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

Percentage Accurate: 85.8% → 91.8%

Time: 17.7s

Alternatives: 12

Speedup: 0.7×

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: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+110}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.1e+135)
   (/ y (- a (/ t z)))
   (if (<= z 1.22e+110) (/ (- x (* z y)) (- t (* z a))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+135) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.22e+110) {
		tmp = (x - (z * y)) / (t - (z * a));
	} 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) :: tmp
    if (z <= (-4.1d+135)) then
        tmp = y / (a - (t / z))
    else if (z <= 1.22d+110) then
        tmp = (x - (z * y)) / (t - (z * a))
    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 tmp;
	if (z <= -4.1e+135) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.22e+110) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.1e+135:
		tmp = y / (a - (t / z))
	elif z <= 1.22e+110:
		tmp = (x - (z * y)) / (t - (z * a))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.1e+135)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 1.22e+110)
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.1e+135)
		tmp = y / (a - (t / z));
	elseif (z <= 1.22e+110)
		tmp = (x - (z * y)) / (t - (z * a));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.1e+135], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+110], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e135

   1. Initial program 63.4%

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

      1. *-commutative 63.4%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in x around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. mul-1-neg 55.6%

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

      3. distribute-rgt-neg-out 55.6%

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

      4. *-commutative 55.6%

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

      5. associate-/l* 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in t around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

   9. Simplified 89.4%

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

   if -4.1e135 < z < 1.22000000000000002e110

   1. Initial program 97.6%

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

   if 1.22000000000000002e110 < z

   1. Initial program 47.5%

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

      1. *-commutative 47.5%

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

   3. Simplified 47.5%

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

      1. div-sub 47.5%

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

   5. Applied egg-rr 47.5%

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

   6. Taylor expanded in t around 0 82.7%

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

      1. distribute-lft-out-- 82.7%

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

      2. associate-/l/ 95.5%

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

      3. div-sub 95.4%

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

      4. mul-1-neg 95.4%

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

   8. Simplified 95.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+110}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 2: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16} \lor \neg \left(z \leq 1.05 \cdot 10^{+24}\right) \land z \leq 2.8 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ y (- a (/ t z)))))
   (if (<= z -8.2e+46)
     t_2
     (if (<= z -4.2e-30)
       t_1
       (if (<= z -2.2e-82)
         t_2
         (if (<= z 2.8e-41)
           t_1
           (if (or (<= z 5.8e-16) (and (not (<= z 1.05e+24)) (<= z 2.8e+110)))
             t_2
             (/ (- y (/ x z)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -8.2e+46) {
		tmp = t_2;
	} else if (z <= -4.2e-30) {
		tmp = t_1;
	} else if (z <= -2.2e-82) {
		tmp = t_2;
	} else if (z <= 2.8e-41) {
		tmp = t_1;
	} else if ((z <= 5.8e-16) || (!(z <= 1.05e+24) && (z <= 2.8e+110))) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    t_2 = y / (a - (t / z))
    if (z <= (-8.2d+46)) then
        tmp = t_2
    else if (z <= (-4.2d-30)) then
        tmp = t_1
    else if (z <= (-2.2d-82)) then
        tmp = t_2
    else if (z <= 2.8d-41) then
        tmp = t_1
    else if ((z <= 5.8d-16) .or. (.not. (z <= 1.05d+24)) .and. (z <= 2.8d+110)) then
        tmp = t_2
    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 / (t - (z * a));
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -8.2e+46) {
		tmp = t_2;
	} else if (z <= -4.2e-30) {
		tmp = t_1;
	} else if (z <= -2.2e-82) {
		tmp = t_2;
	} else if (z <= 2.8e-41) {
		tmp = t_1;
	} else if ((z <= 5.8e-16) || (!(z <= 1.05e+24) && (z <= 2.8e+110))) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = y / (a - (t / z))
	tmp = 0
	if z <= -8.2e+46:
		tmp = t_2
	elif z <= -4.2e-30:
		tmp = t_1
	elif z <= -2.2e-82:
		tmp = t_2
	elif z <= 2.8e-41:
		tmp = t_1
	elif (z <= 5.8e-16) or (not (z <= 1.05e+24) and (z <= 2.8e+110)):
		tmp = t_2
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -8.2e+46)
		tmp = t_2;
	elseif (z <= -4.2e-30)
		tmp = t_1;
	elseif (z <= -2.2e-82)
		tmp = t_2;
	elseif (z <= 2.8e-41)
		tmp = t_1;
	elseif ((z <= 5.8e-16) || (!(z <= 1.05e+24) && (z <= 2.8e+110)))
		tmp = t_2;
	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 / (t - (z * a));
	t_2 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -8.2e+46)
		tmp = t_2;
	elseif (z <= -4.2e-30)
		tmp = t_1;
	elseif (z <= -2.2e-82)
		tmp = t_2;
	elseif (z <= 2.8e-41)
		tmp = t_1;
	elseif ((z <= 5.8e-16) || (~((z <= 1.05e+24)) && (z <= 2.8e+110)))
		tmp = t_2;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+46], t$95$2, If[LessEqual[z, -4.2e-30], t$95$1, If[LessEqual[z, -2.2e-82], t$95$2, If[LessEqual[z, 2.8e-41], t$95$1, If[Or[LessEqual[z, 5.8e-16], And[N[Not[LessEqual[z, 1.05e+24]], $MachinePrecision], LessEqual[z, 2.8e+110]]], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999999e46 or -4.2000000000000004e-30 < z < -2.19999999999999986e-82 or 2.8000000000000002e-41 < z < 5.7999999999999996e-16 or 1.0500000000000001e24 < z < 2.79999999999999987e110

