Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.4% → 95.5%

Time: 17.2s

Alternatives: 14

Speedup: 1.0×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.45e-143) (+ x (/ z (/ t (- y x)))) (+ x (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.45e-143) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 1.45d-143) then
        tmp = x + (z / (t / (y - x)))
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.45e-143) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.45e-143:
		tmp = x + (z / (t / (y - x)))
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.45e-143)
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.45e-143)
		tmp = x + (z / (t / (y - x)));
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.45e-143], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.45e-143

   1. Initial program 92.6%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

      1. *-commutative 95.9%

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

      2. clear-num 95.9%

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

      3. un-div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   if 1.45e-143 < x

   1. Initial program 91.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 2: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ t_2 := z \cdot \frac{x}{-t}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.86:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))) (t_2 (* z (/ x (- t)))))
   (if (<= z -1.4e+259)
     (/ z (/ t y))
     (if (<= z -1.05e+211)
       t_2
       (if (<= z -4.3e+155)
         t_1
         (if (<= z -0.86)
           t_2
           (if (<= z -9.5e-107)
             (/ (* z y) t)
             (if (<= z 2.1e-57) x (if (<= z 5.4e+218) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double t_2 = z * (x / -t);
	double tmp;
	if (z <= -1.4e+259) {
		tmp = z / (t / y);
	} else if (z <= -1.05e+211) {
		tmp = t_2;
	} else if (z <= -4.3e+155) {
		tmp = t_1;
	} else if (z <= -0.86) {
		tmp = t_2;
	} else if (z <= -9.5e-107) {
		tmp = (z * y) / t;
	} else if (z <= 2.1e-57) {
		tmp = x;
	} else if (z <= 5.4e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (y / t)
    t_2 = z * (x / -t)
    if (z <= (-1.4d+259)) then
        tmp = z / (t / y)
    else if (z <= (-1.05d+211)) then
        tmp = t_2
    else if (z <= (-4.3d+155)) then
        tmp = t_1
    else if (z <= (-0.86d0)) then
        tmp = t_2
    else if (z <= (-9.5d-107)) then
        tmp = (z * y) / t
    else if (z <= 2.1d-57) then
        tmp = x
    else if (z <= 5.4d+218) 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 t_1 = z * (y / t);
	double t_2 = z * (x / -t);
	double tmp;
	if (z <= -1.4e+259) {
		tmp = z / (t / y);
	} else if (z <= -1.05e+211) {
		tmp = t_2;
	} else if (z <= -4.3e+155) {
		tmp = t_1;
	} else if (z <= -0.86) {
		tmp = t_2;
	} else if (z <= -9.5e-107) {
		tmp = (z * y) / t;
	} else if (z <= 2.1e-57) {
		tmp = x;
	} else if (z <= 5.4e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	t_2 = z * (x / -t)
	tmp = 0
	if z <= -1.4e+259:
		tmp = z / (t / y)
	elif z <= -1.05e+211:
		tmp = t_2
	elif z <= -4.3e+155:
		tmp = t_1
	elif z <= -0.86:
		tmp = t_2
	elif z <= -9.5e-107:
		tmp = (z * y) / t
	elif z <= 2.1e-57:
		tmp = x
	elif z <= 5.4e+218:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	t_2 = Float64(z * Float64(x / Float64(-t)))
	tmp = 0.0
	if (z <= -1.4e+259)
		tmp = Float64(z / Float64(t / y));
	elseif (z <= -1.05e+211)
		tmp = t_2;
	elseif (z <= -4.3e+155)
		tmp = t_1;
	elseif (z <= -0.86)
		tmp = t_2;
	elseif (z <= -9.5e-107)
		tmp = Float64(Float64(z * y) / t);
	elseif (z <= 2.1e-57)
		tmp = x;
	elseif (z <= 5.4e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	t_2 = z * (x / -t);
	tmp = 0.0;
	if (z <= -1.4e+259)
		tmp = z / (t / y);
	elseif (z <= -1.05e+211)
		tmp = t_2;
	elseif (z <= -4.3e+155)
		tmp = t_1;
	elseif (z <= -0.86)
		tmp = t_2;
	elseif (z <= -9.5e-107)
		tmp = (z * y) / t;
	elseif (z <= 2.1e-57)
		tmp = x;
	elseif (z <= 5.4e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+259], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e+211], t$95$2, If[LessEqual[z, -4.3e+155], t$95$1, If[LessEqual[z, -0.86], t$95$2, If[LessEqual[z, -9.5e-107], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.1e-57], x, If[LessEqual[z, 5.4e+218], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.4e259

