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

Percentage Accurate: 97.4% → 97.4%

Time: 7.8s

Alternatives: 11

Speedup: 1.0×

• 25.0% 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: 97.4% 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: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative 98.4%

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

   2. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000 \lor \neg \left(\frac{z}{t} \leq 10000000\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1000000000.0) (not (<= (/ z t) 10000000.0)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000000000.0) || !((z / t) <= 10000000.0)) {
		tmp = (y - x) / (t / z);
	} 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) <= (-1000000000.0d0)) .or. (.not. ((z / t) <= 10000000.0d0))) then
        tmp = (y - x) / (t / z)
    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) <= -1000000000.0) || !((z / t) <= 10000000.0)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1000000000.0) or not ((z / t) <= 10000000.0):
		tmp = (y - x) / (t / z)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1000000000.0) || !(Float64(z / t) <= 10000000.0))
		tmp = Float64(Float64(y - x) / Float64(t / z));
	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) <= -1000000000.0) || ~(((z / t) <= 10000000.0)))
		tmp = (y - x) / (t / z);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e9 or 1e7 < (/.f64 z t)

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 89.7%

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

      1. *-commutative 89.7%

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

      2. sub-div 92.9%

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

      3. associate-/r/ 96.6%

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

      4. frac-2neg 96.6%

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

      5. frac-2neg 96.6%

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

      6. sub-neg 96.6%

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

      7. distribute-neg-in 96.6%

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

      8. add-sqr-sqrt 49.3%

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

      9. sqrt-unprod 67.1%

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

      10. sqr-neg 67.1%

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

      11. sqrt-unprod 23.5%

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

      12. add-sqr-sqrt 43.4%

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

      13. add-sqr-sqrt 19.9%

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

      14. sqrt-unprod 61.8%

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

      15. sqr-neg 61.8%

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

      16. sqrt-unprod 47.1%

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

      17. add-sqr-sqrt 96.6%

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

      18. distribute-neg-frac 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. distribute-neg-in 96.6%

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

      2. unsub-neg 96.6%

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

      3. remove-double-neg 96.6%

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

      4. distribute-neg-frac 96.6%

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

      5. remove-double-neg 96.6%

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

   6. Simplified 96.6%

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

   if -1e9 < (/.f64 z t) < 1e7

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 93.9%

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

      1. associate-*r/ 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000 \lor \neg \left(\frac{z}{t} \leq 10000000\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 3: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -400000 \lor \neg \left(\frac{z}{t} \leq 10^{-17}\right):\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -400000.0) (not (<= (/ z t) 1e-17))) (* x (- (/ z t))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -400000.0) || !((z / t) <= 1e-17)) {
		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) <= (-400000.0d0)) .or. (.not. ((z / t) <= 1d-17))) 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) <= -400000.0) || !((z / t) <= 1e-17)) {
		tmp = x * -(z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -400000.0) or not ((z / t) <= 1e-17):
		tmp = x * -(z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -400000.0) || !(Float64(z / t) <= 1e-17))
		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) <= -400000.0) || ~(((z / t) <= 1e-17)))
		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], -400000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-17]], $MachinePrecision]], N[(x * (-N[(z / t), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4e5 or 1.00000000000000007e-17 < (/.f64 z t)

