Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.8% → 98.5%

Time: 10.4s

Alternatives: 17

Speedup: 1.0×

• 24.9% 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: 92.8% 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: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-8} \lor \neg \left(t \leq 5 \cdot 10^{-48}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2e-8) (not (<= t 5e-48)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2e-8) || !(t <= 5e-48)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (((y - 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 ((t <= (-2d-8)) .or. (.not. (t <= 5d-48))) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x + (((y - 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 ((t <= -2e-8) || !(t <= 5e-48)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (((y - x) * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2e-8) or not (t <= 5e-48):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + (((y - x) * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2e-8) || !(t <= 5e-48))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2e-8) || ~((t <= 5e-48)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + (((y - x) * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2e-8], N[Not[LessEqual[t, 5e-48]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2e-8 or 4.9999999999999999e-48 < t

   1. Initial program 85.6%

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

      1. associate-*l/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   if -2e-8 < t < 4.9999999999999999e-48

   1. Initial program 98.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-8} \lor \neg \left(t \leq 5 \cdot 10^{-48}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+183}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) t))) (t_2 (* y (/ z t))))
   (if (<= t -3.7e+53)
     x
     (if (<= t -1.2e-74)
       t_2
       (if (<= t -1.05e-139)
         t_1
         (if (<= t -5.2e-216)
           (/ (* y z) t)
           (if (<= t 2.9e-159)
             t_1
             (if (<= t 1.32e-36)
               t_2
               (if (<= t 4.5e+42)
                 x
                 (if (<= t 1.4e+183) (* z (/ y t)) x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / t);
	double t_2 = y * (z / t);
	double tmp;
	if (t <= -3.7e+53) {
		tmp = x;
	} else if (t <= -1.2e-74) {
		tmp = t_2;
	} else if (t <= -1.05e-139) {
		tmp = t_1;
	} else if (t <= -5.2e-216) {
		tmp = (y * z) / t;
	} else if (t <= 2.9e-159) {
		tmp = t_1;
	} else if (t <= 1.32e-36) {
		tmp = t_2;
	} else if (t <= 4.5e+42) {
		tmp = x;
	} else if (t <= 1.4e+183) {
		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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (-z / t)
    t_2 = y * (z / t)
    if (t <= (-3.7d+53)) then
        tmp = x
    else if (t <= (-1.2d-74)) then
        tmp = t_2
    else if (t <= (-1.05d-139)) then
        tmp = t_1
    else if (t <= (-5.2d-216)) then
        tmp = (y * z) / t
    else if (t <= 2.9d-159) then
        tmp = t_1
    else if (t <= 1.32d-36) then
        tmp = t_2
    else if (t <= 4.5d+42) then
        tmp = x
    else if (t <= 1.4d+183) 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 t_1 = x * (-z / t);
	double t_2 = y * (z / t);
	double tmp;
	if (t <= -3.7e+53) {
		tmp = x;
	} else if (t <= -1.2e-74) {
		tmp = t_2;
	} else if (t <= -1.05e-139) {
		tmp = t_1;
	} else if (t <= -5.2e-216) {
		tmp = (y * z) / t;
	} else if (t <= 2.9e-159) {
		tmp = t_1;
	} else if (t <= 1.32e-36) {
		tmp = t_2;
	} else if (t <= 4.5e+42) {
		tmp = x;
	} else if (t <= 1.4e+183) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-z / t)
	t_2 = y * (z / t)
	tmp = 0
	if t <= -3.7e+53:
		tmp = x
	elif t <= -1.2e-74:
		tmp = t_2
	elif t <= -1.05e-139:
		tmp = t_1
	elif t <= -5.2e-216:
		tmp = (y * z) / t
	elif t <= 2.9e-159:
		tmp = t_1
	elif t <= 1.32e-36:
		tmp = t_2
	elif t <= 4.5e+42:
		tmp = x
	elif t <= 1.4e+183:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-z) / t))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -3.7e+53)
		tmp = x;
	elseif (t <= -1.2e-74)
		tmp = t_2;
	elseif (t <= -1.05e-139)
		tmp = t_1;
	elseif (t <= -5.2e-216)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 2.9e-159)
		tmp = t_1;
	elseif (t <= 1.32e-36)
		tmp = t_2;
	elseif (t <= 4.5e+42)
		tmp = x;
	elseif (t <= 1.4e+183)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-z / t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if (t <= -3.7e+53)
		tmp = x;
	elseif (t <= -1.2e-74)
		tmp = t_2;
	elseif (t <= -1.05e-139)
		tmp = t_1;
	elseif (t <= -5.2e-216)
		tmp = (y * z) / t;
	elseif (t <= 2.9e-159)
		tmp = t_1;
	elseif (t <= 1.32e-36)
		tmp = t_2;
	elseif (t <= 4.5e+42)
		tmp = x;
	elseif (t <= 1.4e+183)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+53], x, If[LessEqual[t, -1.2e-74], t$95$2, If[LessEqual[t, -1.05e-139], t$95$1, If[LessEqual[t, -5.2e-216], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.9e-159], t$95$1, If[LessEqual[t, 1.32e-36], t$95$2, If[LessEqual[t, 4.5e+42], x, If[LessEqual[t, 1.4e+183], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.7e53 or 1.31999999999999993e-36 < t < 4.50000000000000012e42 or 1.40000000000000009e183 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -3.7e53 < t < -1.1999999999999999e-74 or 2.8999999999999999e-159 < t < 1.31999999999999993e-36