   1. Initial program 82.9%

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

   2. Taylor expanded in t around 0 82.9%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

      1. associate-/l* 82.5%

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

      2. associate-/r/ 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in z around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 82.5%

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

   10. Simplified 82.5%

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

   if -1.4e259 < z < -1.05e211 or -4.3000000000000002e155 < z < -0.859999999999999987 or 5.40000000000000025e218 < z

   1. Initial program 87.9%

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

   2. Taylor expanded in t around 0 79.8%

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

   3. Taylor expanded in y around 0 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-rgt-neg-out 57.5%

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

   5. Simplified 57.5%

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

      1. frac-2neg 57.5%

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

      2. div-inv 57.4%

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

      3. distribute-rgt-neg-out 57.4%

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

      4. remove-double-neg 57.4%

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

   7. Applied egg-rr 57.4%

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

      1. associate-*l* 63.0%

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

      2. associate-*r/ 63.1%

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

      3. *-rgt-identity 63.1%

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

   9. Simplified 63.1%

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

   if -1.05e211 < z < -4.3000000000000002e155 or 2.0999999999999999e-57 < z < 5.40000000000000025e218

   1. Initial program 87.0%

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

   2. Taylor expanded in t around 0 78.5%

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

   3. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

      1. associate-/l* 68.3%

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

      2. associate-/r/ 64.3%

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

   7. Applied egg-rr 64.3%

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

   8. Taylor expanded in z around 0 58.3%

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

      1. associate-*l/ 68.4%

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

   10. Simplified 68.4%

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

   if -0.859999999999999987 < z < -9.4999999999999999e-107

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 69.7%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if -9.4999999999999999e-107 < z < 2.0999999999999999e-57

   1. Initial program 98.1%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around inf 69.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+211}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -0.86:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \end{array} \]

Alternative 3: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ t_2 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.095:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))) (t_2 (* x (/ (- z) t))))
   (if (<= z -1.7e+259)
     (/ z (/ t y))
     (if (<= z -7.5e+226)
       t_2
       (if (<= z -1.85e+146)
         t_1
         (if (<= z -0.095)
           (* z (/ x (- t)))
           (if (<= z -3.4e-110)
             (/ (* z y) t)
             (if (<= z 1.9e-57) x (if (<= z 2.4e+218) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -1.7e+259) {
		tmp = z / (t / y);
	} else if (z <= -7.5e+226) {
		tmp = t_2;
	} else if (z <= -1.85e+146) {
		tmp = t_1;
	} else if (z <= -0.095) {
		tmp = z * (x / -t);
	} else if (z <= -3.4e-110) {
		tmp = (z * y) / t;
	} else if (z <= 1.9e-57) {
		tmp = x;
	} else if (z <= 2.4e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (y / t)
    t_2 = x * (-z / t)
    if (z <= (-1.7d+259)) then
        tmp = z / (t / y)
    else if (z <= (-7.5d+226)) then
        tmp = t_2
    else if (z <= (-1.85d+146)) then
        tmp = t_1
    else if (z <= (-0.095d0)) then
        tmp = z * (x / -t)
    else if (z <= (-3.4d-110)) then
        tmp = (z * y) / t
    else if (z <= 1.9d-57) then
        tmp = x
    else if (z <= 2.4d+218) 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 t_1 = z * (y / t);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -1.7e+259) {
		tmp = z / (t / y);
	} else if (z <= -7.5e+226) {
		tmp = t_2;
	} else if (z <= -1.85e+146) {
		tmp = t_1;
	} else if (z <= -0.095) {
		tmp = z * (x / -t);
	} else if (z <= -3.4e-110) {
		tmp = (z * y) / t;
	} else if (z <= 1.9e-57) {
		tmp = x;
	} else if (z <= 2.4e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	t_2 = x * (-z / t)
	tmp = 0
	if z <= -1.7e+259:
		tmp = z / (t / y)
	elif z <= -7.5e+226:
		tmp = t_2
	elif z <= -1.85e+146:
		tmp = t_1
	elif z <= -0.095:
		tmp = z * (x / -t)
	elif z <= -3.4e-110:
		tmp = (z * y) / t
	elif z <= 1.9e-57:
		tmp = x
	elif z <= 2.4e+218:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	t_2 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -1.7e+259)
		tmp = Float64(z / Float64(t / y));
	elseif (z <= -7.5e+226)
		tmp = t_2;
	elseif (z <= -1.85e+146)
		tmp = t_1;
	elseif (z <= -0.095)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (z <= -3.4e-110)
		tmp = Float64(Float64(z * y) / t);
	elseif (z <= 1.9e-57)
		tmp = x;
	elseif (z <= 2.4e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	t_2 = x * (-z / t);
	tmp = 0.0;
	if (z <= -1.7e+259)
		tmp = z / (t / y);
	elseif (z <= -7.5e+226)
		tmp = t_2;
	elseif (z <= -1.85e+146)
		tmp = t_1;
	elseif (z <= -0.095)
		tmp = z * (x / -t);
	elseif (z <= -3.4e-110)
		tmp = (z * y) / t;
	elseif (z <= 1.9e-57)
		tmp = x;
	elseif (z <= 2.4e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+259], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e+226], t$95$2, If[LessEqual[z, -1.85e+146], t$95$1, If[LessEqual[z, -0.095], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-110], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.9e-57], x, If[LessEqual[z, 2.4e+218], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.69999999999999995e259

