / a;
	elseif (z <= 2.05e-201)
		tmp = t_1;
	elseif (z <= 8.5e-60)
		tmp = x / (t - (z * a));
	elseif (z <= 1.6e+152)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -1.35e+178], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.1e+45], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.05e-201], t$95$1, If[LessEqual[z, 8.5e-60], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+152], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35000000000000009e178 or 1.60000000000000003e152 < z

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

   3. Simplified 51.5%

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

   5. Taylor expanded in z around inf 70.5%

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

   if -1.35000000000000009e178 < z < -2.09999999999999995e45

   1. Initial program 80.5%

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

      1. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. associate-/r* 61.3%

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

      3. distribute-neg-frac2 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in x around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. associate-/r* 69.1%

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

   10. Simplified 69.1%

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

   11. Taylor expanded in y around 0 69.0%

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

       1. +-commutative 69.0%

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

       2. neg-mul-1 69.0%

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

       3. unsub-neg 69.0%

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

       4. associate-/l/ 76.6%

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

       5. div-sub 76.6%

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

   13. Simplified 76.6%

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

   14. Taylor expanded in y around 0 53.5%

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

       1. associate-*r/ 53.5%

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

       2. neg-mul-1 53.5%

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

   16. Simplified 53.5%

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

   if -2.09999999999999995e45 < z < 2.05000000000000001e-201 or 8.50000000000000044e-60 < z < 1.60000000000000003e152

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 76.7%

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

   if 2.05000000000000001e-201 < z < 8.50000000000000044e-60

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 86.8%

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

      1. *-commutative 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-t}\\ \mathbf{if}\;z \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t)))))
   (if (<= z -3.65e+22)
     (/ y a)
     (if (<= z -1.75e-88)
       (/ x t)
       (if (<= z -3.5e-159)
         t_1
         (if (<= z 1.1e-63) (/ x t) (if (<= z 4.5e+152) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -t);
	double tmp;
	if (z <= -3.65e+22) {
		tmp = y / a;
	} else if (z <= -1.75e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = t_1;
	} else if (z <= 1.1e-63) {
		tmp = x / t;
	} else if (z <= 4.5e+152) {
		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 = y * (z / -t)
    if (z <= (-3.65d+22)) then
        tmp = y / a
    else if (z <= (-1.75d-88)) then
        tmp = x / t
    else if (z <= (-3.5d-159)) then
        tmp = t_1
    else if (z <= 1.1d-63) then
        tmp = x / t
    else if (z <= 4.5d+152) 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 = y * (z / -t);
	double tmp;
	if (z <= -3.65e+22) {
		tmp = y / a;
	} else if (z <= -1.75e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = t_1;
	} else if (z <= 1.1e-63) {
		tmp = x / t;
	} else if (z <= 4.5e+152) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -t)
	tmp = 0
	if z <= -3.65e+22:
		tmp = y / a
	elif z <= -1.75e-88:
		tmp = x / t
	elif z <= -3.5e-159:
		tmp = t_1
	elif z <= 1.1e-63:
		tmp = x / t
	elif z <= 4.5e+152:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-t)))
	tmp = 0.0
	if (z <= -3.65e+22)
		tmp = Float64(y / a);
	elseif (z <= -1.75e-88)
		tmp = Float64(x / t);
	elseif (z <= -3.5e-159)
		tmp = t_1;
	elseif (z <= 1.1e-63)
		tmp = Float64(x / t);
	elseif (z <= 4.5e+152)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -t);
	tmp = 0.0;
	if (z <= -3.65e+22)
		tmp = y / a;
	elseif (z <= -1.75e-88)
		tmp = x / t;
	elseif (z <= -3.5e-159)
		tmp = t_1;
	elseif (z <= 1.1e-63)
		tmp = x / t;
	elseif (z <= 4.5e+152)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.65e+22], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.75e-88], N[(x / t), $MachinePrecision], If[LessEqual[z, -3.5e-159], t$95$1, If[LessEqual[z, 1.1e-63], N[(x / t), $MachinePrecision], If[LessEqual[z, 4.5e+152], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6499999999999999e22 or 4.5000000000000001e152 < z