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 80.0%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. associate-*r/ 60.0%

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

   5. Simplified 60.0%

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

   if -1.1999999999999999e-74 < t < -1.05000000000000004e-139 or -5.1999999999999997e-216 < t < 2.8999999999999999e-159

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 88.5%

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

   3. Taylor expanded in y around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. mul-1-neg 58.4%

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

      3. distribute-rgt-neg-out 58.4%

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

      4. associate-*l/ 60.2%

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

   5. Simplified 60.2%

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

   if -1.05000000000000004e-139 < t < -5.1999999999999997e-216

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 93.2%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if 4.50000000000000012e42 < t < 1.40000000000000009e183

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+183}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -7.8e+43)
     x
     (if (<= t -2e-74)
       t_1
       (if (<= t -2.45e-124)
         (* z (- (/ x t)))
         (if (<= t -9.6e-216)
           (/ (* y z) t)
           (if (<= t 3.3e-161)
             (* x (/ (- z) t))
             (if (<= t 2.9e-30)
               t_1
               (if (<= t 9e+45) x (if (<= t 3.1e+182) (* z (/ y t)) x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -7.8e+43) {
		tmp = x;
	} else if (t <= -2e-74) {
		tmp = t_1;
	} else if (t <= -2.45e-124) {
		tmp = z * -(x / t);
	} else if (t <= -9.6e-216) {
		tmp = (y * z) / t;
	} else if (t <= 3.3e-161) {
		tmp = x * (-z / t);
	} else if (t <= 2.9e-30) {
		tmp = t_1;
	} else if (t <= 9e+45) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (t <= (-7.8d+43)) then
        tmp = x
    else if (t <= (-2d-74)) then
        tmp = t_1
    else if (t <= (-2.45d-124)) then
        tmp = z * -(x / t)
    else if (t <= (-9.6d-216)) then
        tmp = (y * z) / t
    else if (t <= 3.3d-161) then
        tmp = x * (-z / t)
    else if (t <= 2.9d-30) then
        tmp = t_1
    else if (t <= 9d+45) then
        tmp = x
    else if (t <= 3.1d+182) 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 t_1 = y * (z / t);
	double tmp;
	if (t <= -7.8e+43) {
		tmp = x;
	} else if (t <= -2e-74) {
		tmp = t_1;
	} else if (t <= -2.45e-124) {
		tmp = z * -(x / t);
	} else if (t <= -9.6e-216) {
		tmp = (y * z) / t;
	} else if (t <= 3.3e-161) {
		tmp = x * (-z / t);
	} else if (t <= 2.9e-30) {
		tmp = t_1;
	} else if (t <= 9e+45) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if t <= -7.8e+43:
		tmp = x
	elif t <= -2e-74:
		tmp = t_1
	elif t <= -2.45e-124:
		tmp = z * -(x / t)
	elif t <= -9.6e-216:
		tmp = (y * z) / t
	elif t <= 3.3e-161:
		tmp = x * (-z / t)
	elif t <= 2.9e-30:
		tmp = t_1
	elif t <= 9e+45:
		tmp = x
	elif t <= 3.1e+182:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -7.8e+43)
		tmp = x;
	elseif (t <= -2e-74)
		tmp = t_1;
	elseif (t <= -2.45e-124)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (t <= -9.6e-216)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 3.3e-161)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (t <= 2.9e-30)
		tmp = t_1;
	elseif (t <= 9e+45)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (t <= -7.8e+43)
		tmp = x;
	elseif (t <= -2e-74)
		tmp = t_1;
	elseif (t <= -2.45e-124)
		tmp = z * -(x / t);
	elseif (t <= -9.6e-216)
		tmp = (y * z) / t;
	elseif (t <= 3.3e-161)
		tmp = x * (-z / t);
	elseif (t <= 2.9e-30)
		tmp = t_1;
	elseif (t <= 9e+45)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+43], x, If[LessEqual[t, -2e-74], t$95$1, If[LessEqual[t, -2.45e-124], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, -9.6e-216], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3.3e-161], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-30], t$95$1, If[LessEqual[t, 9e+45], x, If[LessEqual[t, 3.1e+182], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.8000000000000001e43 or 2.89999999999999989e-30 < t < 8.9999999999999997e45 or 3.09999999999999996e182 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -7.8000000000000001e43 < t < -1.99999999999999992e-74 or 3.2999999999999998e-161 < t < 2.89999999999999989e-30