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in x around 0 66.0%

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

      1. associate-*r/ 66.0%

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

      2. mul-1-neg 66.0%

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

      3. distribute-rgt-neg-out 66.0%

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

      4. *-commutative 66.0%

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

      5. associate-/l* 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in t around 0 82.9%

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

      1. associate-*r/ 82.9%

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

      2. neg-mul-1 82.9%

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

   9. Simplified 82.9%

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

   if -8.19999999999999999e46 < z < -4.2000000000000004e-30 or -2.19999999999999986e-82 < z < 2.8000000000000002e-41

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 80.4%

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

      1. *-commutative 80.4%

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

   6. Simplified 80.4%

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

   if 5.7999999999999996e-16 < z < 1.0500000000000001e24 or 2.79999999999999987e110 < z

   1. Initial program 57.9%

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

      1. *-commutative 57.9%

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

   3. Simplified 57.9%

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

      1. div-sub 57.9%

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

   5. Applied egg-rr 57.9%

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

   6. Taylor expanded in t around 0 81.5%

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

      1. distribute-lft-out-- 81.5%

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

      2. associate-/l/ 91.8%

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

      3. div-sub 91.8%

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

      4. mul-1-neg 91.8%

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

   8. Simplified 91.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16} \lor \neg \left(z \leq 1.05 \cdot 10^{+24}\right) \land z \leq 2.8 \cdot 10^{+110}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 3: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-16} \lor \neg \left(z \leq 3.1 \cdot 10^{+26}\right) \land z \leq 1.3 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ y (- a (/ t z)))))
   (if (<= z -5.2e+47)
     t_2
     (if (<= z -3.6e-30)
       t_1
       (if (<= z -3.2e-160)
         (* z (/ y (- (* z a) t)))
         (if (<= z 9.2e-42)
           t_1
           (if (or (<= z 3.3e-16) (and (not (<= z 3.1e+26)) (<= z 1.3e+110)))
             t_2
             (/ (- y (/ x z)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -5.2e+47) {
		tmp = t_2;
	} else if (z <= -3.6e-30) {
		tmp = t_1;
	} else if (z <= -3.2e-160) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= 9.2e-42) {
		tmp = t_1;
	} else if ((z <= 3.3e-16) || (!(z <= 3.1e+26) && (z <= 1.3e+110))) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    t_2 = y / (a - (t / z))
    if (z <= (-5.2d+47)) then
        tmp = t_2
    else if (z <= (-3.6d-30)) then
        tmp = t_1
    else if (z <= (-3.2d-160)) then
        tmp = z * (y / ((z * a) - t))
    else if (z <= 9.2d-42) then
        tmp = t_1
    else if ((z <= 3.3d-16) .or. (.not. (z <= 3.1d+26)) .and. (z <= 1.3d+110)) then
        tmp = t_2
    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 / (t - (z * a));
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -5.2e+47) {
		tmp = t_2;
	} else if (z <= -3.6e-30) {
		tmp = t_1;
	} else if (z <= -3.2e-160) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= 9.2e-42) {
		tmp = t_1;
	} else if ((z <= 3.3e-16) || (!(z <= 3.1e+26) && (z <= 1.3e+110))) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = y / (a - (t / z))
	tmp = 0
	if z <= -5.2e+47:
		tmp = t_2
	elif z <= -3.6e-30:
		tmp = t_1
	elif z <= -3.2e-160:
		tmp = z * (y / ((z * a) - t))
	elif z <= 9.2e-42:
		tmp = t_1
	elif (z <= 3.3e-16) or (not (z <= 3.1e+26) and (z <= 1.3e+110)):
		tmp = t_2
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -5.2e+47)
		tmp = t_2;
	elseif (z <= -3.6e-30)
		tmp = t_1;
