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

Percentage Accurate: 85.2% → 98.4%

Time: 12.9s

Alternatives: 13

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: 85.2% 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: 98.4% 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 88.6%

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

5. Final simplification 98.0%

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

Alternative 2: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{a}{z} + -1}\\ t_2 := \frac{t}{a - z}\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;x - z \cdot t_2\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (+ (/ a z) -1.0)))) (t_2 (/ t (- a z))))
   (if (<= z -7.6e+118)
     t_1
     (if (<= z 6.8e-53)
       (+ x (/ t (/ (- a z) y)))
       (if (<= z 7.2e+20)
         (- x (* z t_2))
         (if (<= z 8.1e+114) (+ x (* y t_2)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / ((a / z) + -1.0));
	double t_2 = t / (a - z);
	double tmp;
	if (z <= -7.6e+118) {
		tmp = t_1;
	} else if (z <= 6.8e-53) {
		tmp = x + (t / ((a - z) / y));
	} else if (z <= 7.2e+20) {
		tmp = x - (z * t_2);
	} else if (z <= 8.1e+114) {
		tmp = x + (y * t_2);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x - (t / ((a / z) + (-1.0d0)))
    t_2 = t / (a - z)
    if (z <= (-7.6d+118)) then
        tmp = t_1
    else if (z <= 6.8d-53) then
        tmp = x + (t / ((a - z) / y))
    else if (z <= 7.2d+20) then
        tmp = x - (z * t_2)
    else if (z <= 8.1d+114) then
        tmp = x + (y * t_2)
    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 / ((a / z) + -1.0));
	double t_2 = t / (a - z);
	double tmp;
	if (z <= -7.6e+118) {
		tmp = t_1;
	} else if (z <= 6.8e-53) {
		tmp = x + (t / ((a - z) / y));
	} else if (z <= 7.2e+20) {
		tmp = x - (z * t_2);
	} else if (z <= 8.1e+114) {
		tmp = x + (y * t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / ((a / z) + -1.0))
	t_2 = t / (a - z)
	tmp = 0
	if z <= -7.6e+118:
		tmp = t_1
	elif z <= 6.8e-53:
		tmp = x + (t / ((a - z) / y))
	elif z <= 7.2e+20:
		tmp = x - (z * t_2)
	elif z <= 8.1e+114:
		tmp = x + (y * t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)))
	t_2 = Float64(t / Float64(a - z))
	tmp = 0.0
	if (z <= -7.6e+118)
		tmp = t_1;
	elseif (z <= 6.8e-53)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	elseif (z <= 7.2e+20)
		tmp = Float64(x - Float64(z * t_2));
	elseif (z <= 8.1e+114)
		tmp = Float64(x + Float64(y * t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / ((a / z) + -1.0));
	t_2 = t / (a - z);
	tmp = 0.0;
	if (z <= -7.6e+118)
		tmp = t_1;
	elseif (z <= 6.8e-53)
		tmp = x + (t / ((a - z) / y));
	elseif (z <= 7.2e+20)
		tmp = x - (z * t_2);
	elseif (z <= 8.1e+114)
		tmp = x + (y * t_2);
	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[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.6e+118], t$95$1, If[LessEqual[z, 6.8e-53], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+20], N[(x - N[(z * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.1e+114], N[(x + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.60000000000000033e118 or 8.1000000000000001e114 < z

