Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.9% → 97.9%

Time: 6.1s

Alternatives: 15

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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]

Initial Program: 97.9% 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]

Alternative 1: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (t / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

   1. clear-num 97.3%

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

   2. un-div-inv 97.6%

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

3. Applied egg-rr 97.6%

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

4. Final simplification 97.6%

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

Alternative 2: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))) (t_2 (* x (/ (- z) t))))
   (if (<= (/ z t) -5e+280)
     t_1
     (if (<= (/ z t) -2e+168)
       t_2
       (if (<= (/ z t) -5e+30)
         (* z (/ y t))
         (if (<= (/ z t) 5e-40)
           x
           (if (<= (/ z t) 5e+43)
             t_1
             (if (<= (/ z t) 2e+91) t_2 (/ y (/ t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double t_2 = x * (-z / t);
	double tmp;
	if ((z / t) <= -5e+280) {
		tmp = t_1;
	} else if ((z / t) <= -2e+168) {
		tmp = t_2;
	} else if ((z / t) <= -5e+30) {
		tmp = z * (y / t);
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else if ((z / t) <= 5e+43) {
		tmp = t_1;
	} else if ((z / t) <= 2e+91) {
		tmp = t_2;
	} else {
		tmp = y / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z / t)
    t_2 = x * (-z / t)
    if ((z / t) <= (-5d+280)) then
        tmp = t_1
    else if ((z / t) <= (-2d+168)) then
        tmp = t_2
    else if ((z / t) <= (-5d+30)) then
        tmp = z * (y / t)
    else if ((z / t) <= 5d-40) then
        tmp = x
    else if ((z / t) <= 5d+43) then
        tmp = t_1
    else if ((z / t) <= 2d+91) then
        tmp = t_2
    else
        tmp = y / (t / z)
    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 t_2 = x * (-z / t);
	double tmp;
	if ((z / t) <= -5e+280) {
		tmp = t_1;
	} else if ((z / t) <= -2e+168) {
		tmp = t_2;
	} else if ((z / t) <= -5e+30) {
		tmp = z * (y / t);
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else if ((z / t) <= 5e+43) {
		tmp = t_1;
	} else if ((z / t) <= 2e+91) {
		tmp = t_2;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	t_2 = x * (-z / t)
	tmp = 0
	if (z / t) <= -5e+280:
		tmp = t_1
	elif (z / t) <= -2e+168:
		tmp = t_2
	elif (z / t) <= -5e+30:
		tmp = z * (y / t)
	elif (z / t) <= 5e-40:
		tmp = x
	elif (z / t) <= 5e+43:
		tmp = t_1
	elif (z / t) <= 2e+91:
		tmp = t_2
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	t_2 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+280)
		tmp = t_1;
	elseif (Float64(z / t) <= -2e+168)
		tmp = t_2;
	elseif (Float64(z / t) <= -5e+30)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= 5e-40)
		tmp = x;
	elseif (Float64(z / t) <= 5e+43)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e+91)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	t_2 = x * (-z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+280)
		tmp = t_1;
	elseif ((z / t) <= -2e+168)
		tmp = t_2;
	elseif ((z / t) <= -5e+30)
		tmp = z * (y / t);
	elseif ((z / t) <= 5e-40)
		tmp = x;
	elseif ((z / t) <= 5e+43)
		tmp = t_1;
	elseif ((z / t) <= 2e+91)
		tmp = t_2;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+280], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -2e+168], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], -5e+30], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-40], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+43], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e+91], t$95$2, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -5.0000000000000002e280 or 4.99999999999999965e-40 < (/.f64 z t) < 5.0000000000000004e43

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 74.7%

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

   3. Taylor expanded in y around inf 69.5%

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

      1. associate-/r/ 72.1%

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

   5. Applied egg-rr 72.1%

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

      1. clear-num 72.1%

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

      2. associate-/r/ 74.8%

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

      3. clear-num 74.9%

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

   7. Applied egg-rr 74.9%

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

   if -5.0000000000000002e280 < (/.f64 z t) < -1.9999999999999999e168 or 5.0000000000000004e43 < (/.f64 z t) < 2.00000000000000016e91

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 91.5%

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

   3. Taylor expanded in y around 0 91.5%

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

      1. neg-mul-1 91.5%

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

      2. +-commutative 91.5%

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

      3. sub-neg 91.5%

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

      4. div-sub 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-/l* 67.5%

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

   8. Simplified 67.5%

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

      1. associate-/r/ 68.2%

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

   10. Applied egg-rr 68.2%

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

   if -1.9999999999999999e168 < (/.f64 z t) < -4.9999999999999998e30

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 91.9%

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

   3. Taylor expanded in y around inf 66.4%

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

   if -4.9999999999999998e30 < (/.f64 z t) < 4.99999999999999965e-40

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.2%

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

   if 2.00000000000000016e91 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.4%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. associate-/r/ 63.4%