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in z around inf 58.5%

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

   if -3.6499999999999999e22 < z < -1.7500000000000001e-88 or -3.50000000000000002e-159 < z < 1.1e-63

   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 65.8%

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

   if -1.7500000000000001e-88 < z < -3.50000000000000002e-159 or 1.1e-63 < z < 4.5000000000000001e152

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. distribute-neg-frac2 68.6%

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

      3. sub-neg 68.6%

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

      4. +-commutative 68.6%

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

      5. distribute-neg-in 68.6%

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

      6. unsub-neg 68.6%

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

      7. *-commutative 68.6%

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

      8. remove-double-neg 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. associate-/l* 56.3%

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

      3. distribute-rgt-neg-in 56.3%

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

   10. Simplified 56.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+22)
   (/ y a)
   (if (<= z -4.5e-88)
     (/ x t)
     (if (<= z -3.5e-159)
       (/ (* y z) (- t))
       (if (<= z 1.15e-59)
         (/ x t)
         (if (<= z 1.6e+152) (* y (/ z (- t))) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+22) {
		tmp = y / a;
	} else if (z <= -4.5e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = (y * z) / -t;
	} else if (z <= 1.15e-59) {
		tmp = x / t;
	} else if (z <= 1.6e+152) {
		tmp = y * (z / -t);
	} 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 <= (-2.6d+22)) then
        tmp = y / a
    else if (z <= (-4.5d-88)) then
        tmp = x / t
    else if (z <= (-3.5d-159)) then
        tmp = (y * z) / -t
    else if (z <= 1.15d-59) then
        tmp = x / t
    else if (z <= 1.6d+152) then
        tmp = y * (z / -t)
    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 <= -2.6e+22) {
		tmp = y / a;
	} else if (z <= -4.5e-88) {
		tmp = x / t;
	} else if (z <= -3.5e-159) {
		tmp = (y * z) / -t;
	} else if (z <= 1.15e-59) {
		tmp = x / t;
	} else if (z <= 1.6e+152) {
		tmp = y * (z / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+22:
		tmp = y / a
	elif z <= -4.5e-88:
		tmp = x / t
	elif z <= -3.5e-159:
		tmp = (y * z) / -t
	elif z <= 1.15e-59:
		tmp = x / t
	elif z <= 1.6e+152:
		tmp = y * (z / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+22)
		tmp = Float64(y / a);
	elseif (z <= -4.5e-88)
		tmp = Float64(x / t);
	elseif (z <= -3.5e-159)
		tmp = Float64(Float64(y * z) / Float64(-t));
	elseif (z <= 1.15e-59)
		tmp = Float64(x / t);
	elseif (z <= 1.6e+152)
		tmp = Float64(y * Float64(z / Float64(-t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+22)
		tmp = y / a;
	elseif (z <= -4.5e-88)
		tmp = x / t;
	elseif (z <= -3.5e-159)
		tmp = (y * z) / -t;
	elseif (z <= 1.15e-59)
		tmp = x / t;
	elseif (z <= 1.6e+152)
		tmp = y * (z / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+22], N[(y / a), $MachinePrecision], If[LessEqual[z, -4.5e-88], N[(x / t), $MachinePrecision], If[LessEqual[z, -3.5e-159], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 1.15e-59], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.6e+152], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e22 or 1.60000000000000003e152 < z

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in z around inf 58.5%

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

   if -2.6e22 < z < -4.49999999999999991e-88 or -3.50000000000000002e-159 < z < 1.1499999999999999e-59

   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 65.8%

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

   if -4.49999999999999991e-88 < z < -3.50000000000000002e-159

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-neg-frac2 69.2%

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

      3. sub-neg 69.2%

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

      4. +-commutative 69.2%

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

      5. distribute-neg-in 69.2%

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

      6. unsub-neg 69.2%

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

      7. *-commutative 69.2%

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

      8. remove-double-neg 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in z around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-/l* 62.9%

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

      3. distribute-rgt-neg-in 62.9%

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

   10. Simplified 62.9%

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

       1. distribute-neg-frac2 62.9%

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

       2. associate-*r/ 69.7%

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

   12. Applied egg-rr 69.7%

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

   if 1.1499999999999999e-59 < z < 1.60000000000000003e152

   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 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-neg-frac2 68.5%