   1. Initial program 74.1%

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

   5. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. *-commutative 74.1%

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

      3. associate-*r/ 91.7%

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

      4. unsub-neg 91.7%

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

      5. associate-*r/ 74.1%

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

      6. *-commutative 74.1%

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

      7. associate-/l* 98.7%

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

      8. div-sub 98.7%

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

      9. *-inverses 98.7%

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

   7. Simplified 98.7%

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

   if -7.60000000000000033e118 < z < 6.8e-53

   1. Initial program 94.7%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.5%

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

      2. associate-/r/ 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 90.4%

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

   9. Simplified 90.4%

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

   if 6.8e-53 < z < 7.2e20

   1. Initial program 95.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

   9. Simplified 83.4%

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

       1. +-commutative 83.4%

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

       2. unsub-neg 83.4%

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

       3. associate-/l* 83.5%

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

       4. associate-/r/ 83.5%

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

   11. Applied egg-rr 83.5%

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

   if 7.2e20 < z < 8.1000000000000001e114

   1. Initial program 93.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r/ 95.1%

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

   7. Simplified 95.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-29}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+118)
   (+ x t)
   (if (<= z -1e-29)
     (- x (* t (/ y z)))
     (if (<= z -8.8e-79)
       (- x (/ (* z t) a))
       (if (<= z 6.6e-45) (+ x (/ t (/ a y))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+118) {
		tmp = x + t;
	} else if (z <= -1e-29) {
		tmp = x - (t * (y / z));
	} else if (z <= -8.8e-79) {
		tmp = x - ((z * t) / a);
	} else if (z <= 6.6e-45) {
		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 <= (-6.8d+118)) then
        tmp = x + t
    else if (z <= (-1d-29)) then
        tmp = x - (t * (y / z))
    else if (z <= (-8.8d-79)) then
        tmp = x - ((z * t) / a)
    else if (z <= 6.6d-45) 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 <= -6.8e+118) {
		tmp = x + t;
	} else if (z <= -1e-29) {
		tmp = x - (t * (y / z));
	} else if (z <= -8.8e-79) {
		tmp = x - ((z * t) / a);
	} else if (z <= 6.6e-45) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+118:
		tmp = x + t
	elif z <= -1e-29:
		tmp = x - (t * (y / z))
	elif z <= -8.8e-79:
		tmp = x - ((z * t) / a)
	elif z <= 6.6e-45:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+118)
		tmp = Float64(x + t);
	elseif (z <= -1e-29)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -8.8e-79)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= 6.6e-45)
		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 <= -6.8e+118)
		tmp = x + t;
	elseif (z <= -1e-29)
		tmp = x - (t * (y / z));
	elseif (z <= -8.8e-79)
		tmp = x - ((z * t) / a);
	elseif (z <= 6.6e-45)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+118], N[(x + t), $MachinePrecision], If[LessEqual[z, -1e-29], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.8e-79], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-45], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999973e118 or 6.6000000000000001e-45 < z

   1. Initial program 80.4%

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

   5. Taylor expanded in z around inf 77.5%

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

   if -6.79999999999999973e118 < z < -9.99999999999999943e-30

   1. Initial program 94.4%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 87.4%

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

      1. associate-/l* 92.8%

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

   9. Simplified 92.8%

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

   10. Taylor expanded in a around 0 71.1%

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

       1. +-commutative 71.1%

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

       2. associate-*r/ 71.1%

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

       3. *-commutative 71.1%

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

       4. neg-mul-1 71.1%

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

       5. distribute-rgt-neg-in 71.1%

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

   12. Simplified 71.1%

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

   13. Taylor expanded in y around 0 71.1%

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

       1. mul-1-neg 71.1%

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

       2. associate-*r/ 73.6%

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

       3. distribute-lft-neg-in 73.6%

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

       4. cancel-sign-sub-inv 73.6%

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

   15. Simplified 73.6%

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

   if -9.99999999999999943e-30 < z < -8.7999999999999995e-79

   1. Initial program 100.0%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r/ 91.6%

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

      4. unsub-neg 91.6%

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

      5. associate-*r/ 91.7%

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

      6. *-commutative 91.7%

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

      7. associate-/l* 83.6%

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

      8. div-sub 83.5%

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

      9. *-inverses 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in a around inf 83.3%

