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

Percentage Accurate: 97.8% → 97.9%

Time: 7.2s

Alternatives: 10

Speedup: 1.0×

• 25.1% 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: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

3. Taylor expanded in y around 0 87.6%

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

   1. +-commutative 87.6%

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

   2. mul-1-neg 87.6%

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

   3. sub-neg 87.6%

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

   4. associate-/l* 87.4%

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

   5. associate-/l* 91.0%

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

   6. div-sub 98.4%

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

5. Simplified 98.4%

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

6. Final simplification 98.4%

   \[\leadsto x + \frac{y - x}{\frac{t}{z}} \]
7. Add Preprocessing

Alternative 2: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+34} \lor \neg \left(x \leq 1.75 \cdot 10^{+233}\right):\\ \;\;\;\;-x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e+31)
   x
   (if (<= x 3.3e-15)
     (/ y (/ t z))
     (if (or (<= x 5.4e+34) (not (<= x 1.75e+233))) (- (* x (/ z t))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+31) {
		tmp = x;
	} else if (x <= 3.3e-15) {
		tmp = y / (t / z);
	} else if ((x <= 5.4e+34) || !(x <= 1.75e+233)) {
		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 (x <= (-4d+31)) then
        tmp = x
    else if (x <= 3.3d-15) then
        tmp = y / (t / z)
    else if ((x <= 5.4d+34) .or. (.not. (x <= 1.75d+233))) 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 (x <= -4e+31) {
		tmp = x;
	} else if (x <= 3.3e-15) {
		tmp = y / (t / z);
	} else if ((x <= 5.4e+34) || !(x <= 1.75e+233)) {
		tmp = -(x * (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e+31:
		tmp = x
	elif x <= 3.3e-15:
		tmp = y / (t / z)
	elif (x <= 5.4e+34) or not (x <= 1.75e+233):
		tmp = -(x * (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e+31)
		tmp = x;
	elseif (x <= 3.3e-15)
		tmp = Float64(y / Float64(t / z));
	elseif ((x <= 5.4e+34) || !(x <= 1.75e+233))
		tmp = Float64(-Float64(x * Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e+31)
		tmp = x;
	elseif (x <= 3.3e-15)
		tmp = y / (t / z);
	elseif ((x <= 5.4e+34) || ~((x <= 1.75e+233)))
		tmp = -(x * (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e+31], x, If[LessEqual[x, 3.3e-15], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.4e+34], N[Not[LessEqual[x, 1.75e+233]], $MachinePrecision]], (-N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), x]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999999e31 or 5.4000000000000001e34 < x < 1.7499999999999999e233

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 58.4%

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

   if -3.9999999999999999e31 < x < 3.3e-15

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 64.1%

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

   4. Taylor expanded in y around inf 53.2%

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

      1. associate-*r/ 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-/l* 59.0%

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

   6. Applied egg-rr 59.0%

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

   if 3.3e-15 < x < 5.4000000000000001e34 or 1.7499999999999999e233 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. sub-div 72.2%