   1. Initial program 82.9%

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

   2. Taylor expanded in t around 0 82.9%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

      1. associate-/l* 82.5%

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

      2. associate-/r/ 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in z around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 82.5%

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

   10. Simplified 82.5%

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

   if -1.69999999999999995e259 < z < -7.49999999999999964e226 or 2.39999999999999981e218 < z

   1. Initial program 80.6%

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

   2. Taylor expanded in t around 0 76.5%

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

   3. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-rgt-neg-out 57.4%

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

   5. Simplified 57.4%

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

      1. *-commutative 57.4%

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

      2. distribute-lft-neg-out 57.4%

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

      3. distribute-neg-frac 57.4%

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

      4. associate-*r/ 76.7%

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

      5. *-commutative 76.7%

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

      6. distribute-lft-neg-in 76.7%

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

   7. Applied egg-rr 76.7%

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

   if -7.49999999999999964e226 < z < -1.85000000000000002e146 or 1.8999999999999999e-57 < z < 2.39999999999999981e218

   1. Initial program 86.3%

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

   2. Taylor expanded in t around 0 78.2%

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

   3. Taylor expanded in y around inf 57.5%

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

      1. *-commutative 57.5%

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

   5. Simplified 57.5%

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

      1. associate-/l* 68.3%

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

      2. associate-/r/ 64.4%

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

   7. Applied egg-rr 64.4%

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

   8. Taylor expanded in z around 0 57.5%

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

      1. associate-*l/ 68.3%

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

   10. Simplified 68.3%

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

   if -1.85000000000000002e146 < z < -0.095000000000000001

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 82.8%

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

   3. Taylor expanded in y around 0 56.7%

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

      1. mul-1-neg 56.7%

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

      2. distribute-rgt-neg-out 56.7%

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

   5. Simplified 56.7%

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

      1. frac-2neg 56.7%

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

      2. div-inv 56.6%

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

      3. distribute-rgt-neg-out 56.6%

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

      4. remove-double-neg 56.6%

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

   7. Applied egg-rr 56.6%

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

      1. associate-*l* 56.6%

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

      2. associate-*r/ 56.6%

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

      3. *-rgt-identity 56.6%

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

   9. Simplified 56.6%

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

   if -0.095000000000000001 < z < -3.4000000000000001e-110

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 69.7%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if -3.4000000000000001e-110 < z < 1.8999999999999999e-57