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 80.0%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. associate-*r/ 60.0%

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

   5. Simplified 60.0%

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

   if -1.99999999999999992e-74 < t < -2.44999999999999983e-124

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 80.5%

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

      1. associate-*l/ 99.4%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in y around 0 65.5%

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

      1. neg-mul-1 65.5%

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

      2. distribute-neg-frac 65.5%

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

   7. Simplified 65.5%

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

   if -2.44999999999999983e-124 < t < -9.60000000000000014e-216

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 93.2%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -9.60000000000000014e-216 < t < 3.2999999999999998e-161

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 91.6%

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

   3. Taylor expanded in y around 0 55.5%

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

      1. associate-*r/ 55.5%

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

      2. mul-1-neg 55.5%

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

      3. distribute-rgt-neg-out 55.5%

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

      4. associate-*l/ 60.6%

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

   5. Simplified 60.6%

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

   if 8.9999999999999997e45 < t < 3.09999999999999996e182

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -6.4e+49)
     x
     (if (<= t -1.1e-74)
       t_1
       (if (<= t -4.1e-129)
         (/ (- z) (/ t x))
         (if (<= t -9.8e-216)
           (/ (* y z) t)
           (if (<= t 1.7e-161)
             (* x (/ (- z) t))
             (if (<= t 1.6e-25)
               t_1
               (if (<= t 1.02e+47)
                 x
                 (if (<= t 9.8e+185) (* z (/ y t)) x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -6.4e+49) {
		tmp = x;
	} else if (t <= -1.1e-74) {
		tmp = t_1;
	} else if (t <= -4.1e-129) {
		tmp = -z / (t / x);
	} else if (t <= -9.8e-216) {
		tmp = (y * z) / t;
	} else if (t <= 1.7e-161) {
		tmp = x * (-z / t);
	} else if (t <= 1.6e-25) {
		tmp = t_1;
	} else if (t <= 1.02e+47) {
		tmp = x;
	} else if (t <= 9.8e+185) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (t <= (-6.4d+49)) then
        tmp = x
    else if (t <= (-1.1d-74)) then
        tmp = t_1
    else if (t <= (-4.1d-129)) then
        tmp = -z / (t / x)
    else if (t <= (-9.8d-216)) then
        tmp = (y * z) / t
    else if (t <= 1.7d-161) then
        tmp = x * (-z / t)
    else if (t <= 1.6d-25) then
        tmp = t_1
    else if (t <= 1.02d+47) then
        tmp = x
    else if (t <= 9.8d+185) 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 t_1 = y * (z / t);
	double tmp;
	if (t <= -6.4e+49) {
		tmp = x;
	} else if (t <= -1.1e-74) {
		tmp = t_1;
	} else if (t <= -4.1e-129) {
		tmp = -z / (t / x);
	} else if (t <= -9.8e-216) {
		tmp = (y * z) / t;
	} else if (t <= 1.7e-161) {
		tmp = x * (-z / t);
	} else if (t <= 1.6e-25) {
		tmp = t_1;
	} else if (t <= 1.02e+47) {
		tmp = x;
	} else if (t <= 9.8e+185) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if t <= -6.4e+49:
		tmp = x
	elif t <= -1.1e-74:
		tmp = t_1
	elif t <= -4.1e-129:
		tmp = -z / (t / x)
	elif t <= -9.8e-216:
		tmp = (y * z) / t
	elif t <= 1.7e-161:
		tmp = x * (-z / t)
	elif t <= 1.6e-25:
		tmp = t_1
	elif t <= 1.02e+47:
		tmp = x
	elif t <= 9.8e+185:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -6.4e+49)
		tmp = x;
	elseif (t <= -1.1e-74)
		tmp = t_1;
	elseif (t <= -4.1e-129)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (t <= -9.8e-216)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 1.7e-161)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (t <= 1.6e-25)
		tmp = t_1;
	elseif (t <= 1.02e+47)
		tmp = x;
	elseif (t <= 9.8e+185)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (t <= -6.4e+49)
		tmp = x;
	elseif (t <= -1.1e-74)
		tmp = t_1;
	elseif (t <= -4.1e-129)
		tmp = -z / (t / x);
	elseif (t <= -9.8e-216)
		tmp = (y * z) / t;
	elseif (t <= 1.7e-161)
		tmp = x * (-z / t);
	elseif (t <= 1.6e-25)
		tmp = t_1;
	elseif (t <= 1.02e+47)
		tmp = x;
	elseif (t <= 9.8e+185)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e+49], x, If[LessEqual[t, -1.1e-74], t$95$1, If[LessEqual[t, -4.1e-129], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e-216], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.7e-161], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-25], t$95$1, If[LessEqual[t, 1.02e+47], x, If[LessEqual[t, 9.8e+185], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -6.40000000000000028e49 or 1.6000000000000001e-25 < t < 1.0199999999999999e47 or 9.79999999999999968e185 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -6.40000000000000028e49 < t < -1.10000000000000005e-74 or 1.69999999999999991e-161 < t < 1.6000000000000001e-25

