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

Percentage Accurate: 97.6% → 99.0%

Time: 6.3s

Alternatives: 13

Speedup: 0.4×

• 24.2% 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: 97.6% 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: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+234}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z (- y x)) t)))
   (if (<= (/ z t) -2e+243)
     t_1
     (if (<= (/ z t) 1e+234) (+ x (/ (- y x) (/ t z))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * (y - x)) / t;
	double tmp;
	if ((z / t) <= -2e+243) {
		tmp = t_1;
	} else if ((z / t) <= 1e+234) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = x + t_1;
	}
	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 = (z * (y - x)) / t
    if ((z / t) <= (-2d+243)) then
        tmp = t_1
    else if ((z / t) <= 1d+234) then
        tmp = x + ((y - x) / (t / z))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * (y - x)) / t;
	double tmp;
	if ((z / t) <= -2e+243) {
		tmp = t_1;
	} else if ((z / t) <= 1e+234) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * (y - x)) / t
	tmp = 0
	if (z / t) <= -2e+243:
		tmp = t_1
	elif (z / t) <= 1e+234:
		tmp = x + ((y - x) / (t / z))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * Float64(y - x)) / t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+243)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e+234)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * (y - x)) / t;
	tmp = 0.0;
	if ((z / t) <= -2e+243)
		tmp = t_1;
	elseif ((z / t) <= 1e+234)
		tmp = x + ((y - x) / (t / z));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+243], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e+234], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2.0000000000000001e243

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. *-commutative 83.1%

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

      2. sub-div 99.7%

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

      3. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -2.0000000000000001e243 < (/.f64 z t) < 1.00000000000000002e234

   1. Initial program 99.4%

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

      1. clear-num 99.3%

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

      2. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   if 1.00000000000000002e234 < (/.f64 z t)

   1. Initial program 77.6%

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

      1. associate-*r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+243}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+234}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ t_2 := \frac{z}{t} \cdot \left(-x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)) (t_2 (* (/ z t) (- x))))
   (if (<= (/ z t) -5e+77)
     t_1
     (if (<= (/ z t) -4e+32)
       t_2
       (if (<= (/ z t) -2e-22)
         t_1
         (if (<= (/ z t) 2e-18)
           x
           (if (<= (/ z t) 1e+47)
             t_1
             (if (<= (/ z t) 5e+258) t_2 (/ (* z y) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double t_2 = (z / t) * -x;
	double tmp;
	if ((z / t) <= -5e+77) {
		tmp = t_1;
	} else if ((z / t) <= -4e+32) {
		tmp = t_2;
	} else if ((z / t) <= -2e-22) {
		tmp = t_1;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else if ((z / t) <= 1e+47) {
		tmp = t_1;
	} else if ((z / t) <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / t) * y
    t_2 = (z / t) * -x
    if ((z / t) <= (-5d+77)) then
        tmp = t_1
    else if ((z / t) <= (-4d+32)) then
        tmp = t_2
    else if ((z / t) <= (-2d-22)) then
        tmp = t_1
    else if ((z / t) <= 2d-18) then
        tmp = x
    else if ((z / t) <= 1d+47) then
        tmp = t_1
    else if ((z / t) <= 5d+258) then
        tmp = t_2
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double t_2 = (z / t) * -x;
	double tmp;
	if ((z / t) <= -5e+77) {
		tmp = t_1;
	} else if ((z / t) <= -4e+32) {
		tmp = t_2;
	} else if ((z / t) <= -2e-22) {
		tmp = t_1;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else if ((z / t) <= 1e+47) {
		tmp = t_1;
	} else if ((z / t) <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	t_2 = (z / t) * -x
	tmp = 0
	if (z / t) <= -5e+77:
		tmp = t_1
	elif (z / t) <= -4e+32:
		tmp = t_2
	elif (z / t) <= -2e-22:
		tmp = t_1
	elif (z / t) <= 2e-18:
		tmp = x
	elif (z / t) <= 1e+47:
		tmp = t_1
	elif (z / t) <= 5e+258:
		tmp = t_2
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	t_2 = Float64(Float64(z / t) * Float64(-x))
	tmp = 0.0
	if (Float64(z / t) <= -5e+77)
		tmp = t_1;
	elseif (Float64(z / t) <= -4e+32)
		tmp = t_2;
	elseif (Float64(z / t) <= -2e-22)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e-18)
		tmp = x;
	elseif (Float64(z / t) <= 1e+47)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e+258)
		tmp = t_2;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	t_2 = (z / t) * -x;
	tmp = 0.0;
	if ((z / t) <= -5e+77)
		tmp = t_1;
	elseif ((z / t) <= -4e+32)
		tmp = t_2;
	elseif ((z / t) <= -2e-22)
		tmp = t_1;
	elseif ((z / t) <= 2e-18)
		tmp = x;
	elseif ((z / t) <= 1e+47)
		tmp = t_1;
	elseif ((z / t) <= 5e+258)
		tmp = t_2;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+77], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -4e+32], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], -2e-22], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e-18], x, If[LessEqual[N[(z / t), $MachinePrecision], 1e+47], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e+258], t$95$2, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -5.00000000000000004e77 or -4.00000000000000021e32 < (/.f64 z t) < -2.0000000000000001e-22 or 2.0000000000000001e-18 < (/.f64 z t) < 1e47