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

   if -8.7999999999999995e-79 < z < 6.6000000000000001e-45

   1. Initial program 94.3%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-29}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+74)
   (+ x t)
   (if (<= z 4.9e-256) x (if (<= z 5e-92) (* t (/ y a)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+74) {
		tmp = x + t;
	} else if (z <= 4.9e-256) {
		tmp = x;
	} else if (z <= 5e-92) {
		tmp = t * (y / a);
	} 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 <= (-2.8d+74)) then
        tmp = x + t
    else if (z <= 4.9d-256) then
        tmp = x
    else if (z <= 5d-92) then
        tmp = t * (y / a)
    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 <= -2.8e+74) {
		tmp = x + t;
	} else if (z <= 4.9e-256) {
		tmp = x;
	} else if (z <= 5e-92) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+74:
		tmp = x + t
	elif z <= 4.9e-256:
		tmp = x
	elif z <= 5e-92:
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+74)
		tmp = Float64(x + t);
	elseif (z <= 4.9e-256)
		tmp = x;
	elseif (z <= 5e-92)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+74)
		tmp = x + t;
	elseif (z <= 4.9e-256)
		tmp = x;
	elseif (z <= 5e-92)
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+74], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.9e-256], x, If[LessEqual[z, 5e-92], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.80000000000000002e74 or 5.00000000000000011e-92 < z

   1. Initial program 82.3%

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

   5. Taylor expanded in z around inf 74.5%

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

   if -2.80000000000000002e74 < z < 4.89999999999999996e-256

   1. Initial program 95.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 53.0%

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

   if 4.89999999999999996e-256 < z < 5.00000000000000011e-92

   1. Initial program 94.1%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around inf 88.0%

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

   6. Taylor expanded in t around inf 58.5%

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

   7. Taylor expanded in y around inf 53.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-92}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+74)
   (+ x t)
   (if (<= z 1.9e-256) x (if (<= z 6e-92) (/ t (/ a y)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+74) {
		tmp = x + t;
	} else if (z <= 1.9e-256) {
		tmp = x;
	} else if (z <= 6e-92) {
		tmp = 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 <= (-1.95d+74)) then
        tmp = x + t
    else if (z <= 1.9d-256) then
        tmp = x
    else if (z <= 6d-92) then
        tmp = 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 <= -1.95e+74) {
		tmp = x + t;
	} else if (z <= 1.9e-256) {
		tmp = x;
	} else if (z <= 6e-92) {
		tmp = t / (a / y);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+74:
		tmp = x + t
	elif z <= 1.9e-256:
		tmp = x
	elif z <= 6e-92:
		tmp = t / (a / y)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+74)
		tmp = Float64(x + t);
	elseif (z <= 1.9e-256)
		tmp = x;
	elseif (z <= 6e-92)
		tmp = 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 <= -1.95e+74)
		tmp = x + t;
	elseif (z <= 1.9e-256)
		tmp = x;
	elseif (z <= 6e-92)
		tmp = t / (a / y);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+74], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.9e-256], x, If[LessEqual[z, 6e-92], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000004e74 or 6.00000000000000027e-92 < z

   1. Initial program 82.3%

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

   5. Taylor expanded in z around inf 74.5%

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

   if -1.95000000000000004e74 < z < 1.89999999999999988e-256

   1. Initial program 95.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 53.0%

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

   if 1.89999999999999988e-256 < z < 6.00000000000000027e-92

   1. Initial program 94.1%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around inf 88.0%

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

   6. Taylor expanded in t around inf 58.5%

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

   7. Taylor expanded in y around inf 53.2%

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

      1. clear-num 53.2%

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

      2. un-div-inv 53.3%

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

   9. Applied egg-rr 53.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-92}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+121} \lor \neg \left(z \leq 1.5 \cdot 10^{+117}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e+121) (not (<= z 1.5e+117)))
   (+ x t)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+121) || !(z <= 1.5e+117)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (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 ((z <= (-1.05d+121)) .or. (.not. (z <= 1.5d+117))) then
        tmp = x + t
    else
        tmp = x + (y * (t / (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 ((z <= -1.05e+121) || !(z <= 1.5e+117)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e+121) or not (z <= 1.5e+117):
		tmp = x + t
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e+121) || !(z <= 1.5e+117))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.05e+121) || ~((z <= 1.5e+117)))
		tmp = x + t;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e+121], N[Not[LessEqual[z, 1.5e+117]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e121 or 1.5e117 < z

