Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.5% → 98.1%

Time: 8.8s

Alternatives: 11

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. +-commutative 88.1%

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

   2. associate-/l* 98.4%

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

   3. fma-define 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 93.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+146} \lor \neg \left(z \leq 5.4 \cdot 10^{+72}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+146) (not (<= z 5.4e+72)))
   (+ x (* y (/ z (- z a))))
   (- x (/ (* y (- t z)) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+146) || !(z <= 5.4e+72)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - ((y * (t - z)) / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.5d+146)) .or. (.not. (z <= 5.4d+72))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x - ((y * (t - z)) / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+146) || !(z <= 5.4e+72)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - ((y * (t - z)) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+146) or not (z <= 5.4e+72):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x - ((y * (t - z)) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+146) || !(z <= 5.4e+72))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+146) || ~((z <= 5.4e+72)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x - ((y * (t - z)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+146], N[Not[LessEqual[z, 5.4e+72]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000001e146 or 5.4000000000000001e72 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 97.6%

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

   5. Simplified 97.6%

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

   if -1.50000000000000001e146 < z < 5.4000000000000001e72

   1. Initial program 94.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+146} \lor \neg \left(z \leq 5.4 \cdot 10^{+72}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-21} \lor \neg \left(z \leq 1.55 \cdot 10^{-14}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e-21) (not (<= z 1.55e-14)))
   (+ x (* y (/ z (- z a))))
   (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e-21) || !(z <= 1.55e-14)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.5d-21)) .or. (.not. (z <= 1.55d-14))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e-21) || !(z <= 1.55e-14)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e-21) or not (z <= 1.55e-14):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e-21) || !(z <= 1.55e-14))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e-21) || ~((z <= 1.55e-14)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e-21], N[Not[LessEqual[z, 1.55e-14]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999987e-21 or 1.55000000000000002e-14 < z

   1. Initial program 80.1%

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

   3. Taylor expanded in t around 0 74.2%

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

      1. associate-/l* 91.1%

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

   5. Simplified 91.1%

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

   if -6.49999999999999987e-21 < z < 1.55000000000000002e-14

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. associate-/l* 96.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. unsub-neg 81.5%

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

      3. associate-/l* 82.9%

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

   7. Simplified 82.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-21} \lor \neg \left(z \leq 1.55 \cdot 10^{-14}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-93} \lor \neg \left(a \leq 1.4 \cdot 10^{-210}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e-93) (not (<= a 1.4e-210)))
   (+ x (* y (/ z (- z a))))
   (+ x (- y (* t (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-93) || !(a <= 1.4e-210)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y - (t * (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.3d-93)) .or. (.not. (a <= 1.4d-210))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y - (t * (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-93) || !(a <= 1.4e-210)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y - (t * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e-93) or not (a <= 1.4e-210):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y - (t * (y / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e-93) || !(a <= 1.4e-210))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y - Float64(t * Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.3e-93) || ~((a <= 1.4e-210)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y - (t * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e-93], N[Not[LessEqual[a, 1.4e-210]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3000000000000001e-93 or 1.4e-210 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   if -3.3000000000000001e-93 < a < 1.4e-210

   1. Initial program 90.9%

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

   3. Taylor expanded in a around 0 82.7%

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

      1. associate-/l* 87.2%

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

      2. div-sub 87.2%

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

      3. *-inverses 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in t around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

      3. associate-/l* 90.1%

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

   8. Simplified 90.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-93} \lor \neg \left(a \leq 1.4 \cdot 10^{-210}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-93} \lor \neg \left(a \leq 1.32 \cdot 10^{-148}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e-93) (not (<= a 1.32e-148)))
   (+ x (* y (/ z (- z a))))
   (+ x (* y (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-93) || !(a <= 1.32e-148)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3d-93)) .or. (.not. (a <= 1.32d-148))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-93) || !(a <= 1.32e-148)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3e-93) or not (a <= 1.32e-148):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e-93) || !(a <= 1.32e-148))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3e-93) || ~((a <= 1.32e-148)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e-93], N[Not[LessEqual[a, 1.32e-148]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0000000000000001e-93 or 1.32000000000000007e-148 < a