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

      3. sub-neg 68.5%

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

      4. +-commutative 68.5%

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

      5. distribute-neg-in 68.5%

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

      6. unsub-neg 68.5%

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

      7. *-commutative 68.5%

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

      8. remove-double-neg 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. associate-/l* 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

   10. Simplified 54.4%

       \[\leadsto \color{blue}{y \cdot \left(-\frac{z}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -5e+43)
     t_1
     (if (<= z 2.55e-201)
       (/ (- x (* y z)) t)
       (if (<= z 1.55e-66)
         (/ x (- t (* z a)))
         (if (<= z 2.6e+151) (* z (/ y (- (* z a) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5e+43) {
		tmp = t_1;
	} else if (z <= 2.55e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.55e-66) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.6e+151) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	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 (z <= (-5d+43)) then
        tmp = t_1
    else if (z <= 2.55d-201) then
        tmp = (x - (y * z)) / t
    else if (z <= 1.55d-66) then
        tmp = x / (t - (z * a))
    else if (z <= 2.6d+151) then
        tmp = z * (y / ((z * a) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5e+43) {
		tmp = t_1;
	} else if (z <= 2.55e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.55e-66) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.6e+151) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -5e+43:
		tmp = t_1
	elif z <= 2.55e-201:
		tmp = (x - (y * z)) / t
	elif z <= 1.55e-66:
		tmp = x / (t - (z * a))
	elif z <= 2.6e+151:
		tmp = z * (y / ((z * a) - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -5e+43)
		tmp = t_1;
	elseif (z <= 2.55e-201)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 1.55e-66)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.6e+151)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -5e+43)
		tmp = t_1;
	elseif (z <= 2.55e-201)
		tmp = (x - (y * z)) / t;
	elseif (z <= 1.55e-66)
		tmp = x / (t - (z * a));
	elseif (z <= 2.6e+151)
		tmp = z * (y / ((z * a) - t));
	else
		tmp = t_1;
	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[z, -5e+43], t$95$1, If[LessEqual[z, 2.55e-201], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.55e-66], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+151], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.0000000000000004e43 or 2.60000000000000013e151 < z

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-/r* 59.8%

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

      3. distribute-neg-frac2 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/r* 77.4%

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

   10. Simplified 77.4%

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

   11. Taylor expanded in y around 0 75.2%

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

       1. +-commutative 75.2%

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

       2. neg-mul-1 75.2%

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

       3. unsub-neg 75.2%

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

       4. associate-/l/ 83.2%

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

       5. div-sub 83.2%

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

   13. Simplified 83.2%

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

   if -5.0000000000000004e43 < z < 2.5500000000000001e-201

   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 t around inf 82.9%

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

   if 2.5500000000000001e-201 < z < 1.5499999999999999e-66

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. *-commutative 89.7%

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

   7. Simplified 89.7%

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

   if 1.5499999999999999e-66 < z < 2.60000000000000013e151

   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 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-neg-frac2 70.5%

