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

Percentage Accurate: 97.7% → 97.7%

Time: 6.1s

Alternatives: 10

Speedup: 1.0×

• 25.2% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

   1. clear-num 98.0%

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

   2. un-div-inv 98.2%

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

3. Applied egg-rr 98.2%

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

4. Final simplification 98.2%

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

Alternative 2: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 0.5\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -200.0) (not (<= (/ z t) 0.5))) (* x (/ (- z) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -200.0) || !((z / t) <= 0.5)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-200.0d0)) .or. (.not. ((z / t) <= 0.5d0))) then
        tmp = x * (-z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -200.0) || !((z / t) <= 0.5)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -200.0) or not ((z / t) <= 0.5):
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -200.0) || !(Float64(z / t) <= 0.5))
		tmp = Float64(x * Float64(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) <= -200.0) || ~(((z / t) <= 0.5)))
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -200.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.5]], $MachinePrecision]], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -200 or 0.5 < (/.f64 z t)

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. associate-*r/ 48.1%

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

      3. neg-mul-1 48.1%

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

   4. Simplified 48.1%

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

   5. Taylor expanded in z around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. distribute-neg-frac 44.9%

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

   7. Simplified 44.9%

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

   if -200 < (/.f64 z t) < 0.5

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.3%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200 \lor \neg \left(\frac{z}{t} \leq 0.5\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 41.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1.5 \cdot 10^{+218} \lor \neg \left(\frac{z}{t} \leq 4.6 \cdot 10^{+176}\right):\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1.5e+218) (not (<= (/ z t) 4.6e+176))) (* x (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1.5e+218) || !((z / t) <= 4.6e+176)) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1.5d+218)) .or. (.not. ((z / t) <= 4.6d+176))) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1.5e+218) || !((z / t) <= 4.6e+176)) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1.5e+218) or not ((z / t) <= 4.6e+176):
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1.5e+218) || !(Float64(z / t) <= 4.6e+176))
		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) <= -1.5e+218) || ~(((z / t) <= 4.6e+176)))
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1.5e+218], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4.6e+176]], $MachinePrecision]], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.5e218 or 4.59999999999999992e176 < (/.f64 z t)

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-*r/ 47.1%

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

      3. neg-mul-1 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in z around inf 47.1%

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

      1. mul-1-neg 47.1%

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

      2. distribute-neg-frac 47.1%

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

   7. Simplified 47.1%

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

      1. associate-*r/ 41.8%

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

      2. add-sqr-sqrt 27.9%

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

      3. sqrt-unprod 30.8%

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

      4. sqr-neg 30.8%

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

      5. sqrt-unprod 2.7%

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

      6. add-sqr-sqrt 13.2%

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

      7. associate-/l* 18.8%

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

   9. Applied egg-rr 18.8%

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

       1. clear-num 18.8%

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

       2. associate-/r/ 20.6%

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

       3. clear-num 20.6%

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

   11. Applied egg-rr 20.6%

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

   if -1.5e218 < (/.f64 z t) < 4.59999999999999992e176

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 52.0%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1.5 \cdot 10^{+218} \lor \neg \left(\frac{z}{t} \leq 4.6 \cdot 10^{+176}\right):\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 41.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e+220)
   (* x (/ z t))
   (if (<= (/ z t) 2e+176) x (/ x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e+220) {
		tmp = x * (z / t);
	} else if ((z / t) <= 2e+176) {
		tmp = x;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-5d+220)) then
        tmp = x * (z / t)
    else if ((z / t) <= 2d+176) then
        tmp = x
    else
        tmp = x / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e+220) {
		tmp = x * (z / t);
	} else if ((z / t) <= 2e+176) {
		tmp = x;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e+220:
		tmp = x * (z / t)
	elif (z / t) <= 2e+176:
		tmp = x
	else:
		tmp = x / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e+220)
		tmp = Float64(x * Float64(z / t));
	elseif (Float64(z / t) <= 2e+176)
		tmp = x;
	else
		tmp = Float64(x / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e+220)
		tmp = x * (z / t);
	elseif ((z / t) <= 2e+176)
		tmp = x;
	else
		tmp = x / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e+220], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e+176], x, N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -5.0000000000000002e220

   1. Initial program 92.6%

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

   2. Taylor expanded in x around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*r/ 59.0%

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

      3. neg-mul-1 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in z around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-neg-frac 59.0%

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

   7. Simplified 59.0%

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

      1. associate-*r/ 55.1%

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

      2. add-sqr-sqrt 33.7%

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

      3. sqrt-unprod 42.9%

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

      4. sqr-neg 42.9%

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

      5. sqrt-unprod 4.8%

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

      6. add-sqr-sqrt 13.8%

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

      7. associate-/l* 21.8%

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

   9. Applied egg-rr 21.8%

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

       1. clear-num 21.8%

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

       2. associate-/r/ 25.6%

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

       3. clear-num 25.6%

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

   11. Applied egg-rr 25.6%

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

   if -5.0000000000000002e220 < (/.f64 z t) < 2e176

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 52.0%

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

   if 2e176 < (/.f64 z t)