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 78.9%

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

   4. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 64.9%

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

   6. Simplified 64.9%

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

   if -5.00000000000000004e77 < (/.f64 z t) < -4.00000000000000021e32 or 1e47 < (/.f64 z t) < 5e258

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 91.8%

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

   4. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-*r/ 72.3%

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

      3. distribute-lft-neg-out 72.3%

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

      4. *-commutative 72.3%

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

   6. Simplified 72.3%

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

   if -2.0000000000000001e-22 < (/.f64 z t) < 2.0000000000000001e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 82.6%

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

   if 5e258 < (/.f64 z t)

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 96.3%

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

   4. Taylor expanded in y around inf 65.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+32}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+47}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot y\\ t_2 := z \cdot \frac{-x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) y)) (t_2 (* z (/ (- x) t))))
   (if (<= (/ z t) -5e+83)
     t_1
     (if (<= (/ z t) -4e+32)
       t_2
       (if (<= (/ z t) -2e-22)
         t_1
         (if (<= (/ z t) 2e-18)
           x
           (if (<= (/ z t) 1e+47)
             t_1
             (if (<= (/ z t) 5e+258) t_2 (/ (* z y) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double t_2 = z * (-x / t);
	double tmp;
	if ((z / t) <= -5e+83) {
		tmp = t_1;
	} else if ((z / t) <= -4e+32) {
		tmp = t_2;
	} else if ((z / t) <= -2e-22) {
		tmp = t_1;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else if ((z / t) <= 1e+47) {
		tmp = t_1;
	} else if ((z / t) <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / t) * y
    t_2 = z * (-x / t)
    if ((z / t) <= (-5d+83)) then
        tmp = t_1
    else if ((z / t) <= (-4d+32)) then
        tmp = t_2
    else if ((z / t) <= (-2d-22)) then
        tmp = t_1
    else if ((z / t) <= 2d-18) then
        tmp = x
    else if ((z / t) <= 1d+47) then
        tmp = t_1
    else if ((z / t) <= 5d+258) then
        tmp = t_2
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * y;
	double t_2 = z * (-x / t);
	double tmp;
	if ((z / t) <= -5e+83) {
		tmp = t_1;
	} else if ((z / t) <= -4e+32) {
		tmp = t_2;
	} else if ((z / t) <= -2e-22) {
		tmp = t_1;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else if ((z / t) <= 1e+47) {
		tmp = t_1;
	} else if ((z / t) <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * y
	t_2 = z * (-x / t)
	tmp = 0
	if (z / t) <= -5e+83:
		tmp = t_1
	elif (z / t) <= -4e+32:
		tmp = t_2
	elif (z / t) <= -2e-22:
		tmp = t_1
	elif (z / t) <= 2e-18:
		tmp = x
	elif (z / t) <= 1e+47:
		tmp = t_1
	elif (z / t) <= 5e+258:
		tmp = t_2
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * y)
	t_2 = Float64(z * Float64(Float64(-x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+83)
		tmp = t_1;
	elseif (Float64(z / t) <= -4e+32)
		tmp = t_2;
	elseif (Float64(z / t) <= -2e-22)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e-18)
		tmp = x;
	elseif (Float64(z / t) <= 1e+47)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e+258)
		tmp = t_2;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * y;
	t_2 = z * (-x / t);
	tmp = 0.0;
	if ((z / t) <= -5e+83)
		tmp = t_1;
	elseif ((z / t) <= -4e+32)
		tmp = t_2;
	elseif ((z / t) <= -2e-22)
		tmp = t_1;
	elseif ((z / t) <= 2e-18)
		tmp = x;
	elseif ((z / t) <= 1e+47)
		tmp = t_1;
	elseif ((z / t) <= 5e+258)
		tmp = t_2;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+83], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -4e+32], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], -2e-22], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e-18], x, If[LessEqual[N[(z / t), $MachinePrecision], 1e+47], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e+258], t$95$2, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -5.00000000000000029e83 or -4.00000000000000021e32 < (/.f64 z t) < -2.0000000000000001e-22 or 2.0000000000000001e-18 < (/.f64 z t) < 1e47