   1. Initial program 98.1%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around inf 69.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -0.095:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 4: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ t_2 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-110}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))) (t_2 (* x (/ (- z) t))))
   (if (<= z -2.5e+259)
     (/ z (/ t y))
     (if (<= z -2.3e+226)
       t_2
       (if (<= z -1.7e+146)
         t_1
         (if (<= z -1.0)
           (/ (* x (- z)) t)
           (if (<= z -4.8e-110)
             (/ (* z y) t)
             (if (<= z 1.6e-57) x (if (<= z 2.35e+213) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -2.5e+259) {
		tmp = z / (t / y);
	} else if (z <= -2.3e+226) {
		tmp = t_2;
	} else if (z <= -1.7e+146) {
		tmp = t_1;
	} else if (z <= -1.0) {
		tmp = (x * -z) / t;
	} else if (z <= -4.8e-110) {
		tmp = (z * y) / t;
	} else if (z <= 1.6e-57) {
		tmp = x;
	} else if (z <= 2.35e+213) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (y / t)
    t_2 = x * (-z / t)
    if (z <= (-2.5d+259)) then
        tmp = z / (t / y)
    else if (z <= (-2.3d+226)) then
        tmp = t_2
    else if (z <= (-1.7d+146)) then
        tmp = t_1
    else if (z <= (-1.0d0)) then
        tmp = (x * -z) / t
    else if (z <= (-4.8d-110)) then
        tmp = (z * y) / t
    else if (z <= 1.6d-57) then
        tmp = x
    else if (z <= 2.35d+213) 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 t_1 = z * (y / t);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -2.5e+259) {
		tmp = z / (t / y);
	} else if (z <= -2.3e+226) {
		tmp = t_2;
	} else if (z <= -1.7e+146) {
		tmp = t_1;
	} else if (z <= -1.0) {
		tmp = (x * -z) / t;
	} else if (z <= -4.8e-110) {
		tmp = (z * y) / t;
	} else if (z <= 1.6e-57) {
		tmp = x;
	} else if (z <= 2.35e+213) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	t_2 = x * (-z / t)
	tmp = 0
	if z <= -2.5e+259:
		tmp = z / (t / y)
	elif z <= -2.3e+226:
		tmp = t_2
	elif z <= -1.7e+146:
		tmp = t_1
	elif z <= -1.0:
		tmp = (x * -z) / t
	elif z <= -4.8e-110:
		tmp = (z * y) / t
	elif z <= 1.6e-57:
		tmp = x
	elif z <= 2.35e+213:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	t_2 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -2.5e+259)
		tmp = Float64(z / Float64(t / y));
	elseif (z <= -2.3e+226)
		tmp = t_2;
	elseif (z <= -1.7e+146)
		tmp = t_1;
	elseif (z <= -1.0)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= -4.8e-110)
		tmp = Float64(Float64(z * y) / t);
	elseif (z <= 1.6e-57)
		tmp = x;
	elseif (z <= 2.35e+213)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	t_2 = x * (-z / t);
	tmp = 0.0;
	if (z <= -2.5e+259)
		tmp = z / (t / y);
	elseif (z <= -2.3e+226)
		tmp = t_2;
	elseif (z <= -1.7e+146)
		tmp = t_1;
	elseif (z <= -1.0)
		tmp = (x * -z) / t;
	elseif (z <= -4.8e-110)
		tmp = (z * y) / t;
	elseif (z <= 1.6e-57)
		tmp = x;
	elseif (z <= 2.35e+213)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+259], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e+226], t$95$2, If[LessEqual[z, -1.7e+146], t$95$1, If[LessEqual[z, -1.0], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -4.8e-110], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.6e-57], x, If[LessEqual[z, 2.35e+213], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.50000000000000016e259

   1. Initial program 82.9%

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

   2. Taylor expanded in t around 0 82.9%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

      1. associate-/l* 82.5%

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

      2. associate-/r/ 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in z around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 82.5%

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

   10. Simplified 82.5%

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

   if -2.50000000000000016e259 < z < -2.29999999999999995e226 or 2.3499999999999999e213 < z

   1. Initial program 80.6%

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

   2. Taylor expanded in t around 0 76.5%

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

   3. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-rgt-neg-out 57.4%

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

   5. Simplified 57.4%

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

      1. *-commutative 57.4%

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

      2. distribute-lft-neg-out 57.4%

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

      3. distribute-neg-frac 57.4%

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

      4. associate-*r/ 76.7%

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

      5. *-commutative 76.7%

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

      6. distribute-lft-neg-in 76.7%

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

   7. Applied egg-rr 76.7%

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

   if -2.29999999999999995e226 < z < -1.69999999999999995e146 or 1.6e-57 < z < 2.3499999999999999e213