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 80.0%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. associate-*r/ 60.0%

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

   5. Simplified 60.0%

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

   if -1.10000000000000005e-74 < t < -4.1e-129

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 80.5%

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

   3. Taylor expanded in y around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. mul-1-neg 65.8%

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

      3. distribute-rgt-neg-out 65.8%

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

      4. associate-*l/ 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in z around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-/l* 65.6%

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

      3. distribute-neg-frac 65.6%

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

   8. Simplified 65.6%

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

   if -4.1e-129 < t < -9.8000000000000003e-216

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 93.2%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -9.8000000000000003e-216 < t < 1.69999999999999991e-161

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 91.6%

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

   3. Taylor expanded in y around 0 55.5%

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

      1. associate-*r/ 55.5%

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

      2. mul-1-neg 55.5%

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

      3. distribute-rgt-neg-out 55.5%

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

      4. associate-*l/ 60.6%

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

   5. Simplified 60.6%

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

   if 1.0199999999999999e47 < t < 9.79999999999999968e185

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-129}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 51.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-215}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -4.2e+48)
     x
     (if (<= t -2e-74)
       t_1
       (if (<= t -7.2e-135)
         (/ (* x (- z)) t)
         (if (<= t -1.25e-215)
           (/ (* y z) t)
           (if (<= t 2.4e-159)
             (* x (/ (- z) t))
             (if (<= t 1.7e-32)
               t_1
               (if (<= t 1.9e+47)
                 x
                 (if (<= t 3.2e+182) (* z (/ y t)) x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -4.2e+48) {
		tmp = x;
	} else if (t <= -2e-74) {
		tmp = t_1;
	} else if (t <= -7.2e-135) {
		tmp = (x * -z) / t;
	} else if (t <= -1.25e-215) {
		tmp = (y * z) / t;
	} else if (t <= 2.4e-159) {
		tmp = x * (-z / t);
	} else if (t <= 1.7e-32) {
		tmp = t_1;
	} else if (t <= 1.9e+47) {
		tmp = x;
	} else if (t <= 3.2e+182) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (t <= (-4.2d+48)) then
        tmp = x
    else if (t <= (-2d-74)) then
        tmp = t_1
    else if (t <= (-7.2d-135)) then
        tmp = (x * -z) / t
    else if (t <= (-1.25d-215)) then
        tmp = (y * z) / t
    else if (t <= 2.4d-159) then
        tmp = x * (-z / t)
    else if (t <= 1.7d-32) then
        tmp = t_1
    else if (t <= 1.9d+47) then
        tmp = x
    else if (t <= 3.2d+182) 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 t_1 = y * (z / t);
	double tmp;
	if (t <= -4.2e+48) {
		tmp = x;
	} else if (t <= -2e-74) {
		tmp = t_1;
	} else if (t <= -7.2e-135) {
		tmp = (x * -z) / t;
	} else if (t <= -1.25e-215) {
		tmp = (y * z) / t;
	} else if (t <= 2.4e-159) {
		tmp = x * (-z / t);
	} else if (t <= 1.7e-32) {
		tmp = t_1;
	} else if (t <= 1.9e+47) {
		tmp = x;
	} else if (t <= 3.2e+182) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if t <= -4.2e+48:
		tmp = x
	elif t <= -2e-74:
		tmp = t_1
	elif t <= -7.2e-135:
		tmp = (x * -z) / t
	elif t <= -1.25e-215:
		tmp = (y * z) / t
	elif t <= 2.4e-159:
		tmp = x * (-z / t)
	elif t <= 1.7e-32:
		tmp = t_1
	elif t <= 1.9e+47:
		tmp = x
	elif t <= 3.2e+182:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -4.2e+48)
		tmp = x;
	elseif (t <= -2e-74)
		tmp = t_1;
	elseif (t <= -7.2e-135)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (t <= -1.25e-215)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 2.4e-159)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (t <= 1.7e-32)
		tmp = t_1;
	elseif (t <= 1.9e+47)
		tmp = x;
	elseif (t <= 3.2e+182)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (t <= -4.2e+48)
		tmp = x;
	elseif (t <= -2e-74)
		tmp = t_1;
	elseif (t <= -7.2e-135)
		tmp = (x * -z) / t;
	elseif (t <= -1.25e-215)
		tmp = (y * z) / t;
	elseif (t <= 2.4e-159)
		tmp = x * (-z / t);
	elseif (t <= 1.7e-32)
		tmp = t_1;
	elseif (t <= 1.9e+47)
		tmp = x;
	elseif (t <= 3.2e+182)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+48], x, If[LessEqual[t, -2e-74], t$95$1, If[LessEqual[t, -7.2e-135], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.25e-215], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.4e-159], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-32], t$95$1, If[LessEqual[t, 1.9e+47], x, If[LessEqual[t, 3.2e+182], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.1999999999999997e48 or 1.69999999999999989e-32 < t < 1.9000000000000002e47 or 3.1999999999999997e182 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -4.1999999999999997e48 < t < -1.99999999999999992e-74 or 2.39999999999999997e-159 < t < 1.69999999999999989e-32