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. sub-div 92.3%

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

      3. associate-/r/ 96.6%

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

      4. div-sub 84.3%

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

      5. associate-/l* 80.2%

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

      6. add-sqr-sqrt 38.4%

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

      7. sqrt-unprod 47.1%

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

      8. sqr-neg 47.1%

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

      9. sqrt-unprod 14.6%

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

      10. add-sqr-sqrt 33.1%

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

      11. un-div-inv 33.1%

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

      12. clear-num 33.1%

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

      13. *-commutative 33.1%

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

      14. associate-*l/ 34.6%

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

      15. sub-div 39.2%

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

      16. add-sqr-sqrt 18.4%

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

      17. sqrt-unprod 56.4%

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

      18. sqr-neg 56.4%

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

      19. sqrt-unprod 41.6%

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

      20. add-sqr-sqrt 85.0%

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

   4. Applied egg-rr 85.0%

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

   5. Taylor expanded in y around 0 55.2%

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

      1. associate-*r* 55.2%

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

      2. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

      1. associate-*r/ 60.1%

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

      2. distribute-lft-neg-in 60.1%

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

      3. *-commutative 60.1%

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

      4. distribute-lft-neg-in 60.1%

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

   9. Applied egg-rr 60.1%

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

   if -4e5 < (/.f64 z t) < 1.00000000000000007e-17

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 75.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -400000 \lor \neg \left(\frac{z}{t} \leq 10^{-17}\right):\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1000000000.0)
   (/ (* x (- z)) t)
   (if (<= (/ z t) 1e-17) x (* x (- (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1000000000.0) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= 1e-17) {
		tmp = x;
	} else {
		tmp = x * -(z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1000000000.0d0)) then
        tmp = (x * -z) / t
    else if ((z / t) <= 1d-17) then
        tmp = x
    else
        tmp = x * -(z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1000000000.0) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= 1e-17) {
		tmp = x;
	} else {
		tmp = x * -(z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1000000000.0:
		tmp = (x * -z) / t
	elif (z / t) <= 1e-17:
		tmp = x
	else:
		tmp = x * -(z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1000000000.0)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (Float64(z / t) <= 1e-17)
		tmp = x;
	else
		tmp = Float64(x * Float64(-Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1000000000.0)
		tmp = (x * -z) / t;
	elseif ((z / t) <= 1e-17)
		tmp = x;
	else
		tmp = x * -(z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1000000000.0], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-17], x, N[(x * (-N[(z / t), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e9

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. sub-div 90.8%

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

      3. associate-/r/ 97.3%

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

      4. div-sub 84.0%

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

      5. associate-/l* 83.2%

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

      6. add-sqr-sqrt 41.8%

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

      7. sqrt-unprod 53.8%

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

      8. sqr-neg 53.8%

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

      9. sqrt-unprod 17.3%

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

      10. add-sqr-sqrt 34.4%

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

      11. un-div-inv 34.4%

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

      12. clear-num 34.4%

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

      13. *-commutative 34.4%

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

      14. associate-*l/ 34.2%

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

      15. sub-div 37.1%

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

      16. add-sqr-sqrt 17.2%

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

      17. sqrt-unprod 61.1%

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

      18. sqr-neg 61.1%

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

      19. sqrt-unprod 47.6%

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

      20. add-sqr-sqrt 93.4%

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in y around 0 61.9%

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

      1. associate-*r* 61.9%

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

      2. mul-1-neg 61.9%

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

   7. Simplified 61.9%

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

   if -1e9 < (/.f64 z t) < 1.00000000000000007e-17

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 75.1%

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

   if 1.00000000000000007e-17 < (/.f64 z t)

