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

Percentage Accurate: 97.5% → 97.5%

Time: 5.1s

Alternatives: 11

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 97.5% 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: 97.5% 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 96.4%

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

   1. clear-num 96.3%

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

   2. un-div-inv 96.5%

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

3. Applied egg-rr 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= (/ z t) -2e+173)
     (+ x (/ z (/ t y)))
     (if (<= (/ z t) -5e+139)
       (/ (* x z) (- t))
       (if (<= (/ z t) 5e+36)
         t_1
         (if (<= (/ z t) 2e+81)
           (* x (/ (- z) t))
           (if (<= (/ z t) 2e+169) t_1 (* (/ x t) (- z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if ((z / t) <= -2e+173) {
		tmp = x + (z / (t / y));
	} else if ((z / t) <= -5e+139) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= 5e+36) {
		tmp = t_1;
	} else if ((z / t) <= 2e+81) {
		tmp = x * (-z / t);
	} else if ((z / t) <= 2e+169) {
		tmp = t_1;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if ((z / t) <= (-2d+173)) then
        tmp = x + (z / (t / y))
    else if ((z / t) <= (-5d+139)) then
        tmp = (x * z) / -t
    else if ((z / t) <= 5d+36) then
        tmp = t_1
    else if ((z / t) <= 2d+81) then
        tmp = x * (-z / t)
    else if ((z / t) <= 2d+169) then
        tmp = t_1
    else
        tmp = (x / t) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if ((z / t) <= -2e+173) {
		tmp = x + (z / (t / y));
	} else if ((z / t) <= -5e+139) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= 5e+36) {
		tmp = t_1;
	} else if ((z / t) <= 2e+81) {
		tmp = x * (-z / t);
	} else if ((z / t) <= 2e+169) {
		tmp = t_1;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if (z / t) <= -2e+173:
		tmp = x + (z / (t / y))
	elif (z / t) <= -5e+139:
		tmp = (x * z) / -t
	elif (z / t) <= 5e+36:
		tmp = t_1
	elif (z / t) <= 2e+81:
		tmp = x * (-z / t)
	elif (z / t) <= 2e+169:
		tmp = t_1
	else:
		tmp = (x / t) * -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (Float64(z / t) <= -2e+173)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (Float64(z / t) <= -5e+139)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (Float64(z / t) <= 5e+36)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e+81)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (Float64(z / t) <= 2e+169)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if ((z / t) <= -2e+173)
		tmp = x + (z / (t / y));
	elseif ((z / t) <= -5e+139)
		tmp = (x * z) / -t;
	elseif ((z / t) <= 5e+36)
		tmp = t_1;
	elseif ((z / t) <= 2e+81)
		tmp = x * (-z / t);
	elseif ((z / t) <= 2e+169)
		tmp = t_1;
	else
		tmp = (x / t) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+173], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+139], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e+36], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e+81], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e+169], t$95$1, N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -2e173

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. associate-*r/ 64.9%

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

   4. Simplified 64.9%

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

      1. associate-*r/ 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-/l* 77.6%

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

   6. Applied egg-rr 77.6%

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

   if -2e173 < (/.f64 z t) < -5.0000000000000003e139

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. distribute-rgt1-in 86.0%

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

      3. mul-1-neg 86.0%

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

      4. cancel-sign-sub-inv 86.0%

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

      5. associate-*l/ 86.1%

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

      6. associate-/l* 86.0%

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

   4. Simplified 86.0%

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

      1. clear-num 85.7%

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

      2. associate-/r/ 86.0%

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

      3. clear-num 86.0%

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

   6. Applied egg-rr 86.0%

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

   7. Taylor expanded in t around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

      4. associate-*r/ 86.0%

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

   9. Simplified 86.0%

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

       1. frac-2neg 86.0%

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

       2. remove-double-neg 86.0%

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

       3. associate-*r/ 86.1%

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

   11. Applied egg-rr 86.1%

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

   if -5.0000000000000003e139 < (/.f64 z t) < 4.99999999999999977e36 or 1.99999999999999984e81 < (/.f64 z t) < 1.99999999999999987e169