	elseif (z <= -3.2e-160)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	elseif (z <= 9.2e-42)
		tmp = t_1;
	elseif ((z <= 3.3e-16) || (!(z <= 3.1e+26) && (z <= 1.3e+110)))
		tmp = t_2;
	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 / (t - (z * a));
	t_2 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -5.2e+47)
		tmp = t_2;
	elseif (z <= -3.6e-30)
		tmp = t_1;
	elseif (z <= -3.2e-160)
		tmp = z * (y / ((z * a) - t));
	elseif (z <= 9.2e-42)
		tmp = t_1;
	elseif ((z <= 3.3e-16) || (~((z <= 3.1e+26)) && (z <= 1.3e+110)))
		tmp = t_2;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+47], t$95$2, If[LessEqual[z, -3.6e-30], t$95$1, If[LessEqual[z, -3.2e-160], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-42], t$95$1, If[Or[LessEqual[z, 3.3e-16], And[N[Not[LessEqual[z, 3.1e+26]], $MachinePrecision], LessEqual[z, 1.3e+110]]], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.20000000000000007e47 or 9.20000000000000015e-42 < z < 3.29999999999999988e-16 or 3.1e26 < z < 1.3e110

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around 0 65.1%

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

      1. associate-*r/ 65.1%

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

      2. mul-1-neg 65.1%

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

      3. distribute-rgt-neg-out 65.1%

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

      4. *-commutative 65.1%

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

      5. associate-/l* 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in t around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. neg-mul-1 85.4%

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

   9. Simplified 85.4%

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

   if -5.20000000000000007e47 < z < -3.6000000000000003e-30 or -3.20000000000000009e-160 < z < 9.20000000000000015e-42

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 82.3%

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

      1. *-commutative 82.3%

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

   6. Simplified 82.3%

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

   if -3.6000000000000003e-30 < z < -3.20000000000000009e-160

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 66.9%

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

      1. associate-*r/ 66.9%

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

      2. mul-1-neg 66.9%

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

      3. distribute-rgt-neg-out 66.9%

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

      4. *-commutative 66.9%

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

      5. associate-/l* 51.7%

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

   6. Simplified 51.7%

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

      1. frac-2neg 51.7%

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

      2. remove-double-neg 51.7%

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

      3. div-inv 51.6%

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

      4. sub-neg 51.6%

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

      5. distribute-neg-in 51.6%

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

      6. distribute-lft-neg-in 51.6%

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

      7. add-sqr-sqrt 51.5%

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

      8. sqrt-unprod 51.6%

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

      9. sqr-neg 51.6%

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

      10. sqrt-unprod 0.0%

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

      11. add-sqr-sqrt 26.9%

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

      12. distribute-lft-neg-in 26.9%

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

      13. add-sqr-sqrt 26.9%

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

      14. sqrt-unprod 26.9%

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

      15. sqr-neg 26.9%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 51.6%

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

   8. Applied egg-rr 51.6%

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

   9. Taylor expanded in y around 0 66.9%

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

       1. expm1-log1p-u 49.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{a \cdot z - t}\right)\right)} \]