   1. Initial program 86.3%

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

   2. Taylor expanded in t around 0 78.2%

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

   3. Taylor expanded in y around inf 57.5%

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

      1. *-commutative 57.5%

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

   5. Simplified 57.5%

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

      1. associate-/l* 68.3%

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

      2. associate-/r/ 64.4%

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

   7. Applied egg-rr 64.4%

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

   8. Taylor expanded in z around 0 57.5%

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

      1. associate-*l/ 68.3%

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

   10. Simplified 68.3%

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

   if -1.69999999999999995e146 < z < -1

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 82.8%

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

   3. Taylor expanded in y around 0 56.7%

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

      1. mul-1-neg 56.7%

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

      2. distribute-rgt-neg-out 56.7%

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

   5. Simplified 56.7%

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

   if -1 < z < -4.80000000000000013e-110

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 69.7%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if -4.80000000000000013e-110 < z < 1.6e-57

   1. Initial program 98.1%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around inf 69.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-110}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 5: 71.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= x -6.2e+164)
     t_1
     (if (<= x -4.9e+109)
       (/ (- z) (/ t x))
       (if (<= x 2.8e+123) t_1 (* x (/ (- z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (x <= -6.2e+164) {
		tmp = t_1;
	} else if (x <= -4.9e+109) {
		tmp = -z / (t / x);
	} else if (x <= 2.8e+123) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (x <= (-6.2d+164)) then
        tmp = t_1
    else if (x <= (-4.9d+109)) then
        tmp = -z / (t / x)
    else if (x <= 2.8d+123) then
        tmp = t_1
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (x <= -6.2e+164) {
		tmp = t_1;
	} else if (x <= -4.9e+109) {
		tmp = -z / (t / x);
	} else if (x <= 2.8e+123) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if x <= -6.2e+164:
		tmp = t_1
	elif x <= -4.9e+109:
		tmp = -z / (t / x)
	elif x <= 2.8e+123:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (x <= -6.2e+164)
		tmp = t_1;
	elseif (x <= -4.9e+109)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (x <= 2.8e+123)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (x <= -6.2e+164)
		tmp = t_1;
	elseif (x <= -4.9e+109)
		tmp = -z / (t / x);
	elseif (x <= 2.8e+123)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+164], t$95$1, If[LessEqual[x, -4.9e+109], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+123], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2000000000000003e164 or -4.9000000000000003e109 < x < 2.80000000000000011e123

   1. Initial program 93.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 76.3%

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

      1. associate-*r/ 77.3%

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

   6. Simplified 77.3%

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

   if -6.2000000000000003e164 < x < -4.9000000000000003e109

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 72.0%

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

   3. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-out 71.5%

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

   5. Simplified 71.5%

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

      1. frac-2neg 71.5%

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

      2. div-inv 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

      4. remove-double-neg 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. associate-*l* 79.2%

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

      2. associate-*r/ 79.2%

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

      3. *-rgt-identity 79.2%

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

   9. Simplified 79.2%

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

       1. frac-2neg 79.2%

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

       2. remove-double-neg 79.2%

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

       3. distribute-frac-neg 79.2%

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

       4. distribute-rgt-neg-in 79.2%

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

       5. *-commutative 79.2%

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

       6. clear-num 79.2%

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

       7. associate-/r/ 79.2%

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

       8. clear-num 79.4%

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

       9. distribute-neg-frac 79.4%

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

   11. Applied egg-rr 79.4%

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

   if 2.80000000000000011e123 < x

   1. Initial program 88.2%

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

   2. Taylor expanded in t around 0 63.9%

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

   3. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-rgt-neg-out 63.9%

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

   5. Simplified 63.9%

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

      1. *-commutative 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. distribute-neg-frac 63.9%

