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

Percentage Accurate: 97.7% → 97.7%

Time: 8.5s

Alternatives: 11

Speedup: 1.0×

• 24.7% 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: 97.7% 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: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. +-commutative 98.6%

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

   2. fma-define 98.6%

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

3. Simplified 98.6%

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

Alternative 2: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20000 \lor \neg \left(\frac{z}{t} \leq 0.04\right):\\ \;\;\;\;-\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -20000.0) (not (<= (/ z t) 0.04))) (- (/ x (/ t z))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -20000.0) || !((z / t) <= 0.04)) {
		tmp = -(x / (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-20000.0d0)) .or. (.not. ((z / t) <= 0.04d0))) then
        tmp = -(x / (t / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -20000.0) || !((z / t) <= 0.04)) {
		tmp = -(x / (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -20000.0) or not ((z / t) <= 0.04):
		tmp = -(x / (t / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -20000.0) || !(Float64(z / t) <= 0.04))
		tmp = Float64(-Float64(x / Float64(t / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -20000.0) || ~(((z / t) <= 0.04)))
		tmp = -(x / (t / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -20000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.04]], $MachinePrecision]], (-N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e4 or 0.0400000000000000008 < (/.f64 z t)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. unsub-neg 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in z around inf 55.9%

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

      1. associate-*r/ 55.9%

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

      2. mul-1-neg 55.9%

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

   8. Simplified 55.9%

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

      1. *-commutative 55.9%

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

      2. distribute-frac-neg 55.9%

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

      3. distribute-lft-neg-in 55.9%

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

      4. associate-/r/ 53.7%

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

      5. distribute-neg-frac2 53.7%

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

      6. add-sqr-sqrt 25.2%

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

      7. sqrt-unprod 22.3%

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

      8. sqr-neg 22.3%

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

      9. sqrt-unprod 0.6%

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

      10. add-sqr-sqrt 2.9%

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

      11. distribute-frac-neg2 2.9%

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

      12. distribute-neg-frac 2.9%

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

      13. associate-/r/ 6.6%

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

      14. distribute-lft-neg-in 6.6%

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

      15. distribute-frac-neg 6.6%

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

      16. *-commutative 6.6%

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

      17. clear-num 6.6%

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

      18. un-div-inv 6.6%

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

      19. add-sqr-sqrt 2.8%

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

      20. sqrt-unprod 21.8%

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

      21. sqr-neg 21.8%

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

      22. sqrt-unprod 25.2%

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

      23. add-sqr-sqrt 55.2%

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

   10. Applied egg-rr 55.2%

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

   if -2e4 < (/.f64 z t) < 0.0400000000000000008

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 70.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20000 \lor \neg \left(\frac{z}{t} \leq 0.04\right):\\ \;\;\;\;-\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20000:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.04:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -20000.0)
   (/ (* x z) (- t))
   (if (<= (/ z t) 0.04) x (* x (/ (- z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -20000.0) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= 0.04) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-20000.0d0)) then
        tmp = (x * z) / -t
    else if ((z / t) <= 0.04d0) then
        tmp = x
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -20000.0) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= 0.04) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -20000.0:
		tmp = (x * z) / -t
	elif (z / t) <= 0.04:
		tmp = x
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -20000.0)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (Float64(z / t) <= 0.04)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -20000.0)
		tmp = (x * z) / -t;
	elseif ((z / t) <= 0.04)
		tmp = x;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -20000.0], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.04], x, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e4

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 56.9%

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

      1. associate-*r/ 56.9%

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

      2. mul-1-neg 56.9%

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

   8. Simplified 56.9%

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

      1. distribute-frac-neg 56.9%

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

      2. distribute-frac-neg2 56.9%

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

      3. associate-*r/ 59.9%

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

   10. Applied egg-rr 59.9%

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

   if -2e4 < (/.f64 z t) < 0.0400000000000000008

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 70.8%

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

   if 0.0400000000000000008 < (/.f64 z t)

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in z around inf 55.1%

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

      1. associate-*r/ 55.1%

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

      2. mul-1-neg 55.1%

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

   8. Simplified 55.1%

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

Alternative 4: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20000:\\ \;\;\;\;\frac{z}{\frac{t}{-x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.04:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -20000.0)
   (/ z (/ t (- x)))
   (if (<= (/ z t) 0.04) x (* x (/ (- z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -20000.0) {
		tmp = z / (t / -x);
	} else if ((z / t) <= 0.04) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-20000.0d0)) then
        tmp = z / (t / -x)
    else if ((z / t) <= 0.04d0) then
        tmp = x
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -20000.0) {
		tmp = z / (t / -x);
	} else if ((z / t) <= 0.04) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -20000.0:
		tmp = z / (t / -x)
	elif (z / t) <= 0.04:
		tmp = x
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -20000.0)
		tmp = Float64(z / Float64(t / Float64(-x)));
	elseif (Float64(z / t) <= 0.04)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -20000.0)
		tmp = z / (t / -x);
	elseif ((z / t) <= 0.04)
		tmp = x;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -20000.0], N[(z / N[(t / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.04], x, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e4

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 56.9%

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

      1. associate-*r/ 56.9%

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

      2. mul-1-neg 56.9%

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

   8. Simplified 56.9%

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

      1. *-commutative 56.9%

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

      2. distribute-frac-neg 56.9%

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

      3. distribute-lft-neg-in 56.9%

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

      4. associate-/r/ 56.9%

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

      5. distribute-neg-frac2 56.9%

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

      6. distribute-neg-frac2 56.9%

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

   10. Applied egg-rr 56.9%

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

   if -2e4 < (/.f64 z t) < 0.0400000000000000008

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 70.8%

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

   if 0.0400000000000000008 < (/.f64 z t)