       2. expm1-udef 12.0%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot z}{a \cdot z - t}\right)} - 1} \]

       3. associate-/l* 12.0%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a \cdot z - t}{z}}}\right)} - 1 \]

       4. *-commutative 12.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{z \cdot a} - t}{z}}\right)} - 1 \]

       5. associate-/r/ 15.7%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{z \cdot a - t} \cdot z}\right)} - 1 \]

       6. fma-neg 15.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\mathsf{fma}\left(z, a, -t\right)}} \cdot z\right)} - 1 \]

   11. Applied egg-rr 15.7%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\mathsf{fma}\left(z, a, -t\right)} \cdot z\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 53.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\mathsf{fma}\left(z, a, -t\right)} \cdot z\right)\right)} \]

       2. expm1-log1p 70.7%

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

       3. *-commutative 70.7%

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

       4. fma-def 70.7%

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

       5. unsub-neg 70.7%

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

   13. Simplified 70.7%

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

   if 3.29999999999999988e-16 < z < 3.1e26 or 1.3e110 < z

   1. Initial program 57.9%

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

      1. *-commutative 57.9%

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

   3. Simplified 57.9%

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

      1. div-sub 57.9%

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

   5. Applied egg-rr 57.9%

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

   6. Taylor expanded in t around 0 81.5%

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

      1. distribute-lft-out-- 81.5%

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

      2. associate-/l/ 91.8%

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

      3. div-sub 91.8%

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

      4. mul-1-neg 91.8%

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

   8. Simplified 91.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-16} \lor \neg \left(z \leq 3.1 \cdot 10^{+26}\right) \land z \leq 1.3 \cdot 10^{+110}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 4: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z a))))
   (if (<= z -5.2e+84)
     (/ y a)
     (if (<= z -1.65e-22)
       t_1
       (if (<= z -2.3e-30)
         (/ x t)
         (if (<= z -3.2e-160)
           (/ (* y (- z)) t)
           (if (<= z 1.18e-161)
             (/ x t)
             (if (<= z 1.65e-73)
               t_1
               (if (<= z 1.15e-42) (/ x t) (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (z * a);
	double tmp;
	if (z <= -5.2e+84) {
		tmp = y / a;
	} else if (z <= -1.65e-22) {
		tmp = t_1;
	} else if (z <= -2.3e-30) {
		tmp = x / t;
	} else if (z <= -3.2e-160) {
		tmp = (y * -z) / t;
	} else if (z <= 1.18e-161) {
		tmp = x / t;
	} else if (z <= 1.65e-73) {
		tmp = t_1;
	} else if (z <= 1.15e-42) {
		tmp = x / 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 = -x / (z * a)
    if (z <= (-5.2d+84)) then
        tmp = y / a
    else if (z <= (-1.65d-22)) then
        tmp = t_1
    else if (z <= (-2.3d-30)) then
        tmp = x / t
    else if (z <= (-3.2d-160)) then
        tmp = (y * -z) / t
    else if (z <= 1.18d-161) then
        tmp = x / t
    else if (z <= 1.65d-73) then
        tmp = t_1
    else if (z <= 1.15d-42) then
        tmp = x / 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 = -x / (z * a);
	double tmp;
	if (z <= -5.2e+84) {
		tmp = y / a;
	} else if (z <= -1.65e-22) {
		tmp = t_1;
	} else if (z <= -2.3e-30) {
		tmp = x / t;
	} else if (z <= -3.2e-160) {
		tmp = (y * -z) / t;
	} else if (z <= 1.18e-161) {
		tmp = x / t;
	} else if (z <= 1.65e-73) {
		tmp = t_1;
	} else if (z <= 1.15e-42) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (z * a)
	tmp = 0
	if z <= -5.2e+84:
		tmp = y / a
	elif z <= -1.65e-22:
		tmp = t_1
	elif z <= -2.3e-30:
		tmp = x / t
	elif z <= -3.2e-160:
		tmp = (y * -z) / t
	elif z <= 1.18e-161:
		tmp = x / t
	elif z <= 1.65e-73:
		tmp = t_1
	elif z <= 1.15e-42:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(z * a))
	tmp = 0.0
	if (z <= -5.2e+84)
		tmp = Float64(y / a);
	elseif (z <= -1.65e-22)
		tmp = t_1;
	elseif (z <= -2.3e-30)
		tmp = Float64(x / t);
	elseif (z <= -3.2e-160)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 1.18e-161)
		tmp = Float64(x / t);
	elseif (z <= 1.65e-73)
		tmp = t_1;
	elseif (z <= 1.15e-42)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (z * a);
	tmp = 0.0;
	if (z <= -5.2e+84)
		tmp = y / a;
	elseif (z <= -1.65e-22)
		tmp = t_1;
	elseif (z <= -2.3e-30)
		tmp = x / t;
	elseif (z <= -3.2e-160)
		tmp = (y * -z) / t;
	elseif (z <= 1.18e-161)
		tmp = x / t;
	elseif (z <= 1.65e-73)
		tmp = t_1;
	elseif (z <= 1.15e-42)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+84], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.65e-22], t$95$1, If[LessEqual[z, -2.3e-30], N[(x / t), $MachinePrecision], If[LessEqual[z, -3.2e-160], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.18e-161], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.65e-73], t$95$1, If[LessEqual[z, 1.15e-42], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2000000000000002e84 or 1.15000000000000002e-42 < z

