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

Percentage Accurate: 97.6% → 97.8%
Time: 8.7s
Alternatives: 11
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
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
public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
def code(x, y, z, t):
	return x + ((y - x) * (z / t))
function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end
function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

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

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 11 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 97.6% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
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
public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
def code(x, y, z, t):
	return x + ((y - x) * (z / t))
function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end
function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

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

Alternative 1: 97.8% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x + \frac{y - x}{\frac{t}{z}} \end{array} \]
(FPCore (x y z t) :precision binary64 (+ x (/ (- y x) (/ t z))))
double code(double x, double y, double z, double t) {
	return x + ((y - x) / (t / z));
}
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
public static double code(double x, double y, double z, double t) {
	return x + ((y - x) / (t / z));
}
def code(x, y, z, t):
	return x + ((y - x) / (t / z))
function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) / Float64(t / z)))
end
function tmp = code(x, y, z, t)
	tmp = x + ((y - x) / (t / z));
end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
x + \frac{y - x}{\frac{t}{z}}
\end{array}
Derivation
  1. Initial program 97.2%

    \[x + \left(y - x\right) \cdot \frac{z}{t} \]
  2. Add Preprocessing
  3. Step-by-step derivation
    1. clear-num97.2%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{1}{\frac{t}{z}}} \]
    2. un-div-inv97.4%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
  4. Applied egg-rr97.4%

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

Alternative 2: 63.0% accurate, 0.4× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500 \lor \neg \left(\frac{z}{t} \leq 10^{-45}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -500.0) (not (<= (/ z t) 1e-45))) (* x (/ z (- t))) x))
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500.0) || !((z / t) <= 1e-45)) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-500.0d0)) .or. (.not. ((z / t) <= 1d-45))) then
        tmp = x * (z / -t)
    else
        tmp = x
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500.0) || !((z / t) <= 1e-45)) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -500.0) or not ((z / t) <= 1e-45):
		tmp = x * (z / -t)
	else:
		tmp = x
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -500.0) || !(Float64(z / t) <= 1e-45))
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -500.0) || ~(((z / t) <= 1e-45)))
		tmp = x * (z / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -500.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-45]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq -500 \lor \neg \left(\frac{z}{t} \leq 10^{-45}\right):\\
\;\;\;\;x \cdot \frac{z}{-t}\\

\mathbf{else}:\\
\;\;\;\;x\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if (/.f64 z t) < -500 or 9.99999999999999984e-46 < (/.f64 z t)

    1. Initial program 96.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 57.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg57.0%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg57.0%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified57.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 55.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-155.4%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac255.4%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified55.4%

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

    if -500 < (/.f64 z t) < 9.99999999999999984e-46

    1. Initial program 98.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in z around 0 75.1%

      \[\leadsto \color{blue}{x} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification65.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500 \lor \neg \left(\frac{z}{t} \leq 10^{-45}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
  5. Add Preprocessing

Alternative 3: 62.0% accurate, 0.4× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \end{array} \end{array} \]
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -500.0)
   (* x (/ z (- t)))
   (if (<= (/ z t) 1e-45) x (/ (* x (- z)) t))))
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -500.0) {
		tmp = x * (z / -t);
	} else if ((z / t) <= 1e-45) {
		tmp = x;
	} else {
		tmp = (x * -z) / t;
	}
	return tmp;
}
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-500.0d0)) then
        tmp = x * (z / -t)
    else if ((z / t) <= 1d-45) then
        tmp = x
    else
        tmp = (x * -z) / t
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -500.0) {
		tmp = x * (z / -t);
	} else if ((z / t) <= 1e-45) {
		tmp = x;
	} else {
		tmp = (x * -z) / t;
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -500.0:
		tmp = x * (z / -t)
	elif (z / t) <= 1e-45:
		tmp = x
	else:
		tmp = (x * -z) / t
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -500.0)
		tmp = Float64(x * Float64(z / Float64(-t)));
	elseif (Float64(z / t) <= 1e-45)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(-z)) / t);
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -500.0)
		tmp = x * (z / -t);
	elseif ((z / t) <= 1e-45)
		tmp = x;
	else
		tmp = (x * -z) / t;
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -500.0], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-45], x, N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision]]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq -500:\\
\;\;\;\;x \cdot \frac{z}{-t}\\

\mathbf{elif}\;\frac{z}{t} \leq 10^{-45}:\\
\;\;\;\;x\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes
  2. if (/.f64 z t) < -500

    1. Initial program 98.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg53.8%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg53.8%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified53.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 51.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-151.9%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac251.9%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified51.9%

