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

Percentage Accurate: 85.9% → 98.2%

Time: 7.3s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.5%

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

   1. associate-*l/ 98.9%

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

3. Simplified 98.9%

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

4. Final simplification 98.9%

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

Alternative 2: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-102} \lor \neg \left(z \leq 1.4 \cdot 10^{-15}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-102) (not (<= z 1.4e-15)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-102) || !(z <= 1.4e-15)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-102)) .or. (.not. (z <= 1.4d-15))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-102) || !(z <= 1.4e-15)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-102) or not (z <= 1.4e-15):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-102) || !(z <= 1.4e-15))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-102) || ~((z <= 1.4e-15)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-102], N[Not[LessEqual[z, 1.4e-15]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e-102 or 1.40000000000000007e-15 < z

   1. Initial program 76.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 84.4%

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

      1. associate-*r/ 84.4%

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

      2. neg-mul-1 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in y around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

   9. Simplified 84.4%

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

   if -2.7e-102 < z < 1.40000000000000007e-15

   1. Initial program 97.0%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around 0 80.9%

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

      1. associate-/l* 79.2%

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

      2. associate-/r/ 79.9%

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

   6. Simplified 79.9%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-102} \lor \neg \left(z \leq 1.4 \cdot 10^{-15}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 3: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-106} \lor \neg \left(z \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e-106) (not (<= z 8e+36)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (* (- y z) (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e-106) || !(z <= 8e+36)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d-106)) .or. (.not. (z <= 8d+36))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + ((y - z) * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e-106) || !(z <= 8e+36)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e-106) or not (z <= 8e+36):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + ((y - z) * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e-106) || !(z <= 8e+36))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e-106) || ~((z <= 8e+36)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + ((y - z) * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e-106], N[Not[LessEqual[z, 8e+36]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e-106 or 8.00000000000000034e36 < z

   1. Initial program 74.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   9. Simplified 87.0%

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

   if -3.2e-106 < z < 8.00000000000000034e36

   1. Initial program 96.5%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 79.6%

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

      1. associate-/l* 78.9%

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

      2. associate-/r/ 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-106} \lor \neg \left(z \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 4: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+70} \lor \neg \left(y \leq 1.4 \cdot 10^{-25}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.2e+70) (not (<= y 1.4e-25)))
   (+ x (* t (/ y (- a z))))
   (+ x (/ t (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.2e+70) || !(y <= 1.4e-25)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6.2d+70)) .or. (.not. (y <= 1.4d-25))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.2e+70) || !(y <= 1.4e-25)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.2e+70) or not (y <= 1.4e-25):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.2e+70) || !(y <= 1.4e-25))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.2e+70) || ~((y <= 1.4e-25)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.2e+70], N[Not[LessEqual[y, 1.4e-25]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000006e70 or 1.39999999999999994e-25 < y

   1. Initial program 81.7%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around inf 86.4%

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

   if -6.2000000000000006e70 < y < 1.39999999999999994e-25

   1. Initial program 86.4%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 80.6%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{t \cdot z}{a - z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 80.6%

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

      2. associate-/l* 93.5%

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

      3. distribute-neg-frac 93.5%

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

      4. div-sub 93.5%

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

      5. *-inverses 93.5%

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

   6. Simplified 93.5%

      \[\leadsto x + \color{blue}{\frac{-t}{\frac{a}{z} - 1}} \]
   7. Step-by-step derivation