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in z around inf 62.0%

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

   if -5.2000000000000002e84 < z < -1.65e-22 or 1.17999999999999992e-161 < z < 1.65000000000000002e-73

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

   3. Simplified 97.5%

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

      1. div-sub 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. distribute-lft-out-- 68.9%

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

      2. associate-/l/ 64.4%

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

      3. div-sub 64.4%

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

      4. mul-1-neg 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in x around inf 54.8%

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

       1. *-commutative 54.8%

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

   11. Simplified 54.8%

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

   if -1.65e-22 < z < -2.29999999999999984e-30 or -3.20000000000000009e-160 < z < 1.17999999999999992e-161 or 1.65000000000000002e-73 < z < 1.15000000000000002e-42

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 71.5%

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

   if -2.29999999999999984e-30 < z < -3.20000000000000009e-160

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. associate-*r* 65.5%

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

      3. neg-mul-1 65.5%

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

      4. *-commutative 65.5%

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

   6. Simplified 65.5%

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

   7. Taylor expanded in t around inf 48.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-73}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-165}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -1.3e+89)
     (/ y a)
     (if (<= z -8.5e-40)
       t_1
       (if (<= z -6e-165)
         (/ (- x (* z y)) t)
         (if (<= z 3.3e+27) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -1.3e+89) {
		tmp = y / a;
	} else if (z <= -8.5e-40) {
		tmp = t_1;
	} else if (z <= -6e-165) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.3e+27) {
		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 / (t - (z * a))
    if (z <= (-1.3d+89)) then
        tmp = y / a
    else if (z <= (-8.5d-40)) then
        tmp = t_1
    else if (z <= (-6d-165)) then
        tmp = (x - (z * y)) / t
    else if (z <= 3.3d+27) 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 / (t - (z * a));
	double tmp;
	if (z <= -1.3e+89) {
		tmp = y / a;
	} else if (z <= -8.5e-40) {
		tmp = t_1;
	} else if (z <= -6e-165) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.3e+27) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -1.3e+89:
		tmp = y / a
	elif z <= -8.5e-40:
		tmp = t_1
	elif z <= -6e-165:
		tmp = (x - (z * y)) / t
	elif z <= 3.3e+27:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -1.3e+89)
		tmp = Float64(y / a);
	elseif (z <= -8.5e-40)
		tmp = t_1;
	elseif (z <= -6e-165)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 3.3e+27)
		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 / (t - (z * a));
	tmp = 0.0;
	if (z <= -1.3e+89)
		tmp = y / a;
	elseif (z <= -8.5e-40)
		tmp = t_1;
	elseif (z <= -6e-165)
		tmp = (x - (z * y)) / t;
	elseif (z <= 3.3e+27)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+89], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.5e-40], t$95$1, If[LessEqual[z, -6e-165], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.3e+27], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e89 or 3.2999999999999998e27 < z