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

    if -500 < (/.f64 z t) < 9.99999999999999984e-46

    1. Initial program 98.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in z around 0 75.1%

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

    if 9.99999999999999984e-46 < (/.f64 z t)

    1. Initial program 93.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 60.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg60.9%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg60.9%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified60.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 59.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-159.7%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac259.7%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified59.7%

      \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    9. Step-by-step derivation
      1. *-commutative59.7%

        \[\leadsto \color{blue}{\frac{z}{-t} \cdot x} \]
      2. distribute-frac-neg259.7%

        \[\leadsto \color{blue}{\left(-\frac{z}{t}\right)} \cdot x \]
      3. distribute-frac-neg59.7%

        \[\leadsto \color{blue}{\frac{-z}{t}} \cdot x \]
      4. associate-*l/61.4%

        \[\leadsto \color{blue}{\frac{\left(-z\right) \cdot x}{t}} \]
    10. Applied egg-rr61.4%

      \[\leadsto \color{blue}{\frac{\left(-z\right) \cdot x}{t}} \]
  3. Recombined 3 regimes into one program.
  4. Final simplification65.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \end{array} \]
  5. Add Preprocessing

Alternative 4: 62.1% accurate, 0.4× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \end{array} \end{array} \]
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -500.0)
   (* x (/ z (- t)))
   (if (<= (/ z t) 1e-45) x (* z (/ x (- t))))))
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -500.0) {
		tmp = x * (z / -t);
	} else if ((z / t) <= 1e-45) {
		tmp = x;
	} else {
		tmp = z * (x / -t);
	}
	return tmp;
}
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-500.0d0)) then
        tmp = x * (z / -t)
    else if ((z / t) <= 1d-45) then
        tmp = x
    else
        tmp = z * (x / -t)
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -500.0) {
		tmp = x * (z / -t);
	} else if ((z / t) <= 1e-45) {
		tmp = x;
	} else {
		tmp = z * (x / -t);
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -500.0:
		tmp = x * (z / -t)
	elif (z / t) <= 1e-45:
		tmp = x
	else:
		tmp = z * (x / -t)
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -500.0)
		tmp = Float64(x * Float64(z / Float64(-t)));
	elseif (Float64(z / t) <= 1e-45)
		tmp = x;
	else
		tmp = Float64(z * Float64(x / Float64(-t)));
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -500.0)
		tmp = x * (z / -t);
	elseif ((z / t) <= 1e-45)
		tmp = x;
	else
		tmp = z * (x / -t);
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -500.0], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-45], x, N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq -500:\\
\;\;\;\;x \cdot \frac{z}{-t}\\

\mathbf{elif}\;\frac{z}{t} \leq 10^{-45}:\\
\;\;\;\;x\\

\mathbf{else}:\\
\;\;\;\;z \cdot \frac{x}{-t}\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes
  2. if (/.f64 z t) < -500

    1. Initial program 98.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg53.8%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg53.8%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified53.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 51.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-151.9%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac251.9%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified51.9%

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

    if -500 < (/.f64 z t) < 9.99999999999999984e-46

    1. Initial program 98.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in z around 0 75.1%

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

    if 9.99999999999999984e-46 < (/.f64 z t)

    1. Initial program 93.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 60.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg60.9%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg60.9%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified60.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 59.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-159.7%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac259.7%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified59.7%

      \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    9. Taylor expanded in x around 0 61.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
    10. Step-by-step derivation
      1. mul-1-neg61.4%

        \[\leadsto \color{blue}{-\frac{x \cdot z}{t}} \]
      2. distribute-neg-frac261.4%

        \[\leadsto \color{blue}{\frac{x \cdot z}{-t}} \]
      3. *-commutative61.4%

        \[\leadsto \frac{\color{blue}{z \cdot x}}{-t} \]
      4. associate-/l*59.9%

        \[\leadsto \color{blue}{z \cdot \frac{x}{-t}} \]
    11. Simplified59.9%

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

Alternative 5: 86.1% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.061 \lor \neg \left(y \leq 2.5 \cdot 10^{-33}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.061) (not (<= y 2.5e-33)))
   (+ x (* y (/ z t)))
   (- x (/ x (/ t z)))))
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.061) || !(y <= 2.5e-33)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x / (t / z));
	}
	return tmp;
}
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.061d0)) .or. (.not. (y <= 2.5d-33))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (x / (t / z))
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.061) || !(y <= 2.5e-33)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x / (t / z));
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if (y <= -0.061) or not (y <= 2.5e-33):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (x / (t / z))
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.061) || !(y <= 2.5e-33))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(x / Float64(t / z)));
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.061) || ~((y <= 2.5e-33)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (x / (t / z));
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.061], N[Not[LessEqual[y, 2.5e-33]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.061 \lor \neg \left(y \leq 2.5 \cdot 10^{-33}\right):\\
\;\;\;\;x + y \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{x}{\frac{t}{z}}\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if y < -0.060999999999999999 or 2.50000000000000014e-33 < y