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

   5. Applied egg-rr 63.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+280}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 63.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -5e+280)
     t_1
     (if (<= (/ z t) -2e+168)
       (* x (/ (- z) t))
       (if (<= (/ z t) -5e+30)
         (* z (/ y t))
         (if (<= (/ z t) 5e-40)
           x
           (if (<= (/ z t) 5e+43)
             t_1
             (if (<= (/ z t) 2e+91) (/ (- z) (/ t x)) (/ y (/ t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+280) {
		tmp = t_1;
	} else if ((z / t) <= -2e+168) {
		tmp = x * (-z / t);
	} else if ((z / t) <= -5e+30) {
		tmp = z * (y / t);
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else if ((z / t) <= 5e+43) {
		tmp = t_1;
	} else if ((z / t) <= 2e+91) {
		tmp = -z / (t / x);
	} else {
		tmp = y / (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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-5d+280)) then
        tmp = t_1
    else if ((z / t) <= (-2d+168)) then
        tmp = x * (-z / t)
    else if ((z / t) <= (-5d+30)) then
        tmp = z * (y / t)
    else if ((z / t) <= 5d-40) then
        tmp = x
    else if ((z / t) <= 5d+43) then
        tmp = t_1
    else if ((z / t) <= 2d+91) then
        tmp = -z / (t / x)
    else
        tmp = y / (t / z)
    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 ((z / t) <= -5e+280) {
		tmp = t_1;
	} else if ((z / t) <= -2e+168) {
		tmp = x * (-z / t);
	} else if ((z / t) <= -5e+30) {
		tmp = z * (y / t);
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else if ((z / t) <= 5e+43) {
		tmp = t_1;
	} else if ((z / t) <= 2e+91) {
		tmp = -z / (t / x);
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+280:
		tmp = t_1
	elif (z / t) <= -2e+168:
		tmp = x * (-z / t)
	elif (z / t) <= -5e+30:
		tmp = z * (y / t)
	elif (z / t) <= 5e-40:
		tmp = x
	elif (z / t) <= 5e+43:
		tmp = t_1
	elif (z / t) <= 2e+91:
		tmp = -z / (t / x)
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+280)
		tmp = t_1;
	elseif (Float64(z / t) <= -2e+168)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (Float64(z / t) <= -5e+30)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= 5e-40)
		tmp = x;
	elseif (Float64(z / t) <= 5e+43)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e+91)
		tmp = Float64(Float64(-z) / Float64(t / x));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+280)
		tmp = t_1;
	elseif ((z / t) <= -2e+168)
		tmp = x * (-z / t);
	elseif ((z / t) <= -5e+30)
		tmp = z * (y / t);
	elseif ((z / t) <= 5e-40)
		tmp = x;
	elseif ((z / t) <= 5e+43)
		tmp = t_1;
	elseif ((z / t) <= 2e+91)
		tmp = -z / (t / x);
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+280], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -2e+168], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+30], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-40], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+43], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e+91], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 z t) < -5.0000000000000002e280 or 4.99999999999999965e-40 < (/.f64 z t) < 5.0000000000000004e43

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 74.7%

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

   3. Taylor expanded in y around inf 69.5%

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

      1. associate-/r/ 72.1%

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

   5. Applied egg-rr 72.1%

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

      1. clear-num 72.1%

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

      2. associate-/r/ 74.8%

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

      3. clear-num 74.9%

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

   7. Applied egg-rr 74.9%

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

   if -5.0000000000000002e280 < (/.f64 z t) < -1.9999999999999999e168

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 86.7%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. neg-mul-1 86.7%

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

      2. +-commutative 86.7%

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

      3. sub-neg 86.7%

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

      4. div-sub 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-/l* 62.5%

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

   8. Simplified 62.5%

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

      1. associate-/r/ 67.7%

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

   10. Applied egg-rr 67.7%

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

   if -1.9999999999999999e168 < (/.f64 z t) < -4.9999999999999998e30

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 91.9%

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

   3. Taylor expanded in y around inf 66.4%

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

   if -4.9999999999999998e30 < (/.f64 z t) < 4.99999999999999965e-40

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.2%

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

   if 5.0000000000000004e43 < (/.f64 z t) < 2.00000000000000016e91

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. associate-/l* 76.3%

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

   8. Simplified 76.3%

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

   if 2.00000000000000016e91 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.4%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. associate-/r/ 63.4%