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 80.0%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. associate-*r/ 60.0%

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

   5. Simplified 60.0%

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

   if -1.99999999999999992e-74 < t < -7.19999999999999955e-135

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 80.5%

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

   3. Taylor expanded in y around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. distribute-rgt-neg-out 65.8%

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

   5. Simplified 65.8%

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

   if -7.19999999999999955e-135 < t < -1.24999999999999989e-215

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 93.2%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -1.24999999999999989e-215 < t < 2.39999999999999997e-159

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 91.6%

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

   3. Taylor expanded in y around 0 55.5%

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

      1. associate-*r/ 55.5%

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

      2. mul-1-neg 55.5%

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

      3. distribute-rgt-neg-out 55.5%

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

      4. associate-*l/ 60.6%

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

   5. Simplified 60.6%

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

   if 1.9000000000000002e47 < t < 3.1999999999999997e182

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-215}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+92} \lor \neg \left(t \leq -5.2 \cdot 10^{+57}\right) \land t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e+153)
   x
   (if (or (<= t -7.2e+92) (and (not (<= t -5.2e+57)) (<= t 3.1e+182)))
     (* (- y x) (/ z t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+153) {
		tmp = x;
	} else if ((t <= -7.2e+92) || (!(t <= -5.2e+57) && (t <= 3.1e+182))) {
		tmp = (y - x) * (z / 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 (t <= (-1.6d+153)) then
        tmp = x
    else if ((t <= (-7.2d+92)) .or. (.not. (t <= (-5.2d+57))) .and. (t <= 3.1d+182)) then
        tmp = (y - x) * (z / 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 (t <= -1.6e+153) {
		tmp = x;
	} else if ((t <= -7.2e+92) || (!(t <= -5.2e+57) && (t <= 3.1e+182))) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e+153:
		tmp = x
	elif (t <= -7.2e+92) or (not (t <= -5.2e+57) and (t <= 3.1e+182)):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e+153)
		tmp = x;
	elseif ((t <= -7.2e+92) || (!(t <= -5.2e+57) && (t <= 3.1e+182)))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e+153)
		tmp = x;
	elseif ((t <= -7.2e+92) || (~((t <= -5.2e+57)) && (t <= 3.1e+182)))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e+153], x, If[Or[LessEqual[t, -7.2e+92], And[N[Not[LessEqual[t, -5.2e+57]], $MachinePrecision], LessEqual[t, 3.1e+182]]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6000000000000001e153 or -7.2e92 < t < -5.2e57 or 3.09999999999999996e182 < t

   1. Initial program 79.8%

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

   2. Taylor expanded in z around 0 84.2%

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

   if -1.6000000000000001e153 < t < -7.2e92 or -5.2e57 < t < 3.09999999999999996e182