   1. Initial program 89.9%

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

   2. Taylor expanded in x around inf 36.8%

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

      1. *-commutative 36.8%

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

      2. associate-*r/ 36.8%

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

      3. neg-mul-1 36.8%

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

   4. Simplified 36.8%

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

   5. Taylor expanded in z around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. distribute-neg-frac 36.8%

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

   7. Simplified 36.8%

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

      1. associate-*r/ 30.4%

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

      2. add-sqr-sqrt 22.9%

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

      3. sqrt-unprod 20.3%

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

      4. sqr-neg 20.3%

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

      5. sqrt-unprod 0.9%

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

      6. add-sqr-sqrt 12.6%

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

      7. associate-/l* 16.3%

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

   9. Applied egg-rr 16.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+27} \lor \neg \left(x \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.8e+27) (not (<= x 2e-28)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e+27) || !(x <= 2e-28)) {
		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 ((x <= (-4.8d+27)) .or. (.not. (x <= 2d-28))) 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 ((x <= -4.8e+27) || !(x <= 2e-28)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.8e+27) or not (x <= 2e-28):
		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 ((x <= -4.8e+27) || !(x <= 2e-28))
		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 ((x <= -4.8e+27) || ~((x <= 2e-28)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.8e+27], N[Not[LessEqual[x, 2e-28]], $MachinePrecision]], 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 2 regimes

2. if x < -4.79999999999999995e27 or 1.99999999999999994e-28 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. unsub-neg 91.3%

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

      4. distribute-lft-out-- 91.4%

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

      5. *-rgt-identity 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in x around 0 91.3%

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

   if -4.79999999999999995e27 < x < 1.99999999999999994e-28

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf 86.8%

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

      1. associate-*r/ 88.9%

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

   4. Simplified 88.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+27} \lor \neg \left(x \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+28} \lor \neg \left(x \leq 3.7 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.9e+28) (not (<= x 3.7e-28)))
   (* x (- 1.0 (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+28) || !(x <= 3.7e-28)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.9d+28)) .or. (.not. (x <= 3.7d-28))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+28) || !(x <= 3.7e-28)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.9e+28) or not (x <= 3.7e-28):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.9e+28) || !(x <= 3.7e-28))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.9e+28) || ~((x <= 3.7e-28)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.9e+28], N[Not[LessEqual[x, 3.7e-28]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e28 or 3.7000000000000002e-28 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. unsub-neg 91.3%

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

      4. distribute-lft-out-- 91.4%

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

      5. *-rgt-identity 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in x around 0 91.3%

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

   if -1.8999999999999999e28 < x < 3.7000000000000002e-28

   1. Initial program 96.6%

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

      1. clear-num 96.5%

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

      2. un-div-inv 96.8%

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

   3. Applied egg-rr 96.8%

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

   4. Taylor expanded in y around inf 86.8%

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

      1. associate-/l* 89.1%

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

   6. Simplified 89.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+28} \lor \neg \left(x \leq 3.7 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.6e+29)
   (* x (- 1.0 (/ z t)))
   (if (<= x 1.75e-28) (+ x (/ y (/ t z))) (- x (* x (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.6e+29) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 1.75e-28) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (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 (x <= (-5.6d+29)) then
        tmp = x * (1.0d0 - (z / t))
    else if (x <= 1.75d-28) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (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 (x <= -5.6e+29) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 1.75e-28) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.6e+29:
		tmp = x * (1.0 - (z / t))
	elif x <= 1.75e-28:
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.6e+29)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	elseif (x <= 1.75e-28)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.6e+29)
		tmp = x * (1.0 - (z / t));
	elseif (x <= 1.75e-28)
		tmp = x + (y / (t / z));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.6e+29], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-28], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5999999999999999e29

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.6%

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

      1. *-commutative 90.6%

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

      2. mul-1-neg 90.6%

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

      3. unsub-neg 90.6%

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

      4. distribute-lft-out-- 90.5%

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

      5. *-rgt-identity 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in x around 0 90.6%

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

   if -5.5999999999999999e29 < x < 1.75e-28

   1. Initial program 96.6%

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

      1. clear-num 96.5%

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

      2. un-div-inv 96.8%

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

   3. Applied egg-rr 96.8%

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

   4. Taylor expanded in y around inf 86.8%

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

      1. associate-/l* 89.1%

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

   6. Simplified 89.1%

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

   if 1.75e-28 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 92.3%

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

      1. *-commutative 92.3%

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

      2. mul-1-neg 92.3%

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

      3. unsub-neg 92.3%

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

      4. distribute-lft-out-- 92.3%

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

      5. *-rgt-identity 92.3%

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

   4. Simplified 92.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 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 98.1%

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

2. Final simplification 98.1%

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

Alternative 9: 66.2% 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 98.1%

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

2. Taylor expanded in x around inf 65.2%

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

   1. *-commutative 65.2%

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

   2. mul-1-neg 65.2%

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

   3. unsub-neg 65.2%

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

   4. distribute-lft-out-- 65.2%

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

   5. *-rgt-identity 65.2%

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

4. Simplified 65.2%

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

5. Taylor expanded in x around 0 65.2%

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

6. Final simplification 65.2%

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

Alternative 10: 38.8% 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 98.1%

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

2. Taylor expanded in z around 0 42.1%

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

3. Final simplification 42.1%

   \[\leadsto x \]

Developer target: 97.5% accurate, 0.4× 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 2023257 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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