   1. Initial program 99.0%

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

   2. Taylor expanded in y around inf 84.9%

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

      1. associate-*r/ 89.0%

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

   4. Simplified 89.0%

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

   if 4.99999999999999977e36 < (/.f64 z t) < 1.99999999999999984e81

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. distribute-rgt1-in 75.0%

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

      3. mul-1-neg 75.0%

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

      4. cancel-sign-sub-inv 75.0%

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

      5. associate-*l/ 67.4%

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

      6. associate-/l* 66.6%

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

   4. Simplified 66.6%

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

      1. clear-num 66.9%

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

      2. associate-/r/ 66.6%

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

      3. clear-num 66.8%

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

   6. Applied egg-rr 66.8%

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

   7. Taylor expanded in t around 0 67.4%

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

      1. associate-*r/ 67.4%

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

      2. neg-mul-1 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. associate-*r/ 66.9%

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

   9. Simplified 66.9%

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

   10. Taylor expanded in z around 0 67.4%

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

       1. mul-1-neg 67.4%

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

       2. associate-*l/ 75.0%

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

       3. *-commutative 75.0%

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

       4. distribute-rgt-neg-in 75.0%

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

       5. distribute-neg-frac 75.0%

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

   12. Simplified 75.0%

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

   if 1.99999999999999987e169 < (/.f64 z t)

   1. Initial program 86.7%

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

   2. Taylor expanded in x around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. distribute-rgt1-in 62.1%

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

      3. mul-1-neg 62.1%

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

      4. cancel-sign-sub-inv 62.1%

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

      5. associate-*l/ 71.8%

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

      6. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

      1. clear-num 75.1%

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

      2. associate-/r/ 75.2%

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

      3. clear-num 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in t around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. neg-mul-1 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-*r/ 75.2%

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

   9. Simplified 75.2%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+169}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= (/ z t) 5e+36)
     t_1
     (if (<= (/ z t) 2e+81)
       (* x (/ (- z) t))
       (if (<= (/ z t) 2e+169) t_1 (* (/ x t) (- z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if ((z / t) <= 5e+36) {
		tmp = t_1;
	} else if ((z / t) <= 2e+81) {
		tmp = x * (-z / t);
	} else if ((z / t) <= 2e+169) {
		tmp = t_1;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if ((z / t) <= 5d+36) then
        tmp = t_1
    else if ((z / t) <= 2d+81) then
        tmp = x * (-z / t)
    else if ((z / t) <= 2d+169) then
        tmp = t_1
    else
        tmp = (x / t) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if ((z / t) <= 5e+36) {
		tmp = t_1;
	} else if ((z / t) <= 2e+81) {
		tmp = x * (-z / t);
	} else if ((z / t) <= 2e+169) {
		tmp = t_1;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if (z / t) <= 5e+36:
		tmp = t_1
	elif (z / t) <= 2e+81:
		tmp = x * (-z / t)
	elif (z / t) <= 2e+169:
		tmp = t_1
	else:
		tmp = (x / t) * -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (Float64(z / t) <= 5e+36)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e+81)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (Float64(z / t) <= 2e+169)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if ((z / t) <= 5e+36)
		tmp = t_1;
	elseif ((z / t) <= 2e+81)
		tmp = x * (-z / t);
	elseif ((z / t) <= 2e+169)
		tmp = t_1;
	else
		tmp = (x / t) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], 5e+36], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e+81], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e+169], t$95$1, N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < 4.99999999999999977e36 or 1.99999999999999984e81 < (/.f64 z t) < 1.99999999999999987e169

