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

Percentage Accurate: 85.7% → 98.3%

Time: 9.0s

Alternatives: 11

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: 85.7% 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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in y around 0 86.2%

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

   1. associate-*r/ 86.2%

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

   2. mul-1-neg 86.2%

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

   3. distribute-rgt-neg-out 86.2%

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

   4. associate-*l/ 90.3%

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

   5. associate-*l/ 95.4%

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

   6. distribute-lft-in 96.2%

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

   7. +-commutative 96.2%

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

   8. sub-neg 96.2%

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

   9. associate-*l/ 87.1%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

   1. clear-num 98.8%

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

   2. un-div-inv 98.9%

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

9. Applied egg-rr 98.9%

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

Alternative 2: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ z (- z a))))))
   (if (<= z -3.5e+68)
     t_1
     (if (<= z -2.5e-66)
       (- x (* t (/ y z)))
       (if (<= z 1.65e-92) (+ x (/ t (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (z / (z - a)));
	double tmp;
	if (z <= -3.5e+68) {
		tmp = t_1;
	} else if (z <= -2.5e-66) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.65e-92) {
		tmp = x + (t / (a / y));
	} 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 + (t * (z / (z - a)))
    if (z <= (-3.5d+68)) then
        tmp = t_1
    else if (z <= (-2.5d-66)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.65d-92) then
        tmp = x + (t / (a / y))
    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 + (t * (z / (z - a)));
	double tmp;
	if (z <= -3.5e+68) {
		tmp = t_1;
	} else if (z <= -2.5e-66) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.65e-92) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (z / (z - a)))
	tmp = 0
	if z <= -3.5e+68:
		tmp = t_1
	elif z <= -2.5e-66:
		tmp = x - (t * (y / z))
	elif z <= 1.65e-92:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -3.5e+68)
		tmp = t_1;
	elseif (z <= -2.5e-66)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.65e-92)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (z / (z - a)));
	tmp = 0.0;
	if (z <= -3.5e+68)
		tmp = t_1;
	elseif (z <= -2.5e-66)
		tmp = x - (t * (y / z));
	elseif (z <= 1.65e-92)
		tmp = x + (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+68], t$95$1, If[LessEqual[z, -2.5e-66], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-92], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999977e68 or 1.64999999999999999e-92 < z

   1. Initial program 79.2%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. mul-1-neg 77.5%

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

      3. distribute-rgt-neg-out 77.5%

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

      4. associate-*l/ 88.4%

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

      5. associate-*l/ 95.2%

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

      6. distribute-lft-in 95.2%

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

      7. +-commutative 95.2%

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

      8. sub-neg 95.2%

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

      9. associate-*l/ 79.2%

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

      10. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. associate-*r/ 66.0%

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

      2. sub-neg 66.0%

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

      3. remove-double-neg 66.0%

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

      4. distribute-neg-in 66.0%

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

      5. +-commutative 66.0%

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

      6. sub-neg 66.0%

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

      7. distribute-neg-frac2 66.0%

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

      8. distribute-neg-frac 66.0%

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

      9. mul-1-neg 66.0%

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

      10. remove-double-neg 66.0%

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

      11. associate-*r/ 82.5%

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

   10. Simplified 82.5%

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

   if -3.49999999999999977e68 < z < -2.49999999999999981e-66

   1. Initial program 95.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 93.8%

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

   6. Taylor expanded in a around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

      3. associate-/l* 76.5%

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

   8. Simplified 76.5%

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

   if -2.49999999999999981e-66 < z < 1.64999999999999999e-92

   1. Initial program 95.3%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 83.3%

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

      1. +-commutative 83.3%

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

      2. associate-/l* 87.0%

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

   7. Simplified 87.0%

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

      1. clear-num 87.0%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} + x \]

      2. un-div-inv 87.0%

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

   9. Applied egg-rr 87.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-68}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+91)
   (+ x t)
   (if (<= z -1.02e-68)
     (- x (* t (/ y z)))
     (if (<= z 1.52e+22) (+ x (/ t (/ a y))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+91) {
		tmp = x + t;
	} else if (z <= -1.02e-68) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.52e+22) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+91)) then
        tmp = x + t
    else if (z <= (-1.02d-68)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.52d+22) then
        tmp = x + (t / (a / y))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+91) {
		tmp = x + t;
	} else if (z <= -1.02e-68) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.52e+22) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+91:
		tmp = x + t
	elif z <= -1.02e-68:
		tmp = x - (t * (y / z))
	elif z <= 1.52e+22:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+91)
		tmp = Float64(x + t);
	elseif (z <= -1.02e-68)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.52e+22)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+91)
		tmp = x + t;
	elseif (z <= -1.02e-68)
		tmp = x - (t * (y / z));
	elseif (z <= 1.52e+22)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+91], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.02e-68], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e+22], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004e91 or 1.52e22 < z