    1. Initial program 98.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in y around inf 86.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
    4. Step-by-step derivation
      1. associate-*r/91.6%

        \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]
    5. Simplified91.6%

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

    if -0.060999999999999999 < y < 2.50000000000000014e-33

    1. Initial program 96.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Step-by-step derivation
      1. clear-num96.1%

        \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{1}{\frac{t}{z}}} \]
      2. un-div-inv96.5%

        \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
    4. Applied egg-rr96.5%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
    5. Taylor expanded in y around 0 89.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot x}}{\frac{t}{z}} \]
    6. Step-by-step derivation
      1. neg-mul-189.0%

        \[\leadsto x + \frac{\color{blue}{-x}}{\frac{t}{z}} \]
    7. Simplified89.0%

      \[\leadsto x + \frac{\color{blue}{-x}}{\frac{t}{z}} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification90.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.061 \lor \neg \left(y \leq 2.5 \cdot 10^{-33}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \]
  5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0285 \lor \neg \left(y \leq 2.9 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.0285) (not (<= y 2.9e-34)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0285) || !(y <= 2.9e-34)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.0285d0)) .or. (.not. (y <= 2.9d-34))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0285) || !(y <= 2.9e-34)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if (y <= -0.0285) or not (y <= 2.9e-34):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.0285) || !(y <= 2.9e-34))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.0285) || ~((y <= 2.9e-34)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.0285], N[Not[LessEqual[y, 2.9e-34]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.0285 \lor \neg \left(y \leq 2.9 \cdot 10^{-34}\right):\\
\;\;\;\;x + y \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if y < -0.028500000000000001 or 2.9000000000000002e-34 < y

    1. Initial program 98.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in y around inf 86.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
    4. Step-by-step derivation
      1. associate-*r/91.6%

        \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]
    5. Simplified91.6%

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

    if -0.028500000000000001 < y < 2.9000000000000002e-34

    1. Initial program 96.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 88.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg88.5%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg88.5%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified88.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification90.1%

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0285 \lor \neg \left(y \leq 2.9 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
  5. Add Preprocessing

Alternative 7: 40.5% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]
(FPCore (x y z t) :precision binary64 (if (<= (/ z t) 5e+259) x (/ x (/ t z))))
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 5e+259) {
		tmp = x;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}
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) <= 5d+259) then
        tmp = x
    else
        tmp = x / (t / z)
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 5e+259) {
		tmp = x;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if (z / t) <= 5e+259:
		tmp = x
	else:
		tmp = x / (t / z)
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 5e+259)
		tmp = x;
	else
		tmp = Float64(x / Float64(t / z));
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= 5e+259)
		tmp = x;
	else
		tmp = x / (t / z);
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 5e+259], x, N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{+259}:\\
\;\;\;\;x\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{t}{z}}\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if (/.f64 z t) < 5.00000000000000033e259

    1. Initial program 98.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in z around 0 43.3%

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

    if 5.00000000000000033e259 < (/.f64 z t)

    1. Initial program 83.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 53.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg53.2%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg53.2%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified53.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 53.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-153.2%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac253.2%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified53.2%

      \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    9. Step-by-step derivation
      1. clear-num53.2%

        \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{-t}{z}}} \]
      2. un-div-inv55.5%

        \[\leadsto \color{blue}{\frac{x}{\frac{-t}{z}}} \]
      3. add-sqr-sqrt24.3%

        \[\leadsto \frac{x}{\frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{z}} \]
      4. sqrt-unprod33.0%

        \[\leadsto \frac{x}{\frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{z}} \]
      5. sqr-neg33.0%

        \[\leadsto \frac{x}{\frac{\sqrt{\color{blue}{t \cdot t}}}{z}} \]
      6. sqrt-unprod8.7%

        \[\leadsto \frac{x}{\frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{z}} \]
      7. add-sqr-sqrt22.1%