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*l/ 78.2%

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

   4. Applied egg-rr 78.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+92} \lor \neg \left(t \leq -5.2 \cdot 10^{+57}\right) \land t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+92}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+183}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e+150)
   x
   (if (<= t -9e+92)
     (* z (/ (- y x) t))
     (if (<= t -3.8e+56) x (if (<= t 2.3e+183) (* (- y x) (/ z t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+150) {
		tmp = x;
	} else if (t <= -9e+92) {
		tmp = z * ((y - x) / t);
	} else if (t <= -3.8e+56) {
		tmp = x;
	} else if (t <= 2.3e+183) {
		tmp = (y - x) * (z / 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 (t <= (-5d+150)) then
        tmp = x
    else if (t <= (-9d+92)) then
        tmp = z * ((y - x) / t)
    else if (t <= (-3.8d+56)) then
        tmp = x
    else if (t <= 2.3d+183) then
        tmp = (y - x) * (z / 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 (t <= -5e+150) {
		tmp = x;
	} else if (t <= -9e+92) {
		tmp = z * ((y - x) / t);
	} else if (t <= -3.8e+56) {
		tmp = x;
	} else if (t <= 2.3e+183) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e+150:
		tmp = x
	elif t <= -9e+92:
		tmp = z * ((y - x) / t)
	elif t <= -3.8e+56:
		tmp = x
	elif t <= 2.3e+183:
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e+150)
		tmp = x;
	elseif (t <= -9e+92)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (t <= -3.8e+56)
		tmp = x;
	elseif (t <= 2.3e+183)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5e+150)
		tmp = x;
	elseif (t <= -9e+92)
		tmp = z * ((y - x) / t);
	elseif (t <= -3.8e+56)
		tmp = x;
	elseif (t <= 2.3e+183)
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e+150], x, If[LessEqual[t, -9e+92], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e+56], x, If[LessEqual[t, 2.3e+183], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000009e150 or -8.9999999999999998e92 < t < -3.79999999999999996e56 or 2.2999999999999998e183 < t

   1. Initial program 79.8%

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

   2. Taylor expanded in z around 0 84.2%

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

   if -5.00000000000000009e150 < t < -8.9999999999999998e92

   1. Initial program 92.9%

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

   2. Taylor expanded in t around 0 63.5%

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

      1. associate-*l/ 99.9%

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

   4. Applied egg-rr 70.5%

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

   if -3.79999999999999996e56 < t < 2.2999999999999998e183

   1. Initial program 96.8%

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

   2. Taylor expanded in t around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l/ 78.9%

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

   4. Applied egg-rr 78.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+92}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+183}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-26} \lor \neg \left(t \leq 1.15 \cdot 10^{+43}\right) \land t \leq 5 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.8e+47)
   x
   (if (or (<= t 1.05e-26) (and (not (<= t 1.15e+43)) (<= t 5e+182)))
     (* y (/ z t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e+47) {
		tmp = x;
	} else if ((t <= 1.05e-26) || (!(t <= 1.15e+43) && (t <= 5e+182))) {
		tmp = y * (z / 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 (t <= (-2.8d+47)) then
        tmp = x
    else if ((t <= 1.05d-26) .or. (.not. (t <= 1.15d+43)) .and. (t <= 5d+182)) then
        tmp = y * (z / 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 (t <= -2.8e+47) {
		tmp = x;
	} else if ((t <= 1.05e-26) || (!(t <= 1.15e+43) && (t <= 5e+182))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.8e+47:
		tmp = x
	elif (t <= 1.05e-26) or (not (t <= 1.15e+43) and (t <= 5e+182)):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.8e+47)
		tmp = x;
	elseif ((t <= 1.05e-26) || (!(t <= 1.15e+43) && (t <= 5e+182)))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.8e+47)
		tmp = x;
	elseif ((t <= 1.05e-26) || (~((t <= 1.15e+43)) && (t <= 5e+182)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.8e+47], x, If[Or[LessEqual[t, 1.05e-26], And[N[Not[LessEqual[t, 1.15e+43]], $MachinePrecision], LessEqual[t, 5e+182]]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999988e47 or 1.05000000000000004e-26 < t < 1.1500000000000001e43 or 4.99999999999999973e182 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -2.79999999999999988e47 < t < 1.05000000000000004e-26 or 1.1500000000000001e43 < t < 4.99999999999999973e182

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0 82.2%

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

   3. Taylor expanded in y around inf 53.7%

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

      1. associate-*r/ 54.3%

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

   5. Simplified 54.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-26} \lor \neg \left(t \leq 1.15 \cdot 10^{+43}\right) \land t \leq 5 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.85e+49)
   x
   (if (<= t 4.9e-42)
     (* y (/ z t))
     (if (<= t 7.6e+47) x (if (<= t 3.1e+182) (* z (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.85e+49) {
		tmp = x;
	} else if (t <= 4.9e-42) {
		tmp = y * (z / t);
	} else if (t <= 7.6e+47) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		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 (t <= (-1.85d+49)) then
        tmp = x
    else if (t <= 4.9d-42) then
        tmp = y * (z / t)
    else if (t <= 7.6d+47) then
        tmp = x
    else if (t <= 3.1d+182) 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 (t <= -1.85e+49) {
		tmp = x;
	} else if (t <= 4.9e-42) {
		tmp = y * (z / t);
	} else if (t <= 7.6e+47) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.85e+49:
		tmp = x
	elif t <= 4.9e-42:
		tmp = y * (z / t)
	elif t <= 7.6e+47:
		tmp = x
	elif t <= 3.1e+182:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.85e+49)
		tmp = x;
	elseif (t <= 4.9e-42)
		tmp = Float64(y * Float64(z / t));
	elseif (t <= 7.6e+47)
		tmp = x;
	elseif (t <= 3.1e+182)
		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 (t <= -1.85e+49)
		tmp = x;
	elseif (t <= 4.9e-42)
		tmp = y * (z / t);
	elseif (t <= 7.6e+47)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.85e+49], x, If[LessEqual[t, 4.9e-42], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+47], x, If[LessEqual[t, 3.1e+182], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.85000000000000009e49 or 4.9e-42 < t < 7.6000000000000007e47 or 3.09999999999999996e182 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -1.85000000000000009e49 < t < 4.9e-42