   1. Initial program 73.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 72.1%

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

   if -1.05000000000000004e91 < z < -1.01999999999999997e-68

   1. Initial program 96.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.5%

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

   6. Taylor expanded in a around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   if -1.01999999999999997e-68 < z < 1.52e22

   1. Initial program 95.5%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

      1. clear-num 84.0%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} + x \]

      2. un-div-inv 84.0%

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

   9. Applied egg-rr 84.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-68}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-39} \lor \neg \left(y \leq 4.2 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.3e-39) (not (<= y 4.2e-85)))
   (+ x (/ t (/ (- a z) y)))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e-39) || !(y <= 4.2e-85)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.3d-39)) .or. (.not. (y <= 4.2d-85))) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x + (t * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e-39) || !(y <= 4.2e-85)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.3e-39) or not (y <= 4.2e-85):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.3e-39) || !(y <= 4.2e-85))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.3e-39) || ~((y <= 4.2e-85)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.3e-39], N[Not[LessEqual[y, 4.2e-85]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999985e-39 or 4.2e-85 < y

   1. Initial program 87.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. mul-1-neg 85.7%

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

      3. distribute-rgt-neg-out 85.7%

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

      4. associate-*l/ 86.8%

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

      5. associate-*l/ 94.9%

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

      6. distribute-lft-in 96.1%

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

      7. +-commutative 96.1%

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

      8. sub-neg 96.1%

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

      9. associate-*l/ 87.2%

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

      10. associate-*r/ 98.8%

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

   7. Simplified 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.9%

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

   9. Applied egg-rr 98.9%

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

   10. Taylor expanded in y around inf 87.8%

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

   if -3.29999999999999985e-39 < y < 4.2e-85

   1. Initial program 86.9%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. associate-*r/ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. distribute-rgt-neg-out 86.9%

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

      4. associate-*l/ 96.3%

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

      5. associate-*l/ 96.3%

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

      6. distribute-lft-in 96.2%

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

      7. +-commutative 96.2%

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

      8. sub-neg 96.2%

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

      9. associate-*l/ 86.9%

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

      10. associate-*r/ 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in y around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. sub-neg 82.0%

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

      3. remove-double-neg 82.0%

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

      4. distribute-neg-in 82.0%

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

      5. +-commutative 82.0%

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

      6. sub-neg 82.0%

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

      7. distribute-neg-frac2 82.0%

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

      8. distribute-neg-frac 82.0%

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

      9. mul-1-neg 82.0%

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

      10. remove-double-neg 82.0%

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

      11. associate-*r/ 94.0%

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

   10. Simplified 94.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-39} \lor \neg \left(y \leq 4.2 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-40} \lor \neg \left(y \leq 4.8 \cdot 10^{-85}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e-40) (not (<= y 4.8e-85)))
   (+ x (* y (/ t (- a z))))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-40) || !(y <= 4.8e-85)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.8d-40)) .or. (.not. (y <= 4.8d-85))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (t * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e-40) || !(y <= 4.8e-85)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e-40) or not (y <= 4.8e-85):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.8e-40) || !(y <= 4.8e-85))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.8e-40) || ~((y <= 4.8e-85)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.8e-40], N[Not[LessEqual[y, 4.8e-85]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-40 or 4.8000000000000001e-85 < y

   1. Initial program 87.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf 87.0%

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

   if -1.8e-40 < y < 4.8000000000000001e-85

   1. Initial program 86.9%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. associate-*r/ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. distribute-rgt-neg-out 86.9%

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

      4. associate-*l/ 96.3%

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

      5. associate-*l/ 96.3%

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

      6. distribute-lft-in 96.2%

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

      7. +-commutative 96.2%

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

      8. sub-neg 96.2%

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

      9. associate-*l/ 86.9%

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

      10. associate-*r/ 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in y around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. sub-neg 82.0%

