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

Percentage Accurate: 97.5% → 97.5%

Time: 8.7s

Alternatives: 13

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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{t}{z}}}\right)\right) \]

   2. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{t}{z}}}\right)\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{t}}{z}\right)\right)\right) \]

   5. /-lowering-/.f64 98.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 98.0%

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

Alternative 2: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.5:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e+21)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 0.5) (+ x (/ y (/ t z))) (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 0.5) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y - x) / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1d+21)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 0.5d0) then
        tmp = x + (y / (t / z))
    else
        tmp = (y - x) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 0.5) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y - x) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e+21:
		tmp = z / (t / (y - x))
	elif (z / t) <= 0.5:
		tmp = x + (y / (t / z))
	else:
		tmp = (y - x) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e+21)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 0.5)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(y - x) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e+21)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 0.5)
		tmp = x + (y / (t / z));
	else
		tmp = (y - x) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e+21], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.5], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e21

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 96.7%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 96.7%

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

      1. clear-num N/A

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

      2. div-inv N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{t}{y - x}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{\left(y - x\right)}\right)\right) \]

      5. --lowering--.f64 96.8%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 96.8%

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

   if -1e21 < (/.f64 z t) < 0.5

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(z, t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), \color{blue}{x}\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      6. /-lowering-/.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 97.9%

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

   if 0.5 < (/.f64 z t)

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 92.5%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 92.5%

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

      1. *-commutative N/A

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

      2. div-inv N/A

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

      3. associate-*l* N/A

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

      4. associate-/r/ N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{t}}{z}\right)\right) \]

      8. /-lowering-/.f64 98.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 98.6%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.5:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 2000000:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e+21)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 2000000.0) (+ x (/ y (/ t z))) (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 2000000.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = ((y - 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) <= (-1d+21)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 2000000.0d0) then
        tmp = x + (y / (t / z))
    else
        tmp = ((y - 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) <= -1e+21) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 2000000.0) {
		tmp = x + (y / (t / z));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e+21:
		tmp = z / (t / (y - x))
	elif (z / t) <= 2000000.0:
		tmp = x + (y / (t / z))
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e+21)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 2000000.0)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e+21)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 2000000.0)
		tmp = x + (y / (t / z));
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e+21], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2000000.0], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e21

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 96.7%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 96.7%

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

      1. clear-num N/A

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

      2. div-inv N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{t}{y - x}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{\left(y - x\right)}\right)\right) \]

      5. --lowering--.f64 96.8%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 96.8%

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

   if -1e21 < (/.f64 z t) < 2e6

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(z, t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), \color{blue}{x}\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      6. /-lowering-/.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 97.9%

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

   if 2e6 < (/.f64 z t)

   1. Initial program 98.6%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{t}{z}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{t}{z}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{t}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 98.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(y - x\right)\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y - x\right)\right), t\right) \]

      3. --lowering--.f64 94.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, x\right)\right), t\right) \]

   7. Simplified 94.8%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 2000000:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t (- y x)))))
   (if (<= (/ z t) -1e+21)
     t_1
     (if (<= (/ z t) 4e+37) (+ x (/ y (/ t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / (y - x));
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = t_1;
	} else if ((z / t) <= 4e+37) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (t / (y - x))
    if ((z / t) <= (-1d+21)) then
        tmp = t_1
    else if ((z / t) <= 4d+37) then
        tmp = x + (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / (y - x));
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = t_1;
	} else if ((z / t) <= 4e+37) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / (y - x))
	tmp = 0
	if (z / t) <= -1e+21:
		tmp = t_1
	elif (z / t) <= 4e+37:
		tmp = x + (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / Float64(y - x)))
	tmp = 0.0
	if (Float64(z / t) <= -1e+21)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e+37)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / (y - x));
	tmp = 0.0;
	if ((z / t) <= -1e+21)
		tmp = t_1;
	elseif ((z / t) <= 4e+37)
		tmp = x + (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+21], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e+37], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e21 or 3.99999999999999982e37 < (/.f64 z t)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 96.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 96.2%

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

      1. clear-num N/A

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

      2. div-inv N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{t}{y - x}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{\left(y - x\right)}\right)\right) \]

      5. --lowering--.f64 96.3%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 96.3%

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

   if -1e21 < (/.f64 z t) < 3.99999999999999982e37

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(z, t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), \color{blue}{x}\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      6. /-lowering-/.f64 97.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 97.0%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= (/ z t) -1e+21)
     t_1
     (if (<= (/ z t) 4e+37) (+ x (/ y (/ t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = t_1;
	} else if ((z / t) <= 4e+37) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / t)
    if ((z / t) <= (-1d+21)) then
        tmp = t_1
    else if ((z / t) <= 4d+37) then
        tmp = x + (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = t_1;
	} else if ((z / t) <= 4e+37) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if (z / t) <= -1e+21:
		tmp = t_1
	elif (z / t) <= 4e+37:
		tmp = x + (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+21)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e+37)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if ((z / t) <= -1e+21)
		tmp = t_1;
	elseif ((z / t) <= 4e+37)
		tmp = x + (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+21], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e+37], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e21 or 3.99999999999999982e37 < (/.f64 z t)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 96.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 96.2%