   1. Initial program 93.1%

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

   3. Taylor expanded in z around inf 78.3%

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

   4. Taylor expanded in y around inf 58.5%

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

      1. associate-/l* 65.3%

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

   6. Simplified 65.3%

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

   if -5.00000000000000029e83 < (/.f64 z t) < -4.00000000000000021e32 or 1e47 < (/.f64 z t) < 5e258

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 92.2%

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

   4. Taylor expanded in y around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. associate-*r* 65.5%

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

      3. neg-mul-1 65.5%

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

      4. *-commutative 65.5%

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

      5. associate-/l* 67.0%

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

   6. Simplified 67.0%

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

   if -2.0000000000000001e-22 < (/.f64 z t) < 2.0000000000000001e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 82.6%

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

   if 5e258 < (/.f64 z t)

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 96.3%

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

   4. Taylor expanded in y around inf 65.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+47}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+200} \lor \neg \left(\frac{z}{t} \leq 10^{+234}\right):\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e+200) (not (<= (/ z t) 1e+234)))
   (/ (* z (- y x)) t)
   (+ x (* (/ z t) (- y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+200) || !((z / t) <= 1e+234)) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = x + ((z / t) * (y - 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+200)) .or. (.not. ((z / t) <= 1d+234))) then
        tmp = (z * (y - x)) / t
    else
        tmp = x + ((z / t) * (y - 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+200) || !((z / t) <= 1e+234)) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = x + ((z / t) * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e+200) or not ((z / t) <= 1e+234):
		tmp = (z * (y - x)) / t
	else:
		tmp = x + ((z / t) * (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e+200) || !(Float64(z / t) <= 1e+234))
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	else
		tmp = Float64(x + Float64(Float64(z / t) * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e+200) || ~(((z / t) <= 1e+234)))
		tmp = (z * (y - x)) / t;
	else
		tmp = x + ((z / t) * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e+200], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e+234]], $MachinePrecision]], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.00000000000000019e200 or 1.00000000000000002e234 < (/.f64 z t)

   1. Initial program 81.1%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. sub-div 99.8%

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

      3. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -5.00000000000000019e200 < (/.f64 z t) < 1.00000000000000002e234