   1. Initial program 61.3%

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

      1. *-commutative 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in z around inf 67.4%

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

   if -1.3e89 < z < -8.4999999999999998e-40 or -5.99999999999999958e-165 < z < 3.2999999999999998e27

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 73.5%

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

      1. *-commutative 73.5%

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

   6. Simplified 73.5%

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

   if -8.4999999999999998e-40 < z < -5.99999999999999958e-165

   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. Taylor expanded in t around inf 68.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-165}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z a))))
   (if (<= z -1.2e+86)
     (/ y a)
     (if (<= z -2.45e-23)
       t_1
       (if (<= z 2.15e-161)
         (/ x t)
         (if (<= z 7.6e-74) t_1 (if (<= z 2.6e-39) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (z * a);
	double tmp;
	if (z <= -1.2e+86) {
		tmp = y / a;
	} else if (z <= -2.45e-23) {
		tmp = t_1;
	} else if (z <= 2.15e-161) {
		tmp = x / t;
	} else if (z <= 7.6e-74) {
		tmp = t_1;
	} else if (z <= 2.6e-39) {
		tmp = x / 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 = -x / (z * a)
    if (z <= (-1.2d+86)) then
        tmp = y / a
    else if (z <= (-2.45d-23)) then
        tmp = t_1
    else if (z <= 2.15d-161) then
        tmp = x / t
    else if (z <= 7.6d-74) then
        tmp = t_1
    else if (z <= 2.6d-39) then
        tmp = x / 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 = -x / (z * a);
	double tmp;
	if (z <= -1.2e+86) {
		tmp = y / a;
	} else if (z <= -2.45e-23) {
		tmp = t_1;
	} else if (z <= 2.15e-161) {
		tmp = x / t;
	} else if (z <= 7.6e-74) {
		tmp = t_1;
	} else if (z <= 2.6e-39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (z * a)
	tmp = 0
	if z <= -1.2e+86:
		tmp = y / a
	elif z <= -2.45e-23:
		tmp = t_1
	elif z <= 2.15e-161:
		tmp = x / t
	elif z <= 7.6e-74:
		tmp = t_1
	elif z <= 2.6e-39:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(z * a))
	tmp = 0.0
	if (z <= -1.2e+86)
		tmp = Float64(y / a);
	elseif (z <= -2.45e-23)
		tmp = t_1;
	elseif (z <= 2.15e-161)
		tmp = Float64(x / t);
	elseif (z <= 7.6e-74)
		tmp = t_1;
	elseif (z <= 2.6e-39)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (z * a);
	tmp = 0.0;
	if (z <= -1.2e+86)
		tmp = y / a;
	elseif (z <= -2.45e-23)
		tmp = t_1;
	elseif (z <= 2.15e-161)
		tmp = x / t;
	elseif (z <= 7.6e-74)
		tmp = t_1;
	elseif (z <= 2.6e-39)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+86], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.45e-23], t$95$1, If[LessEqual[z, 2.15e-161], N[(x / t), $MachinePrecision], If[LessEqual[z, 7.6e-74], t$95$1, If[LessEqual[z, 2.6e-39], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e86 or 2.6e-39 < z

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in z around inf 62.0%

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

   if -1.2e86 < z < -2.4499999999999999e-23 or 2.14999999999999983e-161 < z < 7.5999999999999993e-74