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

      3. associate-/r/ 74.6%

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

   5. Applied egg-rr 74.6%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-/l* 64.8%

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

      3. distribute-neg-frac 64.8%

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

   8. Simplified 64.8%

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

   9. Taylor expanded in x around 0 62.6%

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

       1. associate-*r/ 62.6%

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

       2. mul-1-neg 62.6%

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

       3. distribute-rgt-neg-out 62.6%

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

       4. associate-*r/ 64.8%

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

   11. Simplified 64.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+34} \lor \neg \left(x \leq 1.75 \cdot 10^{+233}\right):\\ \;\;\;\;-x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+33} \lor \neg \left(x \leq 2.05 \cdot 10^{+233}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e+39)
   x
   (if (<= x 2.1e-14)
     (/ y (/ t z))
     (if (or (<= x 7e+33) (not (<= x 2.05e+233))) (* (- z) (/ x t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+39) {
		tmp = x;
	} else if (x <= 2.1e-14) {
		tmp = y / (t / z);
	} else if ((x <= 7e+33) || !(x <= 2.05e+233)) {
		tmp = -z * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.8d+39)) then
        tmp = x
    else if (x <= 2.1d-14) then
        tmp = y / (t / z)
    else if ((x <= 7d+33) .or. (.not. (x <= 2.05d+233))) then
        tmp = -z * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+39) {
		tmp = x;
	} else if (x <= 2.1e-14) {
		tmp = y / (t / z);
	} else if ((x <= 7e+33) || !(x <= 2.05e+233)) {
		tmp = -z * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e+39:
		tmp = x
	elif x <= 2.1e-14:
		tmp = y / (t / z)
	elif (x <= 7e+33) or not (x <= 2.05e+233):
		tmp = -z * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e+39)
		tmp = x;
	elseif (x <= 2.1e-14)
		tmp = Float64(y / Float64(t / z));
	elseif ((x <= 7e+33) || !(x <= 2.05e+233))
		tmp = Float64(Float64(-z) * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.8e+39)
		tmp = x;
	elseif (x <= 2.1e-14)
		tmp = y / (t / z);
	elseif ((x <= 7e+33) || ~((x <= 2.05e+233)))
		tmp = -z * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e+39], x, If[LessEqual[x, 2.1e-14], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 7e+33], N[Not[LessEqual[x, 2.05e+233]], $MachinePrecision]], N[((-z) * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.80000000000000001e39 or 7.0000000000000002e33 < x < 2.04999999999999996e233

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 58.4%

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

   if -2.80000000000000001e39 < x < 2.0999999999999999e-14

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 64.1%

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

   4. Taylor expanded in y around inf 53.2%

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

      1. associate-*r/ 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-/l* 59.0%

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

   6. Applied egg-rr 59.0%

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

   if 2.0999999999999999e-14 < x < 7.0000000000000002e33 or 2.04999999999999996e233 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 64.5%

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

   4. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-frac-neg 64.8%

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

   6. Simplified 64.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+33} \lor \neg \left(x \leq 2.05 \cdot 10^{+233}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+45} \lor \neg \left(t \leq -125\right) \land t \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.1e+85)
   x
   (if (or (<= t -7.2e+45) (and (not (<= t -125.0)) (<= t 1.55e+76)))
     (* z (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.1e+85) {
		tmp = x;
	} else if ((t <= -7.2e+45) || (!(t <= -125.0) && (t <= 1.55e+76))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.1d+85)) then
        tmp = x
    else if ((t <= (-7.2d+45)) .or. (.not. (t <= (-125.0d0))) .and. (t <= 1.55d+76)) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.1e+85) {
		tmp = x;
	} else if ((t <= -7.2e+45) || (!(t <= -125.0) && (t <= 1.55e+76))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.1e+85:
		tmp = x
	elif (t <= -7.2e+45) or (not (t <= -125.0) and (t <= 1.55e+76)):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.1e+85)
		tmp = x;
	elseif ((t <= -7.2e+45) || (!(t <= -125.0) && (t <= 1.55e+76)))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.1e+85)
		tmp = x;
	elseif ((t <= -7.2e+45) || (~((t <= -125.0)) && (t <= 1.55e+76)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.1e+85], x, If[Or[LessEqual[t, -7.2e+45], And[N[Not[LessEqual[t, -125.0]], $MachinePrecision], LessEqual[t, 1.55e+76]]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1000000000000001e85 or -7.2e45 < t < -125 or 1.55000000000000006e76 < t

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 76.6%

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

   if -1.1000000000000001e85 < t < -7.2e45 or -125 < t < 1.55000000000000006e76

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 75.1%

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

   4. Taylor expanded in y around inf 45.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+45} \lor \neg \left(t \leq -125\right) \land t \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e+85)
   x
   (if (<= t -1.35e+44)
     (* z (/ y t))
     (if (<= t -1.8e-5) x (if (<= t 1.85e+76) (/ y (/ t z)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+85) {
		tmp = x;
	} else if (t <= -1.35e+44) {
		tmp = z * (y / t);
	} else if (t <= -1.8e-5) {
		tmp = x;
	} else if (t <= 1.85e+76) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.8d+85)) then
        tmp = x
    else if (t <= (-1.35d+44)) then
        tmp = z * (y / t)
    else if (t <= (-1.8d-5)) then
        tmp = x
    else if (t <= 1.85d+76) then
        tmp = y / (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+85) {
		tmp = x;
	} else if (t <= -1.35e+44) {
		tmp = z * (y / t);
	} else if (t <= -1.8e-5) {
		tmp = x;
	} else if (t <= 1.85e+76) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e+85:
		tmp = x
	elif t <= -1.35e+44:
		tmp = z * (y / t)
	elif t <= -1.8e-5:
		tmp = x
	elif t <= 1.85e+76:
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e+85)
		tmp = x;
	elseif (t <= -1.35e+44)
		tmp = Float64(z * Float64(y / t));
	elseif (t <= -1.8e-5)
		tmp = x;
	elseif (t <= 1.85e+76)
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e+85)
		tmp = x;
	elseif (t <= -1.35e+44)
		tmp = z * (y / t);
	elseif (t <= -1.8e-5)
		tmp = x;
	elseif (t <= 1.85e+76)
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e+85], x, If[LessEqual[t, -1.35e+44], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-5], x, If[LessEqual[t, 1.85e+76], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7999999999999999e85 or -1.35e44 < t < -1.80000000000000005e-5 or 1.85e76 < t