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+200} \lor \neg \left(\frac{z}{t} \leq 10^{+234}\right):\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+234}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z (- y x)) t)))
   (if (<= (/ z t) -5e+200)
     t_1
     (if (<= (/ z t) 1e+234) (+ x (* (/ z t) (- y x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * (y - x)) / t;
	double tmp;
	if ((z / t) <= -5e+200) {
		tmp = t_1;
	} else if ((z / t) <= 1e+234) {
		tmp = x + ((z / t) * (y - x));
	} else {
		tmp = x + t_1;
	}
	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 = (z * (y - x)) / t
    if ((z / t) <= (-5d+200)) then
        tmp = t_1
    else if ((z / t) <= 1d+234) then
        tmp = x + ((z / t) * (y - x))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * (y - x)) / t;
	double tmp;
	if ((z / t) <= -5e+200) {
		tmp = t_1;
	} else if ((z / t) <= 1e+234) {
		tmp = x + ((z / t) * (y - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * (y - x)) / t
	tmp = 0
	if (z / t) <= -5e+200:
		tmp = t_1
	elif (z / t) <= 1e+234:
		tmp = x + ((z / t) * (y - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * Float64(y - x)) / t)
	tmp = 0.0
	if (Float64(z / t) <= -5e+200)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e+234)
		tmp = Float64(x + Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * (y - x)) / t;
	tmp = 0.0;
	if ((z / t) <= -5e+200)
		tmp = t_1;
	elseif ((z / t) <= 1e+234)
		tmp = x + ((z / t) * (y - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+200], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e+234], N[(x + N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -5.00000000000000019e200

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf 86.8%

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

      1. *-commutative 86.8%

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

      2. sub-div 99.7%

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

      3. associate-*l/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -5.00000000000000019e200 < (/.f64 z t) < 1.00000000000000002e234

   1. Initial program 99.3%

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

   if 1.00000000000000002e234 < (/.f64 z t)

   1. Initial program 77.6%

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

      1. associate-*r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+200}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+234}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000000000 \lor \neg \left(\frac{z}{t} \leq 200000000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -50000000000.0) (not (<= (/ z t) 200000000.0)))
   (* z (/ (- y x) t))
   (+ x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -50000000000.0) || !((z / t) <= 200000000.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + ((z / t) * y);
	}
	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) <= (-50000000000.0d0)) .or. (.not. ((z / t) <= 200000000.0d0))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + ((z / t) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -50000000000.0) || !((z / t) <= 200000000.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -50000000000.0) or not ((z / t) <= 200000000.0):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -50000000000.0) || !(Float64(z / t) <= 200000000.0))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(Float64(z / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -50000000000.0) || ~(((z / t) <= 200000000.0)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -50000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 200000000.0]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5e10 or 2e8 < (/.f64 z t)

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 87.6%

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

   4. Taylor expanded in y around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. associate-*r/ 76.7%

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

      3. distribute-lft-neg-out 76.7%

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

      4. associate-/l* 78.7%

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

      5. distribute-rgt-out 90.1%

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

      6. +-commutative 90.1%

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

      7. sub-neg 90.1%

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

      8. *-commutative 90.1%

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

      9. associate-/l* 95.7%

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

      10. associate-*l/ 92.3%

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

      11. *-commutative 92.3%

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

   6. Simplified 92.3%

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

   if -5e10 < (/.f64 z t) < 2e8

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 94.2%

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

      1. associate-*r/ 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000000000 \lor \neg \left(\frac{z}{t} \leq 200000000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-22} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e-22) (not (<= (/ z t) 2e-18))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-22) || !((z / t) <= 2e-18)) {
		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) <= (-2d-22)) .or. (.not. ((z / t) <= 2d-18))) 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) <= -2e-22) || !((z / t) <= 2e-18)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e-22) or not ((z / t) <= 2e-18):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2e-22) || !(Float64(z / t) <= 2e-18))
		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) <= -2e-22) || ~(((z / t) <= 2e-18)))
		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], -2e-22], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-18]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.0000000000000001e-22 or 2.0000000000000001e-18 < (/.f64 z t)