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

      4. associate-*r/ 69.5%

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

      5. *-commutative 69.5%

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

      6. distribute-lft-neg-in 69.5%

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

   7. Applied egg-rr 69.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+164}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 6: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+110}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= x -6.2e+164)
     t_1
     (if (<= x -2.35e+110)
       (/ (- z) (/ t x))
       (if (<= x 5e+121) t_1 (* x (/ (- z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (x <= -6.2e+164) {
		tmp = t_1;
	} else if (x <= -2.35e+110) {
		tmp = -z / (t / x);
	} else if (x <= 5e+121) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    if (x <= (-6.2d+164)) then
        tmp = t_1
    else if (x <= (-2.35d+110)) then
        tmp = -z / (t / x)
    else if (x <= 5d+121) then
        tmp = t_1
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (x <= -6.2e+164) {
		tmp = t_1;
	} else if (x <= -2.35e+110) {
		tmp = -z / (t / x);
	} else if (x <= 5e+121) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (y / t))
	tmp = 0
	if x <= -6.2e+164:
		tmp = t_1
	elif x <= -2.35e+110:
		tmp = -z / (t / x)
	elif x <= 5e+121:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (x <= -6.2e+164)
		tmp = t_1;
	elseif (x <= -2.35e+110)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (x <= 5e+121)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (x <= -6.2e+164)
		tmp = t_1;
	elseif (x <= -2.35e+110)
		tmp = -z / (t / x);
	elseif (x <= 5e+121)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+164], t$95$1, If[LessEqual[x, -2.35e+110], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+121], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2000000000000003e164 or -2.3499999999999999e110 < x < 5.00000000000000007e121

   1. Initial program 93.3%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 77.7%

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

   if -6.2000000000000003e164 < x < -2.3499999999999999e110

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 72.0%

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

   3. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-out 71.5%

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

   5. Simplified 71.5%

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

      1. frac-2neg 71.5%

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

      2. div-inv 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

      4. remove-double-neg 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. associate-*l* 79.2%

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

      2. associate-*r/ 79.2%

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

      3. *-rgt-identity 79.2%

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

   9. Simplified 79.2%

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

       1. frac-2neg 79.2%

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

       2. remove-double-neg 79.2%

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

       3. distribute-frac-neg 79.2%

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

       4. distribute-rgt-neg-in 79.2%

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

       5. *-commutative 79.2%

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

       6. clear-num 79.2%

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

       7. associate-/r/ 79.2%

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

       8. clear-num 79.4%

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

       9. distribute-neg-frac 79.4%

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

   11. Applied egg-rr 79.4%

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

   if 5.00000000000000007e121 < x

   1. Initial program 88.2%

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

   2. Taylor expanded in t around 0 63.9%

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

   3. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-rgt-neg-out 63.9%

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

   5. Simplified 63.9%

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

      1. *-commutative 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. distribute-neg-frac 63.9%

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

      4. associate-*r/ 69.5%

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

      5. *-commutative 69.5%

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

      6. distribute-lft-neg-in 69.5%

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

   7. Applied egg-rr 69.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+110}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+121}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 7: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e+164)
   (+ x (* z (/ y t)))
   (if (<= x -2.5e+110)
     (/ (- z) (/ t x))
     (if (<= x 6.2e+122) (+ x (/ z (/ t y))) (* x (/ (- z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+164) {
		tmp = x + (z * (y / t));
	} else if (x <= -2.5e+110) {
		tmp = -z / (t / x);
	} else if (x <= 6.2e+122) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-5.5d+164)) then
        tmp = x + (z * (y / t))
    else if (x <= (-2.5d+110)) then
        tmp = -z / (t / x)
    else if (x <= 6.2d+122) then
        tmp = x + (z / (t / y))
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+164) {
		tmp = x + (z * (y / t));
	} else if (x <= -2.5e+110) {
		tmp = -z / (t / x);
	} else if (x <= 6.2e+122) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e+164:
		tmp = x + (z * (y / t))
	elif x <= -2.5e+110:
		tmp = -z / (t / x)
	elif x <= 6.2e+122:
		tmp = x + (z / (t / y))
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e+164)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (x <= -2.5e+110)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (x <= 6.2e+122)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e+164)
		tmp = x + (z * (y / t));
	elseif (x <= -2.5e+110)
		tmp = -z / (t / x);
	elseif (x <= 6.2e+122)
		tmp = x + (z / (t / y));
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e+164], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e+110], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+122], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.4999999999999998e164