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

   5. Applied egg-rr 63.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+280}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 64.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -5e+30)
     t_1
     (if (<= (/ z t) 5e-40)
       x
       (if (<= (/ z t) 5e+43)
         t_1
         (if (<= (/ z t) 2e+91) (* z (/ (- x) t)) (/ y (/ t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+30) {
		tmp = t_1;
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else if ((z / t) <= 5e+43) {
		tmp = t_1;
	} else if ((z / t) <= 2e+91) {
		tmp = z * (-x / t);
	} else {
		tmp = y / (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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-5d+30)) then
        tmp = t_1
    else if ((z / t) <= 5d-40) then
        tmp = x
    else if ((z / t) <= 5d+43) then
        tmp = t_1
    else if ((z / t) <= 2d+91) then
        tmp = z * (-x / t)
    else
        tmp = y / (t / z)
    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 ((z / t) <= -5e+30) {
		tmp = t_1;
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else if ((z / t) <= 5e+43) {
		tmp = t_1;
	} else if ((z / t) <= 2e+91) {
		tmp = z * (-x / t);
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+30:
		tmp = t_1
	elif (z / t) <= 5e-40:
		tmp = x
	elif (z / t) <= 5e+43:
		tmp = t_1
	elif (z / t) <= 2e+91:
		tmp = z * (-x / t)
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+30)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-40)
		tmp = x;
	elseif (Float64(z / t) <= 5e+43)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e+91)
		tmp = Float64(z * Float64(Float64(-x) / t));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+30)
		tmp = t_1;
	elseif ((z / t) <= 5e-40)
		tmp = x;
	elseif ((z / t) <= 5e+43)
		tmp = t_1;
	elseif ((z / t) <= 2e+91)
		tmp = z * (-x / t);
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+30], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-40], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+43], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e+91], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -4.9999999999999998e30 or 4.99999999999999965e-40 < (/.f64 z t) < 5.0000000000000004e43

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 82.9%

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

   3. Taylor expanded in y around inf 60.1%

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

      1. associate-/r/ 61.2%

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

   5. Applied egg-rr 61.2%

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

      1. clear-num 61.2%

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

      2. associate-/r/ 62.3%

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

      3. clear-num 62.4%

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

   7. Applied egg-rr 62.4%

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

   if -4.9999999999999998e30 < (/.f64 z t) < 4.99999999999999965e-40

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.2%

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

   if 5.0000000000000004e43 < (/.f64 z t) < 2.00000000000000016e91

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.9%

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

   3. Taylor expanded in y around 0 84.0%

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

      1. neg-mul-1 84.0%

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

      2. distribute-neg-frac 84.0%

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

   5. Simplified 84.0%

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

   if 2.00000000000000016e91 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.4%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. associate-/r/ 63.4%

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

   5. Applied egg-rr 63.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -200.0) (not (<= (/ z t) 2e-28))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -200.0) || !((z / t) <= 2e-28)) {
		tmp = z * ((y - x) / 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 / t) <= (-200.0d0)) .or. (.not. ((z / t) <= 2d-28))) then
        tmp = z * ((y - x) / 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 / t) <= -200.0) || !((z / t) <= 2e-28)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -200.0) or not ((z / t) <= 2e-28):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -200.0) || !(Float64(z / t) <= 2e-28))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -200.0) || ~(((z / t) <= 2e-28)))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -200.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-28]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -200 or 1.99999999999999994e-28 < (/.f64 z t)

   1. Initial program 96.3%

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

   2. Taylor expanded in z around inf 89.2%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

      2. +-commutative 89.2%

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

      3. sub-neg 89.2%

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

      4. div-sub 92.2%

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

   5. Simplified 92.2%

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

   if -200 < (/.f64 z t) < 1.99999999999999994e-28

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 79.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 10000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -200.0) (not (<= (/ z t) 10000.0)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -200.0) || !((z / t) <= 10000.0)) {
		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 (((z / t) <= (-200.0d0)) .or. (.not. ((z / t) <= 10000.0d0))) 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 (((z / t) <= -200.0) || !((z / t) <= 10000.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -200.0) or not ((z / t) <= 10000.0):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -200.0) || !(Float64(z / t) <= 10000.0))
		tmp = Float64(z * Float64(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 (((z / t) <= -200.0) || ~(((z / t) <= 10000.0)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -200.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 10000.0]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -200 or 1e4 < (/.f64 z t)