   1. Initial program 91.5%

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

   3. Taylor expanded in z around inf 86.4%

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

   4. Taylor expanded in y around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. associate-*r/ 75.5%

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

      3. distribute-lft-neg-out 75.5%

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

      4. associate-/l* 79.8%

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

      5. distribute-rgt-out 89.9%

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

      6. +-commutative 89.9%

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

      7. sub-neg 89.9%

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

      8. *-commutative 89.9%

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

      9. associate-/l* 92.3%

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

      10. associate-*l/ 90.6%

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

      11. *-commutative 90.6%

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

   6. Simplified 90.6%

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

   if -2.0000000000000001e-22 < (/.f64 z t) < 2.0000000000000001e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 82.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-22} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000000000:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 200000000:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -50000000000.0)
   (* z (/ (- y x) t))
   (if (<= (/ z t) 200000000.0) (+ x (* (/ z t) y)) (/ (* z (- y x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -50000000000.0) {
		tmp = z * ((y - x) / t);
	} else if ((z / t) <= 200000000.0) {
		tmp = x + ((z / t) * y);
	} 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) <= (-50000000000.0d0)) then
        tmp = z * ((y - x) / t)
    else if ((z / t) <= 200000000.0d0) then
        tmp = x + ((z / t) * y)
    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) <= -50000000000.0) {
		tmp = z * ((y - x) / t);
	} else if ((z / t) <= 200000000.0) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = (z * (y - x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -50000000000.0:
		tmp = z * ((y - x) / t)
	elif (z / t) <= 200000000.0:
		tmp = x + ((z / t) * y)
	else:
		tmp = (z * (y - x)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -50000000000.0)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (Float64(z / t) <= 200000000.0)
		tmp = Float64(x + Float64(Float64(z / t) * y));
	else
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -50000000000.0)
		tmp = z * ((y - x) / t);
	elseif ((z / t) <= 200000000.0)
		tmp = x + ((z / t) * y);
	else
		tmp = (z * (y - x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -50000000000.0], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 200000000.0], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -5e10

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 87.0%

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

   4. Taylor expanded in y around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. associate-*r/ 76.0%

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

      3. distribute-lft-neg-out 76.0%

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

      4. associate-/l* 79.0%

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

      5. distribute-rgt-out 92.1%

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

      6. +-commutative 92.1%

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

      7. sub-neg 92.1%

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

      8. *-commutative 92.1%

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

      9. associate-/l* 95.0%

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

      10. associate-*l/ 95.2%

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

      11. *-commutative 95.2%

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

   6. Simplified 95.2%

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

   if -5e10 < (/.f64 z t) < 2e8

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 94.2%

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

      1. associate-*r/ 98.7%

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

   5. Simplified 98.7%

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

   if 2e8 < (/.f64 z t)

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. sub-div 89.6%

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

      3. associate-*l/ 96.3%

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

   5. Applied egg-rr 96.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000000000:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 200000000:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2.4 \cdot 10^{-22} \lor \neg \left(\frac{z}{t} \leq 8.4 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.4e-22) (not (<= (/ z t) 8.4e-18))) (* (/ z t) y) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.4e-22) || !((z / t) <= 8.4e-18)) {
		tmp = (z / t) * y;
	} 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) <= (-2.4d-22)) .or. (.not. ((z / t) <= 8.4d-18))) then
        tmp = (z / t) * y
    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) <= -2.4e-22) || !((z / t) <= 8.4e-18)) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2.4e-22) or not ((z / t) <= 8.4e-18):
		tmp = (z / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2.4e-22) || !(Float64(z / t) <= 8.4e-18))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2.4e-22) || ~(((z / t) <= 8.4e-18)))
		tmp = (z / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2.4e-22], N[Not[LessEqual[N[(z / t), $MachinePrecision], 8.4e-18]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.40000000000000002e-22 or 8.39999999999999998e-18 < (/.f64 z t)