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 90.5%

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

      1. *-commutative 90.5%

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

      2. sub-div 93.8%

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

      3. associate-/r/ 95.9%

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

      4. div-sub 84.3%

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

      5. associate-/l* 76.7%

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

      6. add-sqr-sqrt 33.7%

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

      7. sqrt-unprod 38.7%

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

      8. sqr-neg 38.7%

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

      9. sqrt-unprod 11.9%

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

      10. add-sqr-sqrt 30.7%

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

      11. un-div-inv 30.7%

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

      12. clear-num 30.7%

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

      13. *-commutative 30.7%

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

      14. associate-*l/ 34.0%

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

      15. sub-div 40.5%

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

      16. add-sqr-sqrt 20.1%

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

      17. sqrt-unprod 50.5%

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

      18. sqr-neg 50.5%

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

      19. sqrt-unprod 34.0%

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

      20. add-sqr-sqrt 75.5%

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

   4. Applied egg-rr 75.5%

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

   5. Taylor expanded in y around 0 48.7%

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

      1. associate-*r* 48.7%

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

      2. mul-1-neg 48.7%

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

   7. Simplified 48.7%

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

      1. associate-*r/ 59.6%

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

      2. distribute-lft-neg-in 59.6%

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

      3. *-commutative 59.6%

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

      4. distribute-lft-neg-in 59.6%

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

   9. Applied egg-rr 59.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \end{array} \]

Alternative 5: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-19} \lor \neg \left(\frac{z}{t} \leq 10^{-27}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e-19) (not (<= (/ z t) 1e-27))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e-19) || !((z / t) <= 1e-27)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-4d-19)) .or. (.not. ((z / t) <= 1d-27))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e-19) || !((z / t) <= 1e-27)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -4e-19) or not ((z / t) <= 1e-27):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -4e-19) || !(Float64(z / t) <= 1e-27))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -4e-19) || ~(((z / t) <= 1e-27)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -4e-19], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-27]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -3.9999999999999999e-19 or 1e-27 < (/.f64 z t)

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. sub-div 90.6%

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

      3. associate-/r/ 95.5%

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

      4. div-sub 83.7%

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

      5. associate-/l* 79.1%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 47.2%

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

      8. sqr-neg 47.2%

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

      9. sqrt-unprod 14.0%

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

      10. add-sqr-sqrt 33.9%

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

      11. un-div-inv 33.9%

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

      12. clear-num 33.9%

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

      13. *-commutative 33.9%

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

      14. associate-*l/ 35.3%

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

      15. sub-div 39.7%

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

      16. add-sqr-sqrt 17.6%

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

      17. sqrt-unprod 56.2%

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

      18. sqr-neg 56.2%

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

      19. sqrt-unprod 42.0%

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

      20. add-sqr-sqrt 83.6%

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

   4. Applied egg-rr 83.6%

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

   5. Taylor expanded in y around inf 46.3%

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

      1. *-commutative 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in z around 0 46.3%

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

      1. associate-*r/ 53.6%

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

      2. *-commutative 53.6%

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

   10. Simplified 53.6%

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

   if -3.9999999999999999e-19 < (/.f64 z t) < 1e-27

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 78.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-19} \lor \neg \left(\frac{z}{t} \leq 10^{-27}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -100000000000:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -100000000000.0)
   (* z (/ (- x) t))
   (if (<= (/ z t) 1e-27) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -100000000000.0) {
		tmp = z * (-x / t);
	} else if ((z / t) <= 1e-27) {
		tmp = x;
	} else {
		tmp = 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) <= (-100000000000.0d0)) then
        tmp = z * (-x / t)
    else if ((z / t) <= 1d-27) then
        tmp = x
    else
        tmp = 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) <= -100000000000.0) {
		tmp = z * (-x / t);
	} else if ((z / t) <= 1e-27) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -100000000000.0:
		tmp = z * (-x / t)
	elif (z / t) <= 1e-27:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -100000000000.0)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (Float64(z / t) <= 1e-27)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -100000000000.0)
		tmp = z * (-x / t);
	elseif ((z / t) <= 1e-27)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -100000000000.0], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-27], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e11

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 90.4%

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

   3. Taylor expanded in y around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. mul-1-neg 57.9%

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

   5. Simplified 57.9%

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

   if -1e11 < (/.f64 z t) < 1e-27

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 75.2%

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

   if 1e-27 < (/.f64 z t)