   1. Initial program 91.5%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -5.4999999999999998e164 < x < -2.49999999999999989e110

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 72.0%

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

   3. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-out 71.5%

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

   5. Simplified 71.5%

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

      1. frac-2neg 71.5%

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

      2. div-inv 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

      4. remove-double-neg 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. associate-*l* 79.2%

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

      2. associate-*r/ 79.2%

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

      3. *-rgt-identity 79.2%

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

   9. Simplified 79.2%

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

       1. frac-2neg 79.2%

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

       2. remove-double-neg 79.2%

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

       3. distribute-frac-neg 79.2%

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

       4. distribute-rgt-neg-in 79.2%

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

       5. *-commutative 79.2%

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

       6. clear-num 79.2%

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

       7. associate-/r/ 79.2%

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

       8. clear-num 79.4%

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

       9. distribute-neg-frac 79.4%

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

   11. Applied egg-rr 79.4%

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

   if -2.49999999999999989e110 < x < 6.19999999999999998e122

   1. Initial program 93.5%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. clear-num 95.4%

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

      3. un-div-inv 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in y around inf 79.7%

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

   if 6.19999999999999998e122 < x

   1. Initial program 88.2%

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

   2. Taylor expanded in t around 0 63.9%

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

   3. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-rgt-neg-out 63.9%

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

   5. Simplified 63.9%

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

      1. *-commutative 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. distribute-neg-frac 63.9%

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

      4. associate-*r/ 69.5%

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

      5. *-commutative 69.5%

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

      6. distribute-lft-neg-in 69.5%

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

   7. Applied egg-rr 69.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 8: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 17000000:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-69)
   (+ x (* z (/ y t)))
   (if (<= y 4.5e-156)
     (- x (* x (/ z t)))
     (if (<= y 17000000.0) (/ (* z (- y x)) t) (+ x (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-69) {
		tmp = x + (z * (y / t));
	} else if (y <= 4.5e-156) {
		tmp = x - (x * (z / t));
	} else if (y <= 17000000.0) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d-69)) then
        tmp = x + (z * (y / t))
    else if (y <= 4.5d-156) then
        tmp = x - (x * (z / t))
    else if (y <= 17000000.0d0) then
        tmp = (z * (y - x)) / t
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-69) {
		tmp = x + (z * (y / t));
	} else if (y <= 4.5e-156) {
		tmp = x - (x * (z / t));
	} else if (y <= 17000000.0) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-69:
		tmp = x + (z * (y / t))
	elif y <= 4.5e-156:
		tmp = x - (x * (z / t))
	elif y <= 17000000.0:
		tmp = (z * (y - x)) / t
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-69)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (y <= 4.5e-156)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	elseif (y <= 17000000.0)
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-69)
		tmp = x + (z * (y / t));
	elseif (y <= 4.5e-156)
		tmp = x - (x * (z / t));
	elseif (y <= 17000000.0)
		tmp = (z * (y - x)) / t;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-69], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-156], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 17000000.0], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.50000000000000006e-69

   1. Initial program 91.6%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 86.9%

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

   if -5.50000000000000006e-69 < y < 4.49999999999999986e-156

   1. Initial program 95.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in y around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. mul-1-neg 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

      4. associate-*l/ 88.1%

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

   6. Simplified 88.1%

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

      1. distribute-rgt-neg-out 88.1%

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

      2. unsub-neg 88.1%

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

      3. *-commutative 88.1%

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

   8. Applied egg-rr 88.1%

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

   if 4.49999999999999986e-156 < y < 1.7e7

   1. Initial program 97.6%

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

   2. Taylor expanded in t around 0 80.4%

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

   if 1.7e7 < y

   1. Initial program 85.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 79.4%

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

      1. associate-*r/ 90.5%

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

   6. Simplified 90.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 17000000:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e-70)
   (+ x (* z (/ y t)))
   (if (<= y 7.2e-96) (- x (* x (/ z t))) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e-70) {
		tmp = x + (z * (y / t));
	} else if (y <= 7.2e-96) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.2d-70)) then
        tmp = x + (z * (y / t))
    else if (y <= 7.2d-96) then
        tmp = x - (x * (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e-70) {
		tmp = x + (z * (y / t));
	} else if (y <= 7.2e-96) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e-70:
		tmp = x + (z * (y / t))
	elif y <= 7.2e-96:
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e-70)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (y <= 7.2e-96)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e-70)
		tmp = x + (z * (y / t));
	elseif (y <= 7.2e-96)
		tmp = x - (x * (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e-70], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-96], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000002e-70