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

      3. sub-neg 70.5%

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

      4. +-commutative 70.5%

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

      5. distribute-neg-in 70.5%

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

      6. unsub-neg 70.5%

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

      7. *-commutative 70.5%

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

      8. remove-double-neg 70.5%

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

   7. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 70.4%

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

      3. *-commutative 70.4%

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

   9. Applied egg-rr 70.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+151}:\\ \;\;\;\;\frac{z}{\frac{z \cdot a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.15e+43)
     t_1
     (if (<= z 1.35e-201)
       (/ (- x (* y z)) t)
       (if (<= z 7.6e-66)
         (/ x (- t (* z a)))
         (if (<= z 2.1e+151) (/ z (/ (- (* z a) t) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.15e+43) {
		tmp = t_1;
	} else if (z <= 1.35e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 7.6e-66) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.1e+151) {
		tmp = z / (((z * a) - t) / y);
	} else {
		tmp = t_1;
	}
	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 (z <= (-1.15d+43)) then
        tmp = t_1
    else if (z <= 1.35d-201) then
        tmp = (x - (y * z)) / t
    else if (z <= 7.6d-66) then
        tmp = x / (t - (z * a))
    else if (z <= 2.1d+151) then
        tmp = z / (((z * a) - t) / y)
    else
        tmp = t_1
    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 (z <= -1.15e+43) {
		tmp = t_1;
	} else if (z <= 1.35e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 7.6e-66) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.1e+151) {
		tmp = z / (((z * a) - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.15e+43:
		tmp = t_1
	elif z <= 1.35e-201:
		tmp = (x - (y * z)) / t
	elif z <= 7.6e-66:
		tmp = x / (t - (z * a))
	elif z <= 2.1e+151:
		tmp = z / (((z * a) - t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.15e+43)
		tmp = t_1;
	elseif (z <= 1.35e-201)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 7.6e-66)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.1e+151)
		tmp = Float64(z / Float64(Float64(Float64(z * a) - t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.15e+43)
		tmp = t_1;
	elseif (z <= 1.35e-201)
		tmp = (x - (y * z)) / t;
	elseif (z <= 7.6e-66)
		tmp = x / (t - (z * a));
	elseif (z <= 2.1e+151)
		tmp = z / (((z * a) - t) / y);
	else
		tmp = t_1;
	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[z, -1.15e+43], t$95$1, If[LessEqual[z, 1.35e-201], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 7.6e-66], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+151], N[(z / N[(N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1500000000000001e43 or 2.1000000000000001e151 < z

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-/r* 59.8%

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

      3. distribute-neg-frac2 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/r* 77.4%

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

   10. Simplified 77.4%

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

   11. Taylor expanded in y around 0 75.2%

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

       1. +-commutative 75.2%

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

       2. neg-mul-1 75.2%

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

       3. unsub-neg 75.2%

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

       4. associate-/l/ 83.2%

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

       5. div-sub 83.2%

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

   13. Simplified 83.2%

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

   if -1.1500000000000001e43 < z < 1.35000000000000003e-201

   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 t around inf 82.9%

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

   if 1.35000000000000003e-201 < z < 7.5999999999999995e-66

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. *-commutative 89.7%

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

   7. Simplified 89.7%

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

   if 7.5999999999999995e-66 < z < 2.1000000000000001e151

   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 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-neg-frac2 70.5%

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

      3. sub-neg 70.5%

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

      4. +-commutative 70.5%

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

      5. distribute-neg-in 70.5%

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

      6. unsub-neg 70.5%

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

      7. *-commutative 70.5%

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

      8. remove-double-neg 70.5%

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

   7. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 70.4%

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

      3. *-commutative 70.4%

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

   9. Applied egg-rr 70.4%

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

       1. clear-num 70.3%

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

       2. un-div-inv 70.4%

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

       3. *-commutative 70.4%

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

   11. Applied egg-rr 70.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+43}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+151}:\\ \;\;\;\;\frac{z}{\frac{z \cdot a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.5e+44)
     t_1
     (if (<= z 2.3e-201)
       (/ (- x (* y z)) t)
       (if (<= z 1.12e-64)
         (/ x (- t (* z a)))
         (if (<= z 2.6e+151) (/ (* y z) (- (* z a) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.5e+44) {
		tmp = t_1;
	} else if (z <= 2.3e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.12e-64) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.6e+151) {
		tmp = (y * z) / ((z * a) - t);
	} else {
		tmp = t_1;
	}
	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 (z <= (-1.5d+44)) then
        tmp = t_1
    else if (z <= 2.3d-201) then
        tmp = (x - (y * z)) / t
    else if (z <= 1.12d-64) then
        tmp = x / (t - (z * a))
    else if (z <= 2.6d+151) then
        tmp = (y * z) / ((z * a) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.5e+44) {
		tmp = t_1;
	} else if (z <= 2.3e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.12e-64) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.6e+151) {
		tmp = (y * z) / ((z * a) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.5e+44:
		tmp = t_1
	elif z <= 2.3e-201:
		tmp = (x - (y * z)) / t
	elif z <= 1.12e-64:
		tmp = x / (t - (z * a))
	elif z <= 2.6e+151:
		tmp = (y * z) / ((z * a) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.5e+44)
		tmp = t_1;
	elseif (z <= 2.3e-201)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 1.12e-64)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.6e+151)
		tmp = Float64(Float64(y * z) / Float64(Float64(z * a) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.5e+44)
		tmp = t_1;
	elseif (z <= 2.3e-201)
		tmp = (x - (y * z)) / t;
	elseif (z <= 1.12e-64)
		tmp = x / (t - (z * a));
	elseif (z <= 2.6e+151)
		tmp = (y * z) / ((z * a) - t);
	else
		tmp = t_1;
	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[z, -1.5e+44], t$95$1, If[LessEqual[z, 2.3e-201], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.12e-64], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+151], N[(N[(y * z), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.49999999999999993e44 or 2.60000000000000013e151 < z