   1. Initial program 97.4%

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

   2. Taylor expanded in y around inf 82.0%

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

      1. associate-*r/ 84.3%

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

   4. Simplified 84.3%

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

   if 4.99999999999999977e36 < (/.f64 z t) < 1.99999999999999984e81

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. distribute-rgt1-in 75.0%

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

      3. mul-1-neg 75.0%

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

      4. cancel-sign-sub-inv 75.0%

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

      5. associate-*l/ 67.4%

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

      6. associate-/l* 66.6%

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

   4. Simplified 66.6%

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

      1. clear-num 66.9%

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

      2. associate-/r/ 66.6%

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

      3. clear-num 66.8%

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

   6. Applied egg-rr 66.8%

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

   7. Taylor expanded in t around 0 67.4%

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

      1. associate-*r/ 67.4%

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

      2. neg-mul-1 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. associate-*r/ 66.9%

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

   9. Simplified 66.9%

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

   10. Taylor expanded in z around 0 67.4%

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

       1. mul-1-neg 67.4%

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

       2. associate-*l/ 75.0%

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

       3. *-commutative 75.0%

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

       4. distribute-rgt-neg-in 75.0%

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

       5. distribute-neg-frac 75.0%

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

   12. Simplified 75.0%

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

   if 1.99999999999999987e169 < (/.f64 z t)

   1. Initial program 86.7%

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

   2. Taylor expanded in x around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. distribute-rgt1-in 62.1%

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

      3. mul-1-neg 62.1%

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

      4. cancel-sign-sub-inv 62.1%

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

      5. associate-*l/ 71.8%

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

      6. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

      1. clear-num 75.1%

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

      2. associate-/r/ 75.2%

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

      3. clear-num 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in t around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. neg-mul-1 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-*r/ 75.2%

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

   9. Simplified 75.2%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+169}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 92.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000000000000 \lor \neg \left(\frac{z}{t} \leq 10^{-9}\right):\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -50000000000000.0) (not (<= (/ z t) 1e-9)))
   (* z (- (/ y t) (/ x t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -50000000000000.0) || !((z / t) <= 1e-9)) {
		tmp = z * ((y / t) - (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) <= (-50000000000000.0d0)) .or. (.not. ((z / t) <= 1d-9))) then
        tmp = z * ((y / t) - (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) <= -50000000000000.0) || !((z / t) <= 1e-9)) {
		tmp = z * ((y / t) - (x / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -50000000000000.0) or not ((z / t) <= 1e-9):
		tmp = z * ((y / t) - (x / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -50000000000000.0) || !(Float64(z / t) <= 1e-9))
		tmp = Float64(z * Float64(Float64(y / t) - Float64(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) <= -50000000000000.0) || ~(((z / t) <= 1e-9)))
		tmp = z * ((y / t) - (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], -50000000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-9]], $MachinePrecision]], N[(z * N[(N[(y / t), $MachinePrecision] - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5e13 or 1.00000000000000006e-9 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 89.8%

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

   if -5e13 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf 95.4%

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

      1. associate-*r/ 97.0%

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

   4. Simplified 97.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000000000000 \lor \neg \left(\frac{z}{t} \leq 10^{-9}\right):\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000000000 \lor \neg \left(\frac{z}{t} \leq 10000000\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2000000000000.0) (not (<= (/ z t) 10000000.0)))
   (* x (/ (- z) t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2000000000000.0) || !((z / t) <= 10000000.0)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-2000000000000.0d0)) .or. (.not. ((z / t) <= 10000000.0d0))) then
        tmp = x * (-z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2000000000000.0) || !((z / t) <= 10000000.0)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2000000000000.0) or not ((z / t) <= 10000000.0):
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2000000000000.0) || !(Float64(z / t) <= 10000000.0))
		tmp = Float64(x * Float64(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) <= -2000000000000.0) || ~(((z / t) <= 10000000.0)))
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2000000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e12 or 1e7 < (/.f64 z t)