   1. Initial program 91.6%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 86.9%

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

   if -4.2000000000000002e-70 < y < 7.20000000000000016e-96

   1. Initial program 96.1%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. mul-1-neg 82.1%

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

      3. distribute-rgt-neg-out 82.1%

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

      4. associate-*l/ 84.9%

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

   6. Simplified 84.9%

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

      1. distribute-rgt-neg-out 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

   8. Applied egg-rr 84.9%

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

   if 7.20000000000000016e-96 < y

   1. Initial program 88.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around inf 77.7%

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

      1. associate-*r/ 83.7%

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

   6. Simplified 83.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-106} \lor \neg \left(z \leq 1.6 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-106) (not (<= z 1.6e-57))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-106) || !(z <= 1.6e-57)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.8d-106)) .or. (.not. (z <= 1.6d-57))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-106) || !(z <= 1.6e-57)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-106) or not (z <= 1.6e-57):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-106) || !(z <= 1.6e-57))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e-106) || ~((z <= 1.6e-57)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-106], N[Not[LessEqual[z, 1.6e-57]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000006e-106 or 1.6e-57 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 78.4%

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

   3. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

   5. Simplified 46.6%

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

      1. associate-/l* 51.9%

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

      2. associate-/r/ 50.3%

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

   7. Applied egg-rr 50.3%

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

   8. Taylor expanded in z around 0 46.6%

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

      1. associate-*l/ 51.5%

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

   10. Simplified 51.5%

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

   if -1.80000000000000006e-106 < z < 1.6e-57

   1. Initial program 98.1%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around inf 69.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-106} \lor \neg \left(z \leq 1.6 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 53.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e-106) (* y (/ z t)) (if (<= z 1.75e-57) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-106) {
		tmp = y * (z / t);
	} else if (z <= 1.75e-57) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.3d-106)) then
        tmp = y * (z / t)
    else if (z <= 1.75d-57) then
        tmp = x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-106) {
		tmp = y * (z / t);
	} else if (z <= 1.75e-57) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e-106:
		tmp = y * (z / t)
	elif z <= 1.75e-57:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e-106)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 1.75e-57)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.3e-106)
		tmp = y * (z / t);
	elseif (z <= 1.75e-57)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e-106], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-57], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e-106

   1. Initial program 86.6%

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

   2. Taylor expanded in t around 0 75.0%

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

   3. Taylor expanded in y around inf 42.5%

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

      1. *-commutative 42.5%

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

   5. Simplified 42.5%

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

      1. associate-/l* 49.5%

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

      2. associate-/r/ 49.6%

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

   7. Applied egg-rr 49.6%

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

   if -1.3e-106 < z < 1.74999999999999996e-57

   1. Initial program 98.1%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around inf 69.9%

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

   if 1.74999999999999996e-57 < z

   1. Initial program 91.0%

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

   2. Taylor expanded in t around 0 83.5%

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

   3. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

   5. Simplified 52.6%

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

      1. associate-/l* 55.5%

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

      2. associate-/r/ 51.3%

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

   7. Applied egg-rr 51.3%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. associate-*l/ 55.6%

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

   10. Simplified 55.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 12: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 95.5%

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

3. Simplified 95.5%

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

4. Final simplification 95.5%

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

Alternative 13: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 95.5%

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

3. Simplified 95.5%

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

   1. *-commutative 95.5%

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

   2. clear-num 95.4%

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

   3. un-div-inv 96.3%

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

5. Applied egg-rr 96.3%

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

6. Final simplification 96.3%

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

Alternative 14: 38.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-/l* 96.3%

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

3. Simplified 96.3%

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

4. Taylor expanded in t around inf 36.5%

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

5. Final simplification 36.5%

   \[\leadsto x \]

Developer target: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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