   1. Initial program 91.5%

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

   3. Taylor expanded in z around inf 86.4%

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

   4. Taylor expanded in y around inf 51.0%

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

      1. associate-/l* 53.0%

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

   6. Simplified 53.0%

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

   if -2.40000000000000002e-22 < (/.f64 z t) < 8.39999999999999998e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 82.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2.4 \cdot 10^{-22} \lor \neg \left(\frac{z}{t} \leq 8.4 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e-22)
   (* (/ z t) y)
   (if (<= (/ z t) 2e-18) x (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-22) {
		tmp = (z / t) * y;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d-22)) then
        tmp = (z / t) * y
    else if ((z / t) <= 2d-18) then
        tmp = x
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-22) {
		tmp = (z / t) * y;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e-22:
		tmp = (z / t) * y
	elif (z / t) <= 2e-18:
		tmp = x
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-22)
		tmp = Float64(Float64(z / t) * y);
	elseif (Float64(z / t) <= 2e-18)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e-22)
		tmp = (z / t) * y;
	elseif ((z / t) <= 2e-18)
		tmp = x;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e-22], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-18], x, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2.0000000000000001e-22

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf 83.5%

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

   4. Taylor expanded in y around inf 48.0%

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

      1. associate-/l* 56.1%

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

   6. Simplified 56.1%

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

   if -2.0000000000000001e-22 < (/.f64 z t) < 2.0000000000000001e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 82.6%

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

   if 2.0000000000000001e-18 < (/.f64 z t)

   1. Initial program 89.9%

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

   3. Taylor expanded in z around inf 89.1%

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

   4. Taylor expanded in y around inf 53.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e-22)
   (* (/ z t) y)
   (if (<= (/ z t) 2e-18) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-22) {
		tmp = (z / t) * y;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d-22)) then
        tmp = (z / t) * y
    else if ((z / t) <= 2d-18) then
        tmp = x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-22) {
		tmp = (z / t) * y;
	} else if ((z / t) <= 2e-18) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e-22:
		tmp = (z / t) * y
	elif (z / t) <= 2e-18:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-22)
		tmp = Float64(Float64(z / t) * y);
	elseif (Float64(z / t) <= 2e-18)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e-22)
		tmp = (z / t) * y;
	elseif ((z / t) <= 2e-18)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e-22], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-18], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2.0000000000000001e-22

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf 83.5%

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

   4. Taylor expanded in y around inf 48.0%

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

      1. associate-/l* 56.1%

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

   6. Simplified 56.1%

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

   if -2.0000000000000001e-22 < (/.f64 z t) < 2.0000000000000001e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 82.6%

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

   if 2.0000000000000001e-18 < (/.f64 z t)

   1. Initial program 89.9%

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

   3. Taylor expanded in z around inf 89.1%

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

   4. Taylor expanded in y around inf 53.9%

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

      1. associate-*l/ 50.3%

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

      2. *-commutative 50.3%

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

   6. Simplified 50.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-199} \lor \neg \left(x \leq 9.5 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.8e-199) (not (<= x 9.5e-164)))
   (* x (- 1.0 (/ z t)))
   (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e-199) || !(x <= 9.5e-164)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.8d-199)) .or. (.not. (x <= 9.5d-164))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e-199) || !(x <= 9.5e-164)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.8e-199) or not (x <= 9.5e-164):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.8e-199) || !(x <= 9.5e-164))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.8e-199) || ~((x <= 9.5e-164)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.8e-199], N[Not[LessEqual[x, 9.5e-164]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000018e-199 or 9.5000000000000001e-164 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   5. Simplified 75.0%

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

   if -2.80000000000000018e-199 < x < 9.5000000000000001e-164

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 88.2%

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

   4. Taylor expanded in y around inf 71.7%

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

      1. associate-*l/ 76.5%

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

      2. *-commutative 76.5%

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

   6. Simplified 76.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-199} \lor \neg \left(x \leq 9.5 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.2% 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 94.8%

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

3. Taylor expanded in z around 0 37.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 97.5% accurate, 0.3× 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 2024103 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (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))))