   1. Initial program 93.7%

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

   2. Taylor expanded in x around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. distribute-rgt1-in 52.8%

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

      3. mul-1-neg 52.8%

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

      4. cancel-sign-sub-inv 52.8%

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

      5. associate-*l/ 51.9%

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

      6. associate-/l* 52.6%

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

   4. Simplified 52.6%

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

      1. clear-num 52.6%

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

      2. associate-/r/ 52.6%

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

      3. clear-num 52.6%

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

   6. Applied egg-rr 52.6%

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

   7. Taylor expanded in t around 0 51.2%

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

      1. associate-*r/ 51.2%

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

      2. neg-mul-1 51.2%

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

      3. distribute-rgt-neg-in 51.2%

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

      4. associate-*r/ 52.0%

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

   9. Simplified 52.0%

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

   10. Taylor expanded in z around 0 51.2%

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

       1. mul-1-neg 51.2%

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

       2. associate-*l/ 52.1%

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

       3. *-commutative 52.1%

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

       4. distribute-rgt-neg-in 52.1%

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

       5. distribute-neg-frac 52.1%

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

   12. Simplified 52.1%

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

   if -2e12 < (/.f64 z t) < 1e7

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 72.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000000000 \lor \neg \left(\frac{z}{t} \leq 10000000\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000000000:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2000000000000.0)
   (* x (/ (- z) t))
   (if (<= (/ z t) 10000000.0) x (* (/ x t) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2000000000000.0) {
		tmp = x * (-z / t);
	} else if ((z / t) <= 10000000.0) {
		tmp = x;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2000000000000.0d0)) then
        tmp = x * (-z / t)
    else if ((z / t) <= 10000000.0d0) then
        tmp = x
    else
        tmp = (x / t) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2000000000000.0) {
		tmp = x * (-z / t);
	} else if ((z / t) <= 10000000.0) {
		tmp = x;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2000000000000.0:
		tmp = x * (-z / t)
	elif (z / t) <= 10000000.0:
		tmp = x
	else:
		tmp = (x / t) * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2000000000000.0)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (Float64(z / t) <= 10000000.0)
		tmp = x;
	else
		tmp = Float64(Float64(x / t) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2000000000000.0)
		tmp = x * (-z / t);
	elseif ((z / t) <= 10000000.0)
		tmp = x;
	else
		tmp = (x / t) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2000000000000.0], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 10000000.0], x, N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e12

   1. Initial program 93.3%

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

   2. Taylor expanded in x around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. distribute-rgt1-in 52.5%

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

      3. mul-1-neg 52.5%

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

      4. cancel-sign-sub-inv 52.5%

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

      5. associate-*l/ 47.4%

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

      6. associate-/l* 47.4%

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

   4. Simplified 47.4%

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

      1. clear-num 47.4%

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

      2. associate-/r/ 47.4%

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

      3. clear-num 47.4%

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

   6. Applied egg-rr 47.4%

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

   7. Taylor expanded in t around 0 47.0%

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

      1. associate-*r/ 47.0%

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

      2. neg-mul-1 47.0%

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

      3. distribute-rgt-neg-in 47.0%

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

      4. associate-*r/ 47.1%

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

   9. Simplified 47.1%

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

   10. Taylor expanded in z around 0 47.0%

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

       1. mul-1-neg 47.0%

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

       2. associate-*l/ 52.1%

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

       3. *-commutative 52.1%

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

       4. distribute-rgt-neg-in 52.1%

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

       5. distribute-neg-frac 52.1%

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

   12. Simplified 52.1%

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

   if -2e12 < (/.f64 z t) < 1e7

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 72.3%

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

   if 1e7 < (/.f64 z t)

   1. Initial program 94.0%

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

   2. Taylor expanded in x around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. distribute-rgt1-in 53.0%

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

      3. mul-1-neg 53.0%

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

      4. cancel-sign-sub-inv 53.0%

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

      5. associate-*l/ 55.9%

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

      6. associate-/l* 57.2%

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

   4. Simplified 57.2%

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

      1. clear-num 57.1%

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

      2. associate-/r/ 57.1%

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

      3. clear-num 57.2%

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

   6. Applied egg-rr 57.2%

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

   7. Taylor expanded in t around 0 55.0%

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

      1. associate-*r/ 55.0%

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

      2. neg-mul-1 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

      4. associate-*r/ 56.3%

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

   9. Simplified 56.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000000000:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]