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 86.9%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. associate-*r/ 53.6%

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

   5. Simplified 53.6%

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

   if 7.6000000000000007e47 < t < 3.09999999999999996e182

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.2e+52)
   x
   (if (<= t 1.42e-39)
     (/ y (/ t z))
     (if (<= t 3.05e+44) x (if (<= t 3.1e+182) (* z (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+52) {
		tmp = x;
	} else if (t <= 1.42e-39) {
		tmp = y / (t / z);
	} else if (t <= 3.05e+44) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		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 (t <= (-2.2d+52)) then
        tmp = x
    else if (t <= 1.42d-39) then
        tmp = y / (t / z)
    else if (t <= 3.05d+44) then
        tmp = x
    else if (t <= 3.1d+182) 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 (t <= -2.2e+52) {
		tmp = x;
	} else if (t <= 1.42e-39) {
		tmp = y / (t / z);
	} else if (t <= 3.05e+44) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.2e+52:
		tmp = x
	elif t <= 1.42e-39:
		tmp = y / (t / z)
	elif t <= 3.05e+44:
		tmp = x
	elif t <= 3.1e+182:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.2e+52)
		tmp = x;
	elseif (t <= 1.42e-39)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= 3.05e+44)
		tmp = x;
	elseif (t <= 3.1e+182)
		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 (t <= -2.2e+52)
		tmp = x;
	elseif (t <= 1.42e-39)
		tmp = y / (t / z);
	elseif (t <= 3.05e+44)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.2e+52], x, If[LessEqual[t, 1.42e-39], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.05e+44], x, If[LessEqual[t, 3.1e+182], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e52 or 1.42000000000000005e-39 < t < 3.04999999999999991e44 or 3.09999999999999996e182 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -2.2e52 < t < 1.42000000000000005e-39

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 86.9%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. associate-*r/ 53.6%

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

   5. Simplified 53.6%

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

      1. clear-num 53.6%

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

      2. un-div-inv 53.7%

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

   7. Applied egg-rr 53.7%

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

   if 3.04999999999999991e44 < t < 3.09999999999999996e182

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.65e+53)
   x
   (if (<= t 1.9e-28)
     (/ (* y z) t)
     (if (<= t 7.2e+45) x (if (<= t 3.1e+182) (* z (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e+53) {
		tmp = x;
	} else if (t <= 1.9e-28) {
		tmp = (y * z) / t;
	} else if (t <= 7.2e+45) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		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 (t <= (-1.65d+53)) then
        tmp = x
    else if (t <= 1.9d-28) then
        tmp = (y * z) / t
    else if (t <= 7.2d+45) then
        tmp = x
    else if (t <= 3.1d+182) 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 (t <= -1.65e+53) {
		tmp = x;
	} else if (t <= 1.9e-28) {
		tmp = (y * z) / t;
	} else if (t <= 7.2e+45) {
		tmp = x;
	} else if (t <= 3.1e+182) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.65e+53:
		tmp = x
	elif t <= 1.9e-28:
		tmp = (y * z) / t
	elif t <= 7.2e+45:
		tmp = x
	elif t <= 3.1e+182:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.65e+53)
		tmp = x;
	elseif (t <= 1.9e-28)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 7.2e+45)
		tmp = x;
	elseif (t <= 3.1e+182)
		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 (t <= -1.65e+53)
		tmp = x;
	elseif (t <= 1.9e-28)
		tmp = (y * z) / t;
	elseif (t <= 7.2e+45)
		tmp = x;
	elseif (t <= 3.1e+182)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.65e+53], x, If[LessEqual[t, 1.9e-28], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 7.2e+45], x, If[LessEqual[t, 3.1e+182], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6500000000000001e53 or 1.90000000000000005e-28 < t < 7.2e45 or 3.09999999999999996e182 < t

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -1.6500000000000001e53 < t < 1.90000000000000005e-28