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

      3. remove-double-neg 82.0%

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

      4. distribute-neg-in 82.0%

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

      5. +-commutative 82.0%

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

      6. sub-neg 82.0%

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

      7. distribute-neg-frac2 82.0%

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

      8. distribute-neg-frac 82.0%

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

      9. mul-1-neg 82.0%

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

      10. remove-double-neg 82.0%

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

      11. associate-*r/ 94.0%

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

   10. Simplified 94.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-40} \lor \neg \left(y \leq 4.8 \cdot 10^{-85}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+76} \lor \neg \left(z \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+76) (not (<= z 1.7e+22))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+76) || !(z <= 1.7e+22)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / 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 <= (-1.4d+76)) .or. (.not. (z <= 1.7d+22))) then
        tmp = x + t
    else
        tmp = x + (t / (a / 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 <= -1.4e+76) || !(z <= 1.7e+22)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+76) or not (z <= 1.7e+22):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+76) || !(z <= 1.7e+22))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+76) || ~((z <= 1.7e+22)))
		tmp = x + t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+76], N[Not[LessEqual[z, 1.7e+22]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e76 or 1.7e22 < z

   1. Initial program 74.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -1.3999999999999999e76 < z < 1.7e22

   1. Initial program 95.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

      1. clear-num 78.4%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} + x \]

      2. un-div-inv 78.4%

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

   9. Applied egg-rr 78.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+76} \lor \neg \left(z \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+78} \lor \neg \left(z \leq 1.96 \cdot 10^{+21}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+78) (not (<= z 1.96e+21))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+78) || !(z <= 1.96e+21)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.8d+78)) .or. (.not. (z <= 1.96d+21))) then
        tmp = x + t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+78) || !(z <= 1.96e+21)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+78) or not (z <= 1.96e+21):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+78) || !(z <= 1.96e+21))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+78) || ~((z <= 1.96e+21)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+78], N[Not[LessEqual[z, 1.96e+21]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e78 or 1.96e21 < z

   1. Initial program 74.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -2.8000000000000001e78 < z < 1.96e21

   1. Initial program 95.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+78} \lor \neg \left(z \leq 1.96 \cdot 10^{+21}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+78} \lor \neg \left(z \leq 2 \cdot 10^{+21}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+78) (not (<= z 2e+21))) (+ x t) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+78) || !(z <= 2e+21)) {
		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 <= (-3.2d+78)) .or. (.not. (z <= 2d+21))) 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 <= -3.2e+78) || !(z <= 2e+21)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+78) or not (z <= 2e+21):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+78) || !(z <= 2e+21))
		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 <= -3.2e+78) || ~((z <= 2e+21)))
		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, -3.2e+78], N[Not[LessEqual[z, 2e+21]], $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 < -3.19999999999999994e78 or 2e21 < z

   1. Initial program 74.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -3.19999999999999994e78 < z < 2e21

   1. Initial program 95.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 91.4%

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

   6. Taylor expanded in a around inf 77.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+78} \lor \neg \left(z \leq 2 \cdot 10^{+21}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-216} \lor \neg \left(z \leq 4.4 \cdot 10^{-35}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e-216) (not (<= z 4.4e-35))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e-216) || !(z <= 4.4e-35)) {
		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 ((z <= (-2.75d-216)) .or. (.not. (z <= 4.4d-35))) 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 ((z <= -2.75e-216) || !(z <= 4.4e-35)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e-216) or not (z <= 4.4e-35):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e-216) || !(z <= 4.4e-35))
		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 ((z <= -2.75e-216) || ~((z <= 4.4e-35)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e-216], N[Not[LessEqual[z, 4.4e-35]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.74999999999999995e-216 or 4.39999999999999987e-35 < z

   1. Initial program 82.2%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 65.2%

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

   if -2.74999999999999995e-216 < z < 4.39999999999999987e-35

   1. Initial program 96.6%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 58.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-216} \lor \neg \left(z \leq 4.4 \cdot 10^{-35}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in y around 0 86.2%

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

   1. associate-*r/ 86.2%

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

   2. mul-1-neg 86.2%

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

   3. distribute-rgt-neg-out 86.2%

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

   4. associate-*l/ 90.3%

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

   5. associate-*l/ 95.4%

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

   6. distribute-lft-in 96.2%

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

   7. +-commutative 96.2%

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

   8. sub-neg 96.2%

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

   9. associate-*l/ 87.1%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

Alternative 11: 51.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in x around inf 51.5%

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

Developer Target 1: 99.3% accurate, 0.5× 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 2024137 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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