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

   3. Simplified 97.5%

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

      1. div-sub 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. distribute-lft-out-- 68.9%

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

      2. associate-/l/ 64.4%

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

      3. div-sub 64.4%

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

      4. mul-1-neg 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in x around inf 54.8%

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

       1. *-commutative 54.8%

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

   11. Simplified 54.8%

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

   if -2.4499999999999999e-23 < z < 2.14999999999999983e-161 or 7.5999999999999993e-74 < z < 2.6e-39

   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. Taylor expanded in z around 0 60.1%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-23}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-74}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-167}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -3.6e-46)
     t_1
     (if (<= z -3.5e-167)
       (/ (- x (* z y)) t)
       (if (<= z 1.16e-39) (/ x (- t (* z a))) 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 <= -3.6e-46) {
		tmp = t_1;
	} else if (z <= -3.5e-167) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 1.16e-39) {
		tmp = x / (t - (z * a));
	} 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 <= (-3.6d-46)) then
        tmp = t_1
    else if (z <= (-3.5d-167)) then
        tmp = (x - (z * y)) / t
    else if (z <= 1.16d-39) then
        tmp = x / (t - (z * a))
    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 <= -3.6e-46) {
		tmp = t_1;
	} else if (z <= -3.5e-167) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 1.16e-39) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -3.6e-46:
		tmp = t_1
	elif z <= -3.5e-167:
		tmp = (x - (z * y)) / t
	elif z <= 1.16e-39:
		tmp = x / (t - (z * a))
	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 <= -3.6e-46)
		tmp = t_1;
	elseif (z <= -3.5e-167)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 1.16e-39)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	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 <= -3.6e-46)
		tmp = t_1;
	elseif (z <= -3.5e-167)
		tmp = (x - (z * y)) / t;
	elseif (z <= 1.16e-39)
		tmp = x / (t - (z * a));
	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, -3.6e-46], t$95$1, If[LessEqual[z, -3.5e-167], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.16e-39], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-46 or 1.16e-39 < z

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

   3. Simplified 74.1%

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

      1. div-sub 74.1%

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

   5. Applied egg-rr 74.1%

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

   6. Taylor expanded in t around 0 72.5%

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

      1. distribute-lft-out-- 72.5%

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

      2. associate-/l/ 76.7%

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

      3. div-sub 76.7%

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

      4. mul-1-neg 76.7%

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

   8. Simplified 76.7%

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

   if -3.6e-46 < z < -3.4999999999999999e-167

   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. Taylor expanded in t around inf 73.1%

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

   if -3.4999999999999999e-167 < z < 1.16e-39

   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. Taylor expanded in x around inf 84.5%

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

      1. *-commutative 84.5%

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

   6. Simplified 84.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-167}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 8: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-15} \lor \neg \left(t \leq 3.5 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e-15) (not (<= t 3.5e+77)))
   (- (/ x t) (/ z (/ t y)))
   (/ (- y (/ x z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-15) || !(t <= 3.5e+77)) {
		tmp = (x / t) - (z / (t / y));
	} 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) :: tmp
    if ((t <= (-1.2d-15)) .or. (.not. (t <= 3.5d+77))) then
        tmp = (x / t) - (z / (t / y))
    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 tmp;
	if ((t <= -1.2e-15) || !(t <= 3.5e+77)) {
		tmp = (x / t) - (z / (t / y));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e-15) or not (t <= 3.5e+77):
		tmp = (x / t) - (z / (t / y))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e-15) || !(t <= 3.5e+77))
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e-15) || ~((t <= 3.5e+77)))
		tmp = (x / t) - (z / (t / y));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e-15], N[Not[LessEqual[t, 3.5e+77]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999997e-15 or 3.5000000000000001e77 < t

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in t around inf 67.2%

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

      1. div-sub 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-/l* 72.6%

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

   6. Applied egg-rr 72.6%

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

   if -1.19999999999999997e-15 < t < 3.5000000000000001e77

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

      1. div-sub 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in t around 0 78.9%