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 90.9%

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

   3. Taylor expanded in y around 0 90.9%

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

      1. neg-mul-1 90.9%

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

      2. +-commutative 90.9%

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

      3. sub-neg 90.9%

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

      4. div-sub 94.1%

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

   5. Simplified 94.1%

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

   if -200 < (/.f64 z t) < 1e4

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 93.8%

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

      1. associate-*r/ 96.9%

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

   4. Simplified 96.9%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 10000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 94.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 20\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -200.0) (not (<= (/ z t) 20.0)))
   (* z (/ (- y x) t))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -200.0) || !((z / t) <= 20.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y / (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 / t) <= (-200.0d0)) .or. (.not. ((z / t) <= 20.0d0))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y / (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 / t) <= -200.0) || !((z / t) <= 20.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -200.0) or not ((z / t) <= 20.0):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -200.0) || !(Float64(z / t) <= 20.0))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -200.0) || ~(((z / t) <= 20.0)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -200.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 20.0]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -200 or 20 < (/.f64 z t)

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 91.0%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. neg-mul-1 91.0%

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

      2. +-commutative 91.0%

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

      3. sub-neg 91.0%

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

      4. div-sub 94.2%

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

   5. Simplified 94.2%

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

   if -200 < (/.f64 z t) < 20

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 93.7%

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

      1. associate-*r/ 96.9%

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

   4. Simplified 96.9%

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

      1. clear-num 96.9%

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

      2. div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 20\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 8: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 20:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -200.0)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 20.0) (+ x (/ y (/ t z))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -200.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 20.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = 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 ((z / t) <= (-200.0d0)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 20.0d0) then
        tmp = x + (y / (t / z))
    else
        tmp = 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 ((z / t) <= -200.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 20.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -200.0:
		tmp = z / (t / (y - x))
	elif (z / t) <= 20.0:
		tmp = x + (y / (t / z))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -200.0)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 20.0)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -200.0)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 20.0)
		tmp = x + (y / (t / z));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -200.0], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 20.0], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -200

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 87.7%

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

   3. Taylor expanded in y around 0 87.7%

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

      1. neg-mul-1 87.7%

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

      2. +-commutative 87.7%

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

      3. sub-neg 87.7%

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

      4. div-sub 91.0%

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

   5. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. clear-num 89.4%

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

      3. un-div-inv 92.1%

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

   7. Applied egg-rr 92.1%

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

   if -200 < (/.f64 z t) < 20

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 93.7%

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

      1. associate-*r/ 96.9%

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

   4. Simplified 96.9%

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

      1. clear-num 96.9%

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

      2. div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   if 20 < (/.f64 z t)

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 94.0%

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

   3. Taylor expanded in y around 0 94.0%

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

      1. neg-mul-1 94.0%

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

      2. +-commutative 94.0%

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

      3. sub-neg 94.0%

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

      4. div-sub 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 20:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 9: 94.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 20:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+31)
   (/ (* (- y x) z) t)
   (if (<= (/ z t) 20.0) (+ x (/ y (/ t z))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+31) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 20.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = 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 ((z / t) <= (-2d+31)) then
        tmp = ((y - x) * z) / t
    else if ((z / t) <= 20.0d0) then
        tmp = x + (y / (t / z))
    else
        tmp = 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 ((z / t) <= -2e+31) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 20.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+31:
		tmp = ((y - x) * z) / t
	elif (z / t) <= 20.0:
		tmp = x + (y / (t / z))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+31)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (Float64(z / t) <= 20.0)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e+31)
		tmp = ((y - x) * z) / t;
	elseif ((z / t) <= 20.0)
		tmp = x + (y / (t / z));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+31], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 20.0], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.9999999999999999e31

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 88.3%

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

   3. Taylor expanded in t around inf 95.0%

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

   if -1.9999999999999999e31 < (/.f64 z t) < 20

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 92.5%

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

      1. associate-*r/ 95.7%

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

   4. Simplified 95.7%

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

      1. clear-num 95.6%

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

      2. div-inv 95.7%

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

   6. Applied egg-rr 95.7%

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

   if 20 < (/.f64 z t)