Alternative 7: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+36} \lor \neg \left(y \leq 7 \cdot 10^{-140}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e+36) (not (<= y 7e-140)))
   (+ x (* y (/ z t)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e+36) || !(y <= 7e-140)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.2d+36)) .or. (.not. (y <= 7d-140))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e+36) || !(y <= 7e-140)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e+36) or not (y <= 7e-140):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e+36) || !(y <= 7e-140))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e+36) || ~((y <= 7e-140)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e+36], N[Not[LessEqual[y, 7e-140]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999999e36 or 6.9999999999999996e-140 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 83.8%

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

      1. associate-*r/ 89.6%

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

   4. Simplified 89.6%

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

   if -3.1999999999999999e36 < y < 6.9999999999999996e-140

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. unsub-neg 83.5%

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

      4. distribute-lft-out-- 83.5%

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

      5. *-rgt-identity 83.5%

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

   4. Simplified 83.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+36} \lor \neg \left(y \leq 7 \cdot 10^{-140}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+38} \lor \neg \left(y \leq 5.1 \cdot 10^{-142}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.36e+38) (not (<= y 5.1e-142)))
   (+ x (* y (/ z t)))
   (- x (* z (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.36e+38) || !(y <= 5.1e-142)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (z * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.36d+38)) .or. (.not. (y <= 5.1d-142))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (z * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.36e+38) || !(y <= 5.1e-142)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.36e+38) or not (y <= 5.1e-142):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (z * (x / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.36e+38) || !(y <= 5.1e-142))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.36e+38) || ~((y <= 5.1e-142)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.36e+38], N[Not[LessEqual[y, 5.1e-142]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.36000000000000002e38 or 5.1000000000000001e-142 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 83.8%

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

      1. associate-*r/ 89.6%

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

   4. Simplified 89.6%

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

   if -1.36000000000000002e38 < y < 5.1000000000000001e-142

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. distribute-rgt1-in 83.5%

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

      3. mul-1-neg 83.5%

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

      4. cancel-sign-sub-inv 83.5%

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

      5. associate-*l/ 85.2%

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

      6. associate-/l* 86.2%

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

   4. Simplified 86.2%

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

      1. clear-num 86.2%

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

      2. associate-/r/ 85.2%

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

      3. clear-num 85.3%

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

   6. Applied egg-rr 85.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+38} \lor \neg \left(y \leq 5.1 \cdot 10^{-142}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 9: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+36} \lor \neg \left(y \leq 1.55 \cdot 10^{-140}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e+36) (not (<= y 1.55e-140)))
   (+ x (* y (/ z t)))
   (- x (/ z (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e+36) || !(y <= 1.55e-140)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (z / (t / 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 ((y <= (-3.1d+36)) .or. (.not. (y <= 1.55d-140))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e+36) || !(y <= 1.55e-140)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e+36) or not (y <= 1.55e-140):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (z / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e+36) || !(y <= 1.55e-140))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e+36) || ~((y <= 1.55e-140)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e+36], N[Not[LessEqual[y, 1.55e-140]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e36 or 1.55e-140 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 83.8%

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

      1. associate-*r/ 89.6%

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

   4. Simplified 89.6%

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

   if -3.0999999999999999e36 < y < 1.55e-140

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. distribute-rgt1-in 83.5%

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

      3. mul-1-neg 83.5%

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

      4. cancel-sign-sub-inv 83.5%

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

      5. associate-*l/ 85.2%

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

      6. associate-/l* 86.2%

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

   4. Simplified 86.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+36} \lor \neg \left(y \leq 1.55 \cdot 10^{-140}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 10: 97.5% 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 96.4%

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

2. Final simplification 96.4%

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

Alternative 11: 38.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in z around 0 39.6%

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

3. Final simplification 39.6%

   \[\leadsto x \]

Developer target: 97.1% 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 2023185 
(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))))