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in z around inf 55.1%

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

      1. associate-*r/ 55.1%

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

      2. mul-1-neg 55.1%

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

   8. Simplified 55.1%

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

Alternative 5: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20000:\\ \;\;\;\;-\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.04:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -20000.0)
   (- (/ x (/ t z)))
   (if (<= (/ z t) 0.04) x (* x (/ (- z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -20000.0) {
		tmp = -(x / (t / z));
	} else if ((z / t) <= 0.04) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-20000.0d0)) then
        tmp = -(x / (t / z))
    else if ((z / t) <= 0.04d0) then
        tmp = x
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -20000.0) {
		tmp = -(x / (t / z));
	} else if ((z / t) <= 0.04) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -20000.0:
		tmp = -(x / (t / z))
	elif (z / t) <= 0.04:
		tmp = x
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -20000.0)
		tmp = Float64(-Float64(x / Float64(t / z)));
	elseif (Float64(z / t) <= 0.04)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -20000.0)
		tmp = -(x / (t / z));
	elseif ((z / t) <= 0.04)
		tmp = x;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -20000.0], (-N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(z / t), $MachinePrecision], 0.04], x, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e4

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 56.9%

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

      1. associate-*r/ 56.9%

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

      2. mul-1-neg 56.9%

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

   8. Simplified 56.9%

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

      1. *-commutative 56.9%

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

      2. distribute-frac-neg 56.9%

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

      3. distribute-lft-neg-in 56.9%

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

      4. associate-/r/ 56.9%

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

      5. distribute-neg-frac2 56.9%

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

      6. add-sqr-sqrt 29.6%

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

      7. sqrt-unprod 29.3%

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

      8. sqr-neg 29.3%

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

      9. sqrt-unprod 0.6%

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

      10. add-sqr-sqrt 3.1%

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

      11. distribute-frac-neg2 3.1%

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

      12. distribute-neg-frac 3.1%

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

      13. associate-/r/ 9.5%

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

      14. distribute-lft-neg-in 9.5%

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

      15. distribute-frac-neg 9.5%

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

      16. *-commutative 9.5%

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

      17. clear-num 9.5%

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

      18. un-div-inv 9.5%

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

      19. add-sqr-sqrt 3.9%

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

      20. sqrt-unprod 27.9%

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

      21. sqr-neg 27.9%

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

      22. sqrt-unprod 29.6%

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

      23. add-sqr-sqrt 56.9%

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

   10. Applied egg-rr 56.9%

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

   if -2e4 < (/.f64 z t) < 0.0400000000000000008

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 70.8%

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

   if 0.0400000000000000008 < (/.f64 z t)

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in z around inf 55.1%

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

      1. associate-*r/ 55.1%

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

      2. mul-1-neg 55.1%

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

   8. Simplified 55.1%

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

Alternative 6: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -58000 \lor \neg \left(y \leq 3200\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -58000.0) (not (<= y 3200.0)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -58000.0) || !(y <= 3200.0)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-58000.0d0)) .or. (.not. (y <= 3200.0d0))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -58000.0) || !(y <= 3200.0)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -58000.0) or not (y <= 3200.0):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -58000.0) || !(y <= 3200.0))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -58000.0) || ~((y <= 3200.0)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -58000.0], N[Not[LessEqual[y, 3200.0]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -58000 or 3200 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. associate-*r/ 91.9%

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

   5. Simplified 91.9%

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

   if -58000 < y < 3200

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -58000 \lor \neg \left(y \leq 3200\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -37:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 330000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -37.0)
   (+ x (/ (* y z) t))
   (if (<= y 330000.0) (* x (- 1.0 (/ z t))) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -37.0) {
		tmp = x + ((y * z) / t);
	} else if (y <= 330000.0) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-37.0d0)) then
        tmp = x + ((y * z) / t)
    else if (y <= 330000.0d0) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -37.0) {
		tmp = x + ((y * z) / t);
	} else if (y <= 330000.0) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -37.0:
		tmp = x + ((y * z) / t)
	elif y <= 330000.0:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -37.0)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (y <= 330000.0)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -37.0)
		tmp = x + ((y * z) / t);
	elseif (y <= 330000.0)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -37.0], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 330000.0], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -37

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 89.6%

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

   if -37 < y < 3.3e5

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

   if 3.3e5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 83.7%

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

      1. associate-*r/ 94.4%

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

   5. Simplified 94.4%

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

Alternative 8: 39.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) (- INFINITY)) (* x (/ z t)) x))

C

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

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -inf.0

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in z around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

   8. Simplified 65.3%

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

      1. div-inv 65.3%

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

      2. add-sqr-sqrt 41.7%

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

      3. sqrt-unprod 59.4%

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

      4. sqr-neg 59.4%

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

      5. sqrt-unprod 17.6%

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

      6. add-sqr-sqrt 29.4%

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

   10. Applied egg-rr 29.4%

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

       1. associate-*r/ 29.4%

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

       2. *-rgt-identity 29.4%

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

   12. Simplified 29.4%

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

   if -inf.0 < (/.f64 z t)

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 38.9%

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

Alternative 9: 97.7% 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 98.6%

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

Alternative 10: 65.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.6%

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

3. Taylor expanded in x around inf 65.1%

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

   1. mul-1-neg 65.1%

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

   2. unsub-neg 65.1%

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

5. Simplified 65.1%

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

Alternative 11: 38.2% 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 98.6%

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

3. Taylor expanded in z around 0 36.6%

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

Developer Target 1: 97.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(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))))