   1. Initial program 74.1%

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

   5. Taylor expanded in z around inf 85.6%

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

   if -1.0500000000000001e121 < z < 1.5e117

   1. Initial program 94.7%

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

   5. Taylor expanded in y around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*r/ 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+121} \lor \neg \left(z \leq 1.5 \cdot 10^{+117}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+118} \lor \neg \left(z \leq 3.5 \cdot 10^{+99}\right):\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+118) (not (<= z 3.5e+99)))
   (+ x (/ t (/ z (- z y))))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+118) || !(z <= 3.5e+99)) {
		tmp = x + (t / (z / (z - y)));
	} else {
		tmp = x + (y * (t / (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 ((z <= (-6.8d+118)) .or. (.not. (z <= 3.5d+99))) then
        tmp = x + (t / (z / (z - y)))
    else
        tmp = x + (y * (t / (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 ((z <= -6.8e+118) || !(z <= 3.5e+99)) {
		tmp = x + (t / (z / (z - y)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+118) or not (z <= 3.5e+99):
		tmp = x + (t / (z / (z - y)))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+118) || !(z <= 3.5e+99))
		tmp = Float64(x + Float64(t / Float64(z / Float64(z - y))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e+118) || ~((z <= 3.5e+99)))
		tmp = x + (t / (z / (z - y)));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+118], N[Not[LessEqual[z, 3.5e+99]], $MachinePrecision]], N[(x + N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.79999999999999973e118 or 3.4999999999999998e99 < z

   1. Initial program 74.7%

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

   5. Taylor expanded in a around 0 87.2%

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

      1. associate-*r/ 87.2%

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

      2. neg-mul-1 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in t around 0 67.8%

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

      1. associate-/l* 87.2%

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

   10. Simplified 87.2%

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

   if -6.79999999999999973e118 < z < 3.4999999999999998e99

   1. Initial program 94.7%

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

   5. Taylor expanded in y around inf 83.3%

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

      1. *-commutative 83.3%

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

      2. associate-*r/ 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+118} \lor \neg \left(z \leq 3.5 \cdot 10^{+99}\right):\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+119} \lor \neg \left(z \leq 3.5 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+119) (not (<= z 3.5e+90)))
   (+ x (/ t (/ z (- z y))))
   (+ x (/ t (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+119) || !(z <= 3.5e+90)) {
		tmp = x + (t / (z / (z - y)));
	} else {
		tmp = x + (t / ((a - 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 <= (-2.3d+119)) .or. (.not. (z <= 3.5d+90))) then
        tmp = x + (t / (z / (z - y)))
    else
        tmp = x + (t / ((a - 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 <= -2.3e+119) || !(z <= 3.5e+90)) {
		tmp = x + (t / (z / (z - y)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+119) or not (z <= 3.5e+90):
		tmp = x + (t / (z / (z - y)))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+119) || !(z <= 3.5e+90))
		tmp = Float64(x + Float64(t / Float64(z / Float64(z - y))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+119) || ~((z <= 3.5e+90)))
		tmp = x + (t / (z / (z - y)));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+119], N[Not[LessEqual[z, 3.5e+90]], $MachinePrecision]], N[(x + N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e119 or 3.4999999999999998e90 < z

   1. Initial program 75.1%

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

   5. Taylor expanded in a around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in t around 0 68.2%

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

      1. associate-/l* 87.3%

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

   10. Simplified 87.3%

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

   if -2.3000000000000001e119 < z < 3.4999999999999998e90

   1. Initial program 94.6%

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

      1. clear-num 97.1%

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

      2. associate-/r/ 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around inf 83.2%

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

      1. associate-/l* 87.3%

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

   9. Simplified 87.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+119} \lor \neg \left(z \leq 3.5 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z}\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-36}:\\ \;\;\;\;x - z \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- a z))))
   (if (<= y -1.42e+41)
     (+ x (* y t_1))
     (if (<= y 5e-36) (- x (* z t_1)) (+ x (/ t (/ (- a z) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if (y <= -1.42e+41) {
		tmp = x + (y * t_1);
	} else if (y <= 5e-36) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (t / ((a - 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) :: t_1
    real(8) :: tmp
    t_1 = t / (a - z)
    if (y <= (-1.42d+41)) then
        tmp = x + (y * t_1)
    else if (y <= 5d-36) then
        tmp = x - (z * t_1)
    else
        tmp = x + (t / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if (y <= -1.42e+41) {
		tmp = x + (y * t_1);
	} else if (y <= 5e-36) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a - z)
	tmp = 0
	if y <= -1.42e+41:
		tmp = x + (y * t_1)
	elif y <= 5e-36:
		tmp = x - (z * t_1)
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a - z))
	tmp = 0.0
	if (y <= -1.42e+41)
		tmp = Float64(x + Float64(y * t_1));
	elseif (y <= 5e-36)
		tmp = Float64(x - Float64(z * t_1));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a - z);
	tmp = 0.0;
	if (y <= -1.42e+41)
		tmp = x + (y * t_1);
	elseif (y <= 5e-36)
		tmp = x - (z * t_1);
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e+41], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-36], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42000000000000007e41