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

      1. distribute-lft-out-- 78.9%

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

      2. associate-/l/ 79.5%

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

      3. div-sub 80.3%

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

      4. mul-1-neg 80.3%

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

   8. Simplified 80.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-15} \lor \neg \left(t \leq 3.5 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 9: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e-13)
   (- (/ x t) (* z (/ y t)))
   (if (<= t 4.6e+79) (/ (- y (/ x z)) a) (- (/ x t) (/ z (/ t y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-13) {
		tmp = (x / t) - (z * (y / t));
	} else if (t <= 4.6e+79) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.4d-13)) then
        tmp = (x / t) - (z * (y / t))
    else if (t <= 4.6d+79) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x / t) - (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-13) {
		tmp = (x / t) - (z * (y / t));
	} else if (t <= 4.6e+79) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e-13:
		tmp = (x / t) - (z * (y / t))
	elif t <= 4.6e+79:
		tmp = (y - (x / z)) / a
	else:
		tmp = (x / t) - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e-13)
		tmp = Float64(Float64(x / t) - Float64(z * Float64(y / t)));
	elseif (t <= 4.6e+79)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e-13)
		tmp = (x / t) - (z * (y / t));
	elseif (t <= 4.6e+79)
		tmp = (y - (x / z)) / a;
	else
		tmp = (x / t) - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e-13], N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+79], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3999999999999999e-13

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around 0 71.7%

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

   5. Taylor expanded in y around inf 71.8%

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

      1. associate-*r/ 71.8%

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

      2. mul-1-neg 71.8%

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

   7. Simplified 71.8%

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

   if -2.3999999999999999e-13 < t < 4.6000000000000001e79

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

      1. div-sub 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in t around 0 78.9%

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

      1. distribute-lft-out-- 78.9%

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

      2. associate-/l/ 79.5%

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

      3. div-sub 80.3%

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

      4. mul-1-neg 80.3%

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

   8. Simplified 80.3%

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

   if 4.6000000000000001e79 < t

   1. Initial program 79.7%

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

      1. *-commutative 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in t around inf 65.2%

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

      1. div-sub 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-/l* 75.6%

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

   6. Applied egg-rr 75.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 10: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+87} \lor \neg \left(z \leq 8.5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+87) (not (<= z 8.5e+26))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+87) || !(z <= 8.5e+26)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.5d+87)) .or. (.not. (z <= 8.5d+26))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+87) || !(z <= 8.5e+26)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+87) or not (z <= 8.5e+26):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+87) || !(z <= 8.5e+26))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e+87) || ~((z <= 8.5e+26)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+87], N[Not[LessEqual[z, 8.5e+26]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000003e87 or 8.5e26 < z

   1. Initial program 61.3%

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

      1. *-commutative 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in z around inf 67.4%

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

   if -4.5000000000000003e87 < z < 8.5e26

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 69.2%

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

      1. *-commutative 69.2%

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

   6. Simplified 69.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+87} \lor \neg \left(z \leq 8.5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 11: 55.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-46} \lor \neg \left(z \leq 2.4 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e-46) (not (<= z 2.4e-39))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-46) || !(z <= 2.4e-39)) {
		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 <= (-3.4d-46)) .or. (.not. (z <= 2.4d-39))) 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 <= -3.4e-46) || !(z <= 2.4e-39)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e-46) or not (z <= 2.4e-39):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e-46) || !(z <= 2.4e-39))
		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 <= -3.4e-46) || ~((z <= 2.4e-39)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e-46], N[Not[LessEqual[z, 2.4e-39]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999996e-46 or 2.40000000000000016e-39 < z

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around inf 55.8%

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

   if -3.39999999999999996e-46 < z < 2.40000000000000016e-39

   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. Taylor expanded in z around 0 57.3%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-46} \lor \neg \left(z \leq 2.4 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 12: 35.3% 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 84.1%

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

   1. *-commutative 84.1%

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

3. Simplified 84.1%

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

4. Taylor expanded in z around 0 29.7%

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

5. Final simplification 29.7%

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

Developer target: 97.7% accurate, 0.6× 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 2023326 
(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))))