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 94.0%

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

   3. Taylor expanded in y around 0 94.0%

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

      1. neg-mul-1 94.0%

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

      2. +-commutative 94.0%

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

      3. sub-neg 94.0%

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

      4. div-sub 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 20:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 10: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 20:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -200.0)
   (/ (- y x) (/ t z))
   (if (<= (/ z t) 20.0) (+ x (/ y (/ t z))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -200.0) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 20.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = 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 ((z / t) <= (-200.0d0)) then
        tmp = (y - x) / (t / z)
    else if ((z / t) <= 20.0d0) then
        tmp = x + (y / (t / z))
    else
        tmp = 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 ((z / t) <= -200.0) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 20.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -200.0:
		tmp = (y - x) / (t / z)
	elif (z / t) <= 20.0:
		tmp = x + (y / (t / z))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -200.0)
		tmp = Float64(Float64(y - x) / Float64(t / z));
	elseif (Float64(z / t) <= 20.0)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -200.0)
		tmp = (y - x) / (t / z);
	elseif ((z / t) <= 20.0)
		tmp = x + (y / (t / z));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -200.0], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 20.0], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -200

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. sub-div 91.0%

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

      2. associate-/r/ 95.5%

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

   4. Applied egg-rr 95.5%

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

   if -200 < (/.f64 z t) < 20

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 93.7%

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

      1. associate-*r/ 96.9%

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

   4. Simplified 96.9%

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

      1. clear-num 96.9%

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

      2. div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   if 20 < (/.f64 z t)

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 94.0%

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

   3. Taylor expanded in y around 0 94.0%

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

      1. neg-mul-1 94.0%

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

      2. +-commutative 94.0%

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

      3. sub-neg 94.0%

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

      4. div-sub 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 20:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 11: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+30} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e+30) (not (<= (/ z t) 5e-40))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+30) || !((z / t) <= 5e-40)) {
		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 (((z / t) <= (-5d+30)) .or. (.not. ((z / t) <= 5d-40))) 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 (((z / t) <= -5e+30) || !((z / t) <= 5e-40)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e+30) or not ((z / t) <= 5e-40):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e+30) || !(Float64(z / t) <= 5e-40))
		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 (((z / t) <= -5e+30) || ~(((z / t) <= 5e-40)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e+30], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-40]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.9999999999999998e30 or 4.99999999999999965e-40 < (/.f64 z t)

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 87.9%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. associate-/r/ 59.6%

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

   5. Applied egg-rr 59.6%

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

      1. clear-num 59.6%

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

      2. associate-/r/ 60.3%

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

      3. clear-num 60.3%

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

   7. Applied egg-rr 60.3%

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

   if -4.9999999999999998e30 < (/.f64 z t) < 4.99999999999999965e-40

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+30} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e+30)
   (* y (/ z t))
   (if (<= (/ z t) 5e-40) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e+30) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else {
		tmp = y / (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 / t) <= (-5d+30)) then
        tmp = y * (z / t)
    else if ((z / t) <= 5d-40) then
        tmp = x
    else
        tmp = y / (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 / t) <= -5e+30) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e-40) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e+30:
		tmp = y * (z / t)
	elif (z / t) <= 5e-40:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e+30)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 5e-40)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e+30)
		tmp = y * (z / t);
	elseif ((z / t) <= 5e-40)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e+30], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-40], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.9999999999999998e30

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 88.7%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. associate-/r/ 58.1%

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

   5. Applied egg-rr 58.1%

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

      1. clear-num 58.1%

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

      2. associate-/r/ 59.7%

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

      3. clear-num 59.7%

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

   7. Applied egg-rr 59.7%

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

   if -4.9999999999999998e30 < (/.f64 z t) < 4.99999999999999965e-40

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 80.2%

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

   if 4.99999999999999965e-40 < (/.f64 z t)

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 87.2%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. associate-/r/ 60.8%

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

   5. Applied egg-rr 60.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 13: 53.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.45e+81) x (if (<= t 4.8e-19) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e+81) {
		tmp = x;
	} else if (t <= 4.8e-19) {
		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 <= (-1.45d+81)) then
        tmp = x
    else if (t <= 4.8d-19) 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 <= -1.45e+81) {
		tmp = x;
	} else if (t <= 4.8e-19) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.45e+81:
		tmp = x
	elif t <= 4.8e-19:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.45e+81)
		tmp = x;
	elseif (t <= 4.8e-19)
		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 <= -1.45e+81)
		tmp = x;
	elseif (t <= 4.8e-19)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.45e+81], x, If[LessEqual[t, 4.8e-19], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e81 or 4.80000000000000046e-19 < t

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 65.1%

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

   if -1.45e81 < t < 4.80000000000000046e-19

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 73.6%

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

   3. Taylor expanded in y around inf 52.4%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 97.9% 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 97.4%

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

2. Final simplification 97.4%

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

Alternative 15: 38.7% 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 97.4%

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

2. Taylor expanded in z around 0 40.1%

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

3. Final simplification 40.1%

   \[\leadsto x \]

Developer target: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t_1 < -1013646692435.8867:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} 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 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    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 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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