   1. Initial program 82.6%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*r/ 81.0%

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

   7. Simplified 81.0%

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

   if -1.42000000000000007e41 < y < 5.00000000000000004e-36

   1. Initial program 93.0%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in y around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

   9. Simplified 84.9%

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

       1. +-commutative 84.9%

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

       2. unsub-neg 84.9%

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

       3. associate-/l* 90.2%

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

       4. associate-/r/ 89.7%

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

   11. Applied egg-rr 89.7%

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

   if 5.00000000000000004e-36 < y

   1. Initial program 84.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in y around inf 82.5%

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

      1. associate-/l* 90.6%

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

   9. Simplified 90.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-36}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+101} \lor \neg \left(z \leq 6.6 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+101) (not (<= z 6.6e-45))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+101) || !(z <= 6.6e-45)) {
		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 <= (-9d+101)) .or. (.not. (z <= 6.6d-45))) 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 <= -9e+101) || !(z <= 6.6e-45)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+101) or not (z <= 6.6e-45):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+101) || !(z <= 6.6e-45))
		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 <= -9e+101) || ~((z <= 6.6e-45)))
		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, -9e+101], N[Not[LessEqual[z, 6.6e-45]], $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 < -9.0000000000000004e101 or 6.6000000000000001e-45 < z

   1. Initial program 80.9%

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

   5. Taylor expanded in z around inf 77.3%

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

   if -9.0000000000000004e101 < z < 6.6000000000000001e-45

   1. Initial program 94.7%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 77.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+101} \lor \neg \left(z \leq 6.6 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+101} \lor \neg \left(z \leq 5.8 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+101) (not (<= z 5.8e-45))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+101) || !(z <= 5.8e-45)) {
		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 <= (-8.2d+101)) .or. (.not. (z <= 5.8d-45))) 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 <= -8.2e+101) || !(z <= 5.8e-45)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+101) or not (z <= 5.8e-45):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+101) || !(z <= 5.8e-45))
		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 <= -8.2e+101) || ~((z <= 5.8e-45)))
		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, -8.2e+101], N[Not[LessEqual[z, 5.8e-45]], $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 < -8.1999999999999999e101 or 5.8e-45 < z

   1. Initial program 80.9%

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

   5. Taylor expanded in z around inf 77.3%

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

   if -8.1999999999999999e101 < z < 5.8e-45

   1. Initial program 94.7%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+101} \lor \neg \left(z \leq 5.8 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+74} \lor \neg \left(z \leq 5.55 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+74) (not (<= z 5.55e-45))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+74) || !(z <= 5.55e-45)) {
		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 <= (-3.2d+74)) .or. (.not. (z <= 5.55d-45))) 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 <= -3.2e+74) || !(z <= 5.55e-45)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+74) or not (z <= 5.55e-45):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+74) || !(z <= 5.55e-45))
		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 <= -3.2e+74) || ~((z <= 5.55e-45)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+74], N[Not[LessEqual[z, 5.55e-45]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999995e74 or 5.55e-45 < z

   1. Initial program 81.2%

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

   5. Taylor expanded in z around inf 75.4%

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

   if -3.19999999999999995e74 < z < 5.55e-45

   1. Initial program 95.1%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 48.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+74} \lor \neg \left(z \leq 5.55 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.1% 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 88.6%

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

5. Taylor expanded in x around inf 51.1%

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

6. Final simplification 51.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 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 2024019 
(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))))