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-/r* 59.8%

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

      3. distribute-neg-frac2 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/r* 77.4%

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

   10. Simplified 77.4%

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

   11. Taylor expanded in y around 0 75.2%

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

       1. +-commutative 75.2%

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

       2. neg-mul-1 75.2%

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

       3. unsub-neg 75.2%

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

       4. associate-/l/ 83.2%

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

       5. div-sub 83.2%

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

   13. Simplified 83.2%

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

   if -1.49999999999999993e44 < z < 2.29999999999999986e-201

   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 t around inf 82.9%

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

   if 2.29999999999999986e-201 < z < 1.12e-64

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. *-commutative 89.7%

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

   7. Simplified 89.7%

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

   if 1.12e-64 < z < 2.60000000000000013e151

   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 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-neg-frac2 70.5%

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

      3. sub-neg 70.5%

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

      4. +-commutative 70.5%

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

      5. distribute-neg-in 70.5%

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

      6. unsub-neg 70.5%

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

      7. *-commutative 70.5%

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

      8. remove-double-neg 70.5%

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

   7. Simplified 70.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.1e+43)
     t_1
     (if (<= z 2.35e-201)
       (/ (- x (* y z)) t)
       (if (<= z 2.35e-67)
         (/ x (- t (* z a)))
         (if (<= z 7.8e+151) (* y (/ z (- (* z a) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.1e+43) {
		tmp = t_1;
	} else if (z <= 2.35e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.35e-67) {
		tmp = x / (t - (z * a));
	} else if (z <= 7.8e+151) {
		tmp = y * (z / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	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 (z <= (-1.1d+43)) then
        tmp = t_1
    else if (z <= 2.35d-201) then
        tmp = (x - (y * z)) / t
    else if (z <= 2.35d-67) then
        tmp = x / (t - (z * a))
    else if (z <= 7.8d+151) then
        tmp = y * (z / ((z * a) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.1e+43) {
		tmp = t_1;
	} else if (z <= 2.35e-201) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.35e-67) {
		tmp = x / (t - (z * a));
	} else if (z <= 7.8e+151) {
		tmp = y * (z / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.1e+43:
		tmp = t_1
	elif z <= 2.35e-201:
		tmp = (x - (y * z)) / t
	elif z <= 2.35e-67:
		tmp = x / (t - (z * a))
	elif z <= 7.8e+151:
		tmp = y * (z / ((z * a) - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.1e+43)
		tmp = t_1;
	elseif (z <= 2.35e-201)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 2.35e-67)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 7.8e+151)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.1e+43)
		tmp = t_1;
	elseif (z <= 2.35e-201)
		tmp = (x - (y * z)) / t;
	elseif (z <= 2.35e-67)
		tmp = x / (t - (z * a));
	elseif (z <= 7.8e+151)
		tmp = y * (z / ((z * a) - t));
	else
		tmp = t_1;
	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[z, -1.1e+43], t$95$1, If[LessEqual[z, 2.35e-201], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.35e-67], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+151], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e43 or 7.79999999999999952e151 < z

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-/r* 59.8%

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

      3. distribute-neg-frac2 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/r* 77.4%