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

   if -1e21 < (/.f64 z t) < 3.99999999999999982e37

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(z, t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), \color{blue}{x}\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      6. /-lowering-/.f64 97.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 97.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= (/ z t) -1e+21)
     t_1
     (if (<= (/ z t) 4e+37) (+ x (* y (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = t_1;
	} else if ((z / t) <= 4e+37) {
		tmp = x + (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / t)
    if ((z / t) <= (-1d+21)) then
        tmp = t_1
    else if ((z / t) <= 4d+37) then
        tmp = x + (y * (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = t_1;
	} else if ((z / t) <= 4e+37) {
		tmp = x + (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if (z / t) <= -1e+21:
		tmp = t_1
	elif (z / t) <= 4e+37:
		tmp = x + (y * (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+21)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e+37)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if ((z / t) <= -1e+21)
		tmp = t_1;
	elseif ((z / t) <= 4e+37)
		tmp = x + (y * (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+21], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e+37], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e21 or 3.99999999999999982e37 < (/.f64 z t)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 96.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 96.2%

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

   if -1e21 < (/.f64 z t) < 3.99999999999999982e37

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(z, t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.0%

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

Alternative 7: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= (/ z t) -2e+24)
     t_1
     (if (<= (/ z t) 5e-54) (* x (- 1.0 (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -2e+24) {
		tmp = t_1;
	} else if ((z / t) <= 5e-54) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / t)
    if ((z / t) <= (-2d+24)) then
        tmp = t_1
    else if ((z / t) <= 5d-54) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -2e+24) {
		tmp = t_1;
	} else if ((z / t) <= 5e-54) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if (z / t) <= -2e+24:
		tmp = t_1
	elif (z / t) <= 5e-54:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -2e+24)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-54)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if ((z / t) <= -2e+24)
		tmp = t_1;
	elseif ((z / t) <= 5e-54)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+24], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-54], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e24 or 5.00000000000000015e-54 < (/.f64 z t)

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 91.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 91.0%

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

   if -2e24 < (/.f64 z t) < 5.00000000000000015e-54

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 78.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 78.1%

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

Alternative 8: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+24)
   (/ z (/ t y))
   (if (<= (/ z t) 5e-54) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+24) {
		tmp = z / (t / y);
	} else if ((z / t) <= 5e-54) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d+24)) then
        tmp = z / (t / y)
    else if ((z / t) <= 5d-54) then
        tmp = x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+24) {
		tmp = z / (t / y);
	} else if ((z / t) <= 5e-54) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+24:
		tmp = z / (t / y)
	elif (z / t) <= 5e-54:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+24)
		tmp = Float64(z / Float64(t / y));
	elseif (Float64(z / t) <= 5e-54)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e+24)
		tmp = z / (t / y);
	elseif ((z / t) <= 5e-54)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+24], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-54], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e24

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 51.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 51.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{t}{y}\right)}\right) \]

      6. /-lowering-/.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 57.8%

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

   if -2e24 < (/.f64 z t) < 5.00000000000000015e-54

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 77.2%

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

   if 5.00000000000000015e-54 < (/.f64 z t)

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 52.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 52.3%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      4. /-lowering-/.f64 58.5%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 58.5%

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

Alternative 9: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= (/ z t) -2e+24) t_1 (if (<= (/ z t) 5e-54) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if ((z / t) <= -2e+24) {
		tmp = t_1;
	} else if ((z / t) <= 5e-54) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t / z)
    if ((z / t) <= (-2d+24)) then
        tmp = t_1
    else if ((z / t) <= 5d-54) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if ((z / t) <= -2e+24) {
		tmp = t_1;
	} else if ((z / t) <= 5e-54) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if (z / t) <= -2e+24:
		tmp = t_1
	elif (z / t) <= 5e-54:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (Float64(z / t) <= -2e+24)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-54)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if ((z / t) <= -2e+24)
		tmp = t_1;
	elseif ((z / t) <= 5e-54)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+24], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-54], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e24 or 5.00000000000000015e-54 < (/.f64 z t)

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 52.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 52.0%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      4. /-lowering-/.f64 56.9%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 56.9%

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

   if -2e24 < (/.f64 z t) < 5.00000000000000015e-54

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 77.2%

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

Alternative 10: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -1.05e+21) t_1 (if (<= (/ z t) 6e-52) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1.05e+21) {
		tmp = t_1;
	} else if ((z / t) <= 6e-52) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-1.05d+21)) then
        tmp = t_1
    else if ((z / t) <= 6d-52) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1.05e+21) {
		tmp = t_1;
	} else if ((z / t) <= 6e-52) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -1.05e+21:
		tmp = t_1
	elif (z / t) <= 6e-52:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1.05e+21)
		tmp = t_1;
	elseif (Float64(z / t) <= 6e-52)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1.05e+21)
		tmp = t_1;
	elseif ((z / t) <= 6e-52)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1.05e+21], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 6e-52], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.05e21 or 6e-52 < (/.f64 z t)

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 52.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 52.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), y\right) \]

   7. Applied egg-rr 56.9%

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

   if -1.05e21 < (/.f64 z t) < 6e-52

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 77.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= y -1e+69) t_1 (if (<= y 1.06e+33) (* x (- 1.0 (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (y <= -1e+69) {
		tmp = t_1;
	} else if (y <= 1.06e+33) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t / z)
    if (y <= (-1d+69)) then
        tmp = t_1
    else if (y <= 1.06d+33) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (y <= -1e+69) {
		tmp = t_1;
	} else if (y <= 1.06e+33) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if y <= -1e+69:
		tmp = t_1
	elif y <= 1.06e+33:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (y <= -1e+69)
		tmp = t_1;
	elseif (y <= 1.06e+33)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if (y <= -1e+69)
		tmp = t_1;
	elseif (y <= 1.06e+33)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+69], t$95$1, If[LessEqual[y, 1.06e+33], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0000000000000001e69 or 1.06e33 < y

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 65.5%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      4. /-lowering-/.f64 72.0%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 72.0%

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

   if -1.0000000000000001e69 < y < 1.06e33

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 80.1%

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

Alternative 12: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

Alternative 13: 39.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 34.4%

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

Developer Target 1: 97.3% 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 2024158 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))

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