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 86.9%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   if 7.2e45 < t < 3.09999999999999996e182

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 56.6%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. associate-*l/ 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-28}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-28} \lor \neg \left(t \leq 3.2 \cdot 10^{-86}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e-28) (not (<= t 3.2e-86)))
   (+ x (* y (/ z t)))
   (* (- y x) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e-28) || !(t <= 3.2e-86)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - 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 ((t <= (-3d-28)) .or. (.not. (t <= 3.2d-86))) then
        tmp = x + (y * (z / t))
    else
        tmp = (y - 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 ((t <= -3e-28) || !(t <= 3.2e-86)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3e-28) or not (t <= 3.2e-86):
		tmp = x + (y * (z / t))
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3e-28) || !(t <= 3.2e-86))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3e-28) || ~((t <= 3.2e-86)))
		tmp = x + (y * (z / t));
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3e-28], N[Not[LessEqual[t, 3.2e-86]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000003e-28 or 3.20000000000000006e-86 < t

   1. Initial program 86.6%

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

   2. Taylor expanded in y around inf 84.3%

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

      1. associate-*r/ 29.8%

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

   4. Simplified 90.0%

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

   if -3.00000000000000003e-28 < t < 3.20000000000000006e-86

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*l/ 88.2%

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

   4. Applied egg-rr 88.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-28} \lor \neg \left(t \leq 3.2 \cdot 10^{-86}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 13: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-6} \lor \neg \left(y \leq 1.65 \cdot 10^{+36}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.8e-6) (not (<= y 1.65e+36)))
   (+ x (* y (/ z t)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-6) || !(y <= 1.65e+36)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (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 ((y <= (-9.8d-6)) .or. (.not. (y <= 1.65d+36))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (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 ((y <= -9.8e-6) || !(y <= 1.65e+36)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.8e-6) or not (y <= 1.65e+36):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.8e-6) || !(y <= 1.65e+36))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.8e-6) || ~((y <= 1.65e+36)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.8e-6], N[Not[LessEqual[y, 1.65e+36]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999934e-6 or 1.6499999999999999e36 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 85.6%

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

      1. associate-*r/ 60.7%

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

   4. Simplified 92.2%

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

   if -9.79999999999999934e-6 < y < 1.6499999999999999e36

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. distribute-lft-in 88.5%

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

      3. *-rgt-identity 88.5%

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

      4. mul-1-neg 88.5%

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

      5. distribute-rgt-neg-in 88.5%

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

      6. unsub-neg 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-6} \lor \neg \left(y \leq 1.65 \cdot 10^{+36}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 14: 93.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+93}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.8e+93) (+ x (* y (/ z t))) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e+93) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + (z * ((y - x) / 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 <= (-7.8d+93)) then
        tmp = x + (y * (z / t))
    else
        tmp = x + (z * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e+93) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.8e+93:
		tmp = x + (y * (z / t))
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.8e+93)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.8e+93)
		tmp = x + (y * (z / t));
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.8e+93], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8000000000000005e93

   1. Initial program 86.7%

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

   2. Taylor expanded in y around inf 86.7%

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

      1. associate-*r/ 60.2%

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

   4. Simplified 98.0%

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

   if -7.8000000000000005e93 < y

   1. Initial program 92.0%

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

      1. associate-*l/ 95.7%

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

   3. Applied egg-rr 95.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+93}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 15: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-212}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e-212) (+ x (* z (/ (- y x) t))) (+ x (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-212) {
		tmp = x + (z * ((y - x) / t));
	} 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 (z <= (-1.1d-212)) then
        tmp = x + (z * ((y - x) / t))
    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 (z <= -1.1e-212) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e-212:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e-212)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	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 (z <= -1.1e-212)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e-212], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $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 z < -1.10000000000000002e-212

   1. Initial program 87.5%

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

      1. associate-*l/ 99.1%

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

   3. Applied egg-rr 99.1%

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

   if -1.10000000000000002e-212 < z

   1. Initial program 94.1%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-212}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 16: 97.8% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.9%

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

   1. +-commutative 90.9%

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

   2. *-commutative 90.9%

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

   3. associate-*l/ 97.8%

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

   4. fma-def 97.8%

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

3. Simplified 97.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)} \]
4. Step-by-step derivation

   1. fma-udef 97.8%

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

   2. associate-*l/ 90.9%

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

   3. *-commutative 90.9%

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

   4. associate-*r/ 97.8%

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

5. Applied egg-rr 97.8%

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

6. Final simplification 97.8%

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

Alternative 17: 38.4% 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 90.9%

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

2. Taylor expanded in z around 0 42.4%

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

3. Final simplification 42.4%

   \[\leadsto x \]

Developer target: 97.8% 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 2023199 
(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)))