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 75.0%

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

      1. associate-/l* 84.3%

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

   5. Simplified 84.3%

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

   if -3.0000000000000001e-93 < a < 1.32000000000000007e-148

   1. Initial program 90.9%

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

   3. Taylor expanded in a around 0 83.8%

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

      1. associate-/l* 88.9%

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

      2. div-sub 89.0%

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

      3. *-inverses 89.0%

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

   5. Simplified 89.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-93} \lor \neg \left(a \leq 1.32 \cdot 10^{-148}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-19} \lor \neg \left(z \leq 2.25 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e-19) (not (<= z 2.25e-10)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e-19) || !(z <= 2.25e-10)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.05d-19)) .or. (.not. (z <= 2.25d-10))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e-19) || !(z <= 2.25e-10)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e-19) or not (z <= 2.25e-10):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e-19) || !(z <= 2.25e-10))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.05e-19) || ~((z <= 2.25e-10)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e-19], N[Not[LessEqual[z, 2.25e-10]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e-19 or 2.25e-10 < z

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 71.1%

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

      1. associate-/l* 85.1%

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

      2. div-sub 85.1%

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

      3. *-inverses 85.1%

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

   5. Simplified 85.1%

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

   if -1.0499999999999999e-19 < z < 2.25e-10

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. associate-/l* 96.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-19} \lor \neg \left(z \leq 2.25 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-19} \lor \neg \left(z \leq 1.26 \cdot 10^{-11}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e-19) (not (<= z 1.26e-11))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-19) || !(z <= 1.26e-11)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d-19)) .or. (.not. (z <= 1.26d-11))) then
        tmp = y + x
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-19) || !(z <= 1.26e-11)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e-19) or not (z <= 1.26e-11):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e-19) || !(z <= 1.26e-11))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e-19) || ~((z <= 1.26e-11)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e-19], N[Not[LessEqual[z, 1.26e-11]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000015e-19 or 1.26e-11 < z

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. +-commutative 80.1%

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

   7. Simplified 80.1%

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

   if -3.50000000000000015e-19 < z < 1.26e-11

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. associate-/l* 96.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-19} \lor \neg \left(z \leq 1.26 \cdot 10^{-11}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-12} \lor \neg \left(z \leq 1.95 \cdot 10^{-11}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.06e-12) (not (<= z 1.95e-11))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e-12) || !(z <= 1.95e-11)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.06d-12)) .or. (.not. (z <= 1.95d-11))) then
        tmp = y + x
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e-12) || !(z <= 1.95e-11)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.06e-12) or not (z <= 1.95e-11):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.06e-12) || !(z <= 1.95e-11))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.06e-12) || ~((z <= 1.95e-11)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.06e-12], N[Not[LessEqual[z, 1.95e-11]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0599999999999999e-12 or 1.95000000000000005e-11 < z

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. +-commutative 80.1%

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

   7. Simplified 80.1%

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

   if -1.0599999999999999e-12 < z < 1.95000000000000005e-11

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 77.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-12} \lor \neg \left(z \leq 1.95 \cdot 10^{-11}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-75} \lor \neg \left(z \leq 2.4 \cdot 10^{-61}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e-75) (not (<= z 2.4e-61))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e-75) || !(z <= 2.4e-61)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.3d-75)) .or. (.not. (z <= 2.4d-61))) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e-75) || !(z <= 2.4e-61)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e-75) or not (z <= 2.4e-61):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e-75) || !(z <= 2.4e-61))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.3e-75) || ~((z <= 2.4e-61)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.3e-75], N[Not[LessEqual[z, 2.4e-61]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-75 or 2.4000000000000001e-61 < z

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.1%

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

      1. +-commutative 75.1%

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

   7. Simplified 75.1%

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

   if -3.3e-75 < z < 2.4000000000000001e-61

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 64.4%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-75} \lor \neg \left(z \leq 2.4 \cdot 10^{-61}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.95e+86) y (if (<= y 2.75e+132) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.95e+86) {
		tmp = y;
	} else if (y <= 2.75e+132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.95d+86)) then
        tmp = y
    else if (y <= 2.75d+132) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.95e+86) {
		tmp = y;
	} else if (y <= 2.75e+132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.95e+86:
		tmp = y
	elif y <= 2.75e+132:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.95e+86)
		tmp = y;
	elseif (y <= 2.75e+132)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.95e+86)
		tmp = y;
	elseif (y <= 2.75e+132)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.95e+86], y, If[LessEqual[y, 2.75e+132], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9500000000000001e86 or 2.75e132 < y

   1. Initial program 64.6%

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

   3. Taylor expanded in a around 0 41.5%

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

      1. associate-/l* 64.3%

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

      2. div-sub 64.3%

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

      3. *-inverses 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in x around 0 58.8%

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

   7. Taylor expanded in t around 0 46.1%

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

   if -1.9500000000000001e86 < y < 2.75e132

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-/l* 97.8%

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

      3. fma-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 69.9%

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

Alternative 11: 50.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. +-commutative 88.1%

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

   2. associate-/l* 98.4%

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

   3. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Taylor expanded in y around 0 54.0%

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

Developer Target 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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