        \[\leadsto \frac{x}{\frac{\color{blue}{t}}{z}} \]
    10. Applied egg-rr22.1%

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

Alternative 8: 40.5% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \end{array} \]
(FPCore (x y z t) :precision binary64 (if (<= (/ z t) 5e+259) x (* x (/ z t))))
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 5e+259) {
		tmp = x;
	} else {
		tmp = x * (z / t);
	}
	return tmp;
}
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) <= 5d+259) then
        tmp = x
    else
        tmp = x * (z / t)
    end if
    code = tmp
end function
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 5e+259) {
		tmp = x;
	} else {
		tmp = x * (z / t);
	}
	return tmp;
}
def code(x, y, z, t):
	tmp = 0
	if (z / t) <= 5e+259:
		tmp = x
	else:
		tmp = x * (z / t)
	return tmp
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 5e+259)
		tmp = x;
	else
		tmp = Float64(x * Float64(z / t));
	end
	return tmp
end
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= 5e+259)
		tmp = x;
	else
		tmp = x * (z / t);
	end
	tmp_2 = tmp;
end
code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 5e+259], x, N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{+259}:\\
\;\;\;\;x\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{z}{t}\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if (/.f64 z t) < 5.00000000000000033e259

    1. Initial program 98.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in z around 0 43.3%

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

    if 5.00000000000000033e259 < (/.f64 z t)

    1. Initial program 83.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf 53.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
    4. Step-by-step derivation
      1. mul-1-neg53.2%

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
      2. unsub-neg53.2%

        \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
    5. Simplified53.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
    6. Taylor expanded in z around inf 53.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{t}\right)} \]
    7. Step-by-step derivation
      1. neg-mul-153.2%

        \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{t}\right)} \]
      2. distribute-neg-frac253.2%

        \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    8. Simplified53.2%

      \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
    9. Step-by-step derivation
      1. add-sqr-sqrt22.1%

        \[\leadsto x \cdot \frac{z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]
      2. sqrt-unprod30.8%

        \[\leadsto x \cdot \frac{z}{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}} \]
      3. sqr-neg30.8%

        \[\leadsto x \cdot \frac{z}{\sqrt{\color{blue}{t \cdot t}}} \]
      4. sqrt-unprod8.7%

        \[\leadsto x \cdot \frac{z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]
      5. add-sqr-sqrt22.1%

        \[\leadsto x \cdot \frac{z}{\color{blue}{t}} \]
      6. div-inv22.1%

        \[\leadsto x \cdot \color{blue}{\left(z \cdot \frac{1}{t}\right)} \]
    10. Applied egg-rr22.1%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \frac{1}{t}\right)} \]
    11. Step-by-step derivation
      1. associate-*r/22.1%

        \[\leadsto x \cdot \color{blue}{\frac{z \cdot 1}{t}} \]
      2. associate-*l/22.1%

        \[\leadsto x \cdot \color{blue}{\left(\frac{z}{t} \cdot 1\right)} \]
      3. *-rgt-identity22.1%

        \[\leadsto x \cdot \color{blue}{\frac{z}{t}} \]
    12. Simplified22.1%

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

Alternative 9: 97.6% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
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
public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
def code(x, y, z, t):
	return x + ((y - x) * (z / t))
function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end
function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
Derivation
  1. Initial program 97.2%

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

Alternative 10: 65.8% accurate, 1.3× speedup?

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]
(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))
double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}
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 * (1.0d0 - (z / t))
end function
public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}
def code(x, y, z, t):
	return x * (1.0 - (z / t))
function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end
function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end
code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
x \cdot \left(1 - \frac{z}{t}\right)
\end{array}
Derivation
  1. Initial program 97.2%

    \[x + \left(y - x\right) \cdot \frac{z}{t} \]
  2. Add Preprocessing
  3. Taylor expanded in x around inf 67.0%

    \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
  4. Step-by-step derivation
    1. mul-1-neg67.0%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]
    2. unsub-neg67.0%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]
  5. Simplified67.0%

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

Alternative 11: 39.2% accurate, 9.0× speedup?

\[\begin{array}{l} \\ x \end{array} \]
(FPCore (x y z t) :precision binary64 x)
double code(double x, double y, double z, double t) {
	return x;
}
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
public static double code(double x, double y, double z, double t) {
	return x;
}
def code(x, y, z, t):
	return x
function code(x, y, z, t)
	return x
end
function tmp = code(x, y, z, t)
	tmp = x;
end
code[x_, y_, z_, t_] := x
\begin{array}{l}

\\
x
\end{array}
Derivation
  1. Initial program 97.2%

    \[x + \left(y - x\right) \cdot \frac{z}{t} \]
  2. Add Preprocessing
  3. Taylor expanded in z around 0 39.5%

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

Developer Target 1: 97.5% accurate, 0.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]
(FPCore (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))))
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;
}
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
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;
}
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
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
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
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]]]]
\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}

Reproduce

?
herbie shell --seed 2024135 
(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))))