      1. frac-2neg 93.5%

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

      2. div-inv 93.5%

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

      3. remove-double-neg 93.5%

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

      4. sub-neg 93.5%

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

      5. distribute-neg-in 93.5%

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

      6. metadata-eval 93.5%

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

      7. metadata-eval 93.5%

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

   8. Applied egg-rr 93.5%

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

      1. associate-*r/ 93.5%

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

      2. *-rgt-identity 93.5%

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

      3. +-commutative 93.5%

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

      4. unsub-neg 93.5%

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

   10. Simplified 93.5%

       \[\leadsto x + \color{blue}{\frac{t}{1 - \frac{a}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+70} \lor \neg \left(y \leq 1.4 \cdot 10^{-25}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 5: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-102}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e-102)
   (+ x (* t (- 1.0 (/ y z))))
   (if (<= z 6e+34) (+ x (* (- y z) (/ t a))) (+ x (* (/ t z) (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e-102) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 6e+34) {
		tmp = x + ((y - z) * (t / a));
	} else {
		tmp = x + ((t / z) * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.7d-102)) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else if (z <= 6d+34) then
        tmp = x + ((y - z) * (t / a))
    else
        tmp = x + ((t / z) * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e-102) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 6e+34) {
		tmp = x + ((y - z) * (t / a));
	} else {
		tmp = x + ((t / z) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e-102:
		tmp = x + (t * (1.0 - (y / z)))
	elif z <= 6e+34:
		tmp = x + ((y - z) * (t / a))
	else:
		tmp = x + ((t / z) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e-102)
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	elseif (z <= 6e+34)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e-102)
		tmp = x + (t * (1.0 - (y / z)));
	elseif (z <= 6e+34)
		tmp = x + ((y - z) * (t / a));
	else
		tmp = x + ((t / z) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e-102], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+34], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e-102

   1. Initial program 74.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 86.6%

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

      1. associate-*r/ 86.6%

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

      2. neg-mul-1 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in y around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   9. Simplified 86.6%

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

   if -2.7e-102 < z < 6.00000000000000037e34

   1. Initial program 96.5%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 79.6%

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

      1. associate-/l* 78.9%

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

      2. associate-/r/ 79.4%

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

   6. Simplified 79.4%

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

   if 6.00000000000000037e34 < z

   1. Initial program 74.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. neg-mul-1 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in t around 0 63.5%

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

      1. associate-/l* 87.7%

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

      2. associate-/r/ 89.0%

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

   9. Simplified 89.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-102}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+21)
   (+ x (* t (- 1.0 (/ y z))))
   (if (<= z 3.4e-15) (+ x (* t (/ y (- a z)))) (+ x (* (/ t z) (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+21) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 3.4e-15) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + ((t / z) * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+21)) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else if (z <= 3.4d-15) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + ((t / z) * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+21) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 3.4e-15) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + ((t / z) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+21:
		tmp = x + (t * (1.0 - (y / z)))
	elif z <= 3.4e-15:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + ((t / z) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+21)
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	elseif (z <= 3.4e-15)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+21)
		tmp = x + (t * (1.0 - (y / z)));
	elseif (z <= 3.4e-15)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + ((t / z) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+21], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-15], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e21

   1. Initial program 69.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 87.5%

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

      1. associate-*r/ 87.5%

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

      2. neg-mul-1 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. unsub-neg 87.5%

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

   9. Simplified 87.5%

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

   if -8.5e21 < z < 3.4e-15

   1. Initial program 97.4%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around inf 89.7%

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

   if 3.4e-15 < z

   1. Initial program 78.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. neg-mul-1 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in t around 0 62.4%

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

      1. associate-/l* 81.4%

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

      2. associate-/r/ 82.5%

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

   9. Simplified 82.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 7: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-8} \lor \neg \left(z \leq 1.18 \cdot 10^{-15}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-8) (not (<= z 1.18e-15))) (+ x t) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-8) || !(z <= 1.18e-15)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d-8)) .or. (.not. (z <= 1.18d-15))) then
        tmp = x + t
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-8) || !(z <= 1.18e-15)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-8) or not (z <= 1.18e-15):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-8) || !(z <= 1.18e-15))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-8) || ~((z <= 1.18e-15)))
		tmp = x + t;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-8], N[Not[LessEqual[z, 1.18e-15]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e-8 or 1.18000000000000004e-15 < z

   1. Initial program 74.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 72.3%

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

   if -2.4999999999999999e-8 < z < 1.18000000000000004e-15

   1. Initial program 97.3%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. associate-/l* 79.5%

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

      2. associate-/r/ 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-8} \lor \neg \left(z \leq 1.18 \cdot 10^{-15}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8: 61.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 4.5e+54) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.5e+54) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 4.5d+54) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.5e+54) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 4.5e+54:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 4.5e+54)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 4.5e+54)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 4.5e+54], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 4.49999999999999984e54

   1. Initial program 84.0%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 63.4%

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

   if 4.49999999999999984e54 < a

   1. Initial program 86.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.9%

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

      1. associate-/l* 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in x around inf 70.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 51.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.5%

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

   1. associate-*l/ 98.9%

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

3. Simplified 98.9%

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

4. Taylor expanded in z around 0 58.0%

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

   1. associate-/l* 57.8%

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

6. Simplified 57.8%

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

7. Taylor expanded in x around inf 49.7%

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

8. Final simplification 49.7%

   \[\leadsto x \]

Developer target: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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