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 76.6%

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

   if -1.7999999999999999e85 < t < -1.35e44

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 85.8%

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

   4. Taylor expanded in y around inf 85.9%

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

   if -1.80000000000000005e-5 < t < 1.85e76

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 74.6%

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

   4. Taylor expanded in y around inf 43.5%

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

      1. associate-*r/ 48.1%

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

      2. *-commutative 48.1%

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

      3. associate-/l* 51.9%

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

   6. Applied egg-rr 51.9%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -500.0) (not (<= (/ z t) 2e-8)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500.0) || !((z / t) <= 2e-8)) {
		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) <= (-500.0d0)) .or. (.not. ((z / t) <= 2d-8))) 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) <= -500.0) || !((z / t) <= 2e-8)) {
		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) <= -500.0) or not ((z / t) <= 2e-8):
		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) <= -500.0) || !(Float64(z / t) <= 2e-8))
		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) <= -500.0) || ~(((z / t) <= 2e-8)))
		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], -500.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-8]], $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) < -500 or 2e-8 < (/.f64 z t)

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 90.2%

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

      1. *-commutative 90.2%

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

      2. sub-div 94.2%

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

      3. associate-/r/ 97.5%

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

   5. Applied egg-rr 97.5%

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

   if -500 < (/.f64 z t) < 2e-8

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf 93.0%

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

      1. associate-*r/ 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+125} \lor \neg \left(y \leq 7.5 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+125) (not (<= y 7.5e+108)))
   (/ y (/ t z))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+125) || !(y <= 7.5e+108)) {
		tmp = y / (t / z);
	} 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 <= (-3.8d+125)) .or. (.not. (y <= 7.5d+108))) then
        tmp = y / (t / z)
    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 <= -3.8e+125) || !(y <= 7.5e+108)) {
		tmp = y / (t / z);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+125) or not (y <= 7.5e+108):
		tmp = y / (t / z)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+125) || !(y <= 7.5e+108))
		tmp = Float64(y / Float64(t / z));
	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 <= -3.8e+125) || ~((y <= 7.5e+108)))
		tmp = y / (t / z);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+125], N[Not[LessEqual[y, 7.5e+108]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000002e125 or 7.50000000000000039e108 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 59.5%

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

   4. Taylor expanded in y around inf 57.9%

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

      1. associate-*r/ 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-/l* 66.5%

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

   6. Applied egg-rr 66.5%

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

   if -3.80000000000000002e125 < y < 7.50000000000000039e108

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+125} \lor \neg \left(y \leq 7.5 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-20} \lor \neg \left(y \leq 4.5 \cdot 10^{-25}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e-20) (not (<= y 4.5e-25)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-20) || !(y <= 4.5e-25)) {
		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 <= (-1.1d-20)) .or. (.not. (y <= 4.5d-25))) 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 <= -1.1e-20) || !(y <= 4.5e-25)) {
		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 <= -1.1e-20) or not (y <= 4.5e-25):
		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 <= -1.1e-20) || !(y <= 4.5e-25))
		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 <= -1.1e-20) || ~((y <= 4.5e-25)))
		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, -1.1e-20], N[Not[LessEqual[y, 4.5e-25]], $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 < -1.09999999999999995e-20 or 4.5000000000000001e-25 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf 84.3%

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

      1. associate-*r/ 87.6%

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

   5. Simplified 87.6%

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

   if -1.09999999999999995e-20 < y < 4.5000000000000001e-25

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-20} \lor \neg \left(y \leq 4.5 \cdot 10^{-25}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

3. Final simplification 98.2%

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

Alternative 10: 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 98.2%

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

3. Taylor expanded in z around 0 39.7%

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

4. Final simplification 39.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024018 
(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))))