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 90.8%

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

      1. *-commutative 90.8%

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

      2. sub-div 94.0%

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

      3. associate-/r/ 96.0%

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

      4. div-sub 84.8%

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

      5. associate-/l* 77.4%

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

      6. add-sqr-sqrt 35.8%

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

      7. sqrt-unprod 40.6%

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

      8. sqr-neg 40.6%

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

      9. sqrt-unprod 11.5%

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

      10. add-sqr-sqrt 32.8%

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

      11. un-div-inv 32.8%

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

      12. clear-num 32.8%

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

      13. *-commutative 32.8%

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

      14. associate-*l/ 36.1%

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

      15. sub-div 42.4%

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

      16. add-sqr-sqrt 19.5%

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

      17. sqrt-unprod 52.0%

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

      18. sqr-neg 52.0%

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

      19. sqrt-unprod 36.1%

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

      20. add-sqr-sqrt 76.2%

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

   4. Applied egg-rr 76.2%

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

   5. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in z around 0 45.3%

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

      1. associate-*r/ 55.0%

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

      2. *-commutative 55.0%

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

   10. Simplified 55.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -100000000000:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7600000000 \lor \neg \left(y \leq 2.2 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7600000000.0) (not (<= y 2.2e+119)))
   (* y (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7600000000.0) || !(y <= 2.2e+119)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (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 <= (-7600000000.0d0)) .or. (.not. (y <= 2.2d+119))) then
        tmp = y * (z / t)
    else
        tmp = x * (1.0d0 - (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 <= -7600000000.0) || !(y <= 2.2e+119)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7600000000.0) or not (y <= 2.2e+119):
		tmp = y * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7600000000.0) || !(y <= 2.2e+119))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7600000000.0) || ~((y <= 2.2e+119)))
		tmp = y * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7600000000.0], N[Not[LessEqual[y, 2.2e+119]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6e9 or 2.2000000000000001e119 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. sub-div 69.4%

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

      3. associate-/r/ 78.0%

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

      4. div-sub 66.6%

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

      5. associate-/l* 57.8%

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

      6. add-sqr-sqrt 31.4%

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

      7. sqrt-unprod 52.8%

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

      8. sqr-neg 52.8%

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

      9. sqrt-unprod 23.6%

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

      10. add-sqr-sqrt 51.3%

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

      11. un-div-inv 51.3%

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

      12. clear-num 51.3%

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

      13. *-commutative 51.3%

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

      14. associate-*l/ 51.3%

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

      15. sub-div 57.0%

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

      16. add-sqr-sqrt 27.1%

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

      17. sqrt-unprod 60.9%

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

      18. sqr-neg 60.9%

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

      19. sqrt-unprod 34.9%

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

      20. add-sqr-sqrt 63.5%

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

   4. Applied egg-rr 63.5%

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

   5. Taylor expanded in y around inf 62.8%

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

      1. *-commutative 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in z around 0 62.8%

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

      1. associate-*r/ 71.0%

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

      2. *-commutative 71.0%

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

   10. Simplified 71.0%

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

   if -7.6e9 < y < 2.2000000000000001e119

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

   4. Simplified 84.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7600000000 \lor \neg \left(y \leq 2.2 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 8: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6400000000 \lor \neg \left(y \leq 2.7 \cdot 10^{-100}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6400000000.0) (not (<= y 2.7e-100)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6400000000.0) || !(y <= 2.7e-100)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (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 <= (-6400000000.0d0)) .or. (.not. (y <= 2.7d-100))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (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 <= -6400000000.0) || !(y <= 2.7e-100)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6400000000.0) or not (y <= 2.7e-100):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6400000000.0) || !(y <= 2.7e-100))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6400000000.0) || ~((y <= 2.7e-100)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6400000000.0], N[Not[LessEqual[y, 2.7e-100]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e9 or 2.70000000000000016e-100 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. associate-*r/ 87.9%

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

   4. Simplified 87.9%

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

   if -6.4e9 < y < 2.70000000000000016e-100

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   4. Simplified 89.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6400000000 \lor \neg \left(y \leq 2.7 \cdot 10^{-100}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 9: 53.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-102} \lor \neg \left(z \leq 1.05 \cdot 10^{+119}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e-102) (not (<= z 1.05e+119))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e-102) || !(z <= 1.05e+119)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.3d-102)) .or. (.not. (z <= 1.05d+119))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e-102) || !(z <= 1.05e+119)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.3e-102) or not (z <= 1.05e+119):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e-102) || !(z <= 1.05e+119))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e-102) || ~((z <= 1.05e+119)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.3e-102], N[Not[LessEqual[z, 1.05e+119]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999987e-102 or 1.04999999999999991e119 < z

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 79.5%

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

   3. Taylor expanded in y around inf 50.8%

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

   if -2.29999999999999987e-102 < z < 1.04999999999999991e119

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 62.0%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-102} \lor \neg \left(z \leq 1.05 \cdot 10^{+119}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 97.4% 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 98.4%

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

2. Final simplification 98.4%

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

Alternative 11: 39.0% 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 98.4%

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

2. Taylor expanded in z around 0 38.9%

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

3. Final simplification 38.9%

   \[\leadsto x \]

Developer target: 97.2% 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 2023339 
(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))))