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

   10. Simplified 77.4%

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

   11. Taylor expanded in y around 0 75.2%

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

       1. +-commutative 75.2%

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

       2. neg-mul-1 75.2%

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

       3. unsub-neg 75.2%

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

       4. associate-/l/ 83.2%

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

       5. div-sub 83.2%

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

   13. Simplified 83.2%

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

   if -1.1e43 < z < 2.34999999999999997e-201

   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 t around inf 82.9%

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

   if 2.34999999999999997e-201 < z < 2.35000000000000002e-67

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. *-commutative 89.7%

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

   7. Simplified 89.7%

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

   if 2.35000000000000002e-67 < z < 7.79999999999999952e151

   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 0 70.5%

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

      1. associate-/l* 72.4%

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

      2. associate-*r* 72.4%

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

      3. neg-mul-1 72.4%

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

      4. *-commutative 72.4%

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

   7. Simplified 72.4%

      \[\leadsto \color{blue}{\left(-y\right) \cdot \frac{z}{t - z \cdot a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+43}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.45e+44)
     t_2
     (if (<= z 1.55e-201)
       t_1
       (if (<= z 1.2e-59) (/ x (- t (* z a))) (if (<= z 1.6e+152) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.45e+44) {
		tmp = t_2;
	} else if (z <= 1.55e-201) {
		tmp = t_1;
	} else if (z <= 1.2e-59) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.6e+152) {
		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 = (x - (y * z)) / t
    t_2 = (y - (x / z)) / a
    if (z <= (-1.45d+44)) then
        tmp = t_2
    else if (z <= 1.55d-201) then
        tmp = t_1
    else if (z <= 1.2d-59) then
        tmp = x / (t - (z * a))
    else if (z <= 1.6d+152) 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 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.45e+44) {
		tmp = t_2;
	} else if (z <= 1.55e-201) {
		tmp = t_1;
	} else if (z <= 1.2e-59) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.6e+152) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.45e+44:
		tmp = t_2
	elif z <= 1.55e-201:
		tmp = t_1
	elif z <= 1.2e-59:
		tmp = x / (t - (z * a))
	elif z <= 1.6e+152:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.45e+44)
		tmp = t_2;
	elseif (z <= 1.55e-201)
		tmp = t_1;
	elseif (z <= 1.2e-59)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.6e+152)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.45e+44)
		tmp = t_2;
	elseif (z <= 1.55e-201)
		tmp = t_1;
	elseif (z <= 1.2e-59)
		tmp = x / (t - (z * a));
	elseif (z <= 1.6e+152)
		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[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.45e+44], t$95$2, If[LessEqual[z, 1.55e-201], t$95$1, If[LessEqual[z, 1.2e-59], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+152], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e44 or 1.60000000000000003e152 < z

   1. Initial program 60.6%

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

      1. *-commutative 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in t around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. associate-/r* 60.5%

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

      3. distribute-neg-frac2 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in x around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. mul-1-neg 76.0%

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

      3. unsub-neg 76.0%

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

      4. associate-/r* 78.3%

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

   10. Simplified 78.3%

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

   11. Taylor expanded in y around 0 76.0%

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

       1. +-commutative 76.0%

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

       2. neg-mul-1 76.0%

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

       3. unsub-neg 76.0%

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

       4. associate-/l/ 84.2%

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

       5. div-sub 84.2%

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

   13. Simplified 84.2%

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

   if -1.4500000000000001e44 < z < 1.5499999999999999e-201 or 1.20000000000000008e-59 < z < 1.60000000000000003e152

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 76.7%

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

   if 1.5499999999999999e-201 < z < 1.20000000000000008e-59

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 86.8%

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

      1. *-commutative 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+44}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-201}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+21} \lor \neg \left(z \leq 3.7 \cdot 10^{-65}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+21) (not (<= z 3.7e-65))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+21) || !(z <= 3.7e-65)) {
		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 <= (-2.75d+21)) .or. (.not. (z <= 3.7d-65))) 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 <= -2.75e+21) || !(z <= 3.7e-65)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e+21) or not (z <= 3.7e-65):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+21) || !(z <= 3.7e-65))
		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 <= -2.75e+21) || ~((z <= 3.7e-65)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+21], N[Not[LessEqual[z, 3.7e-65]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e21 or 3.7e-65 < z

   1. Initial program 74.0%

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

      1. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in z around inf 47.4%

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

   if -2.75e21 < z < 3.7e-65

   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 61.7%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+21} \lor \neg \left(z \leq 3.7 \cdot 10^{-65}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.0% 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 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 z around 0 36.3%

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

6. Final simplification 36.3%

   \[\leadsto \frac{x}{t} \]
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 2024039 
(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))))