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

Percentage Accurate: 85.7% → 95.7%

Time: 9.5s

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: 85.7% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

   1. clear-num 96.4%

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

   2. un-div-inv 96.8%

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

6. Applied egg-rr 96.8%

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

7. Final simplification 96.8%

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

Alternative 2: 77.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y z)))))
   (if (<= z -3.7e+87)
     (+ x t)
     (if (<= z -7500000.0)
       t_1
       (if (<= z 5.6e-53)
         (+ x (* y (/ t a)))
         (if (<= z 5.4e+44) t_1 (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -3.7e+87) {
		tmp = x + t;
	} else if (z <= -7500000.0) {
		tmp = t_1;
	} else if (z <= 5.6e-53) {
		tmp = x + (y * (t / a));
	} else if (z <= 5.4e+44) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / z))
    if (z <= (-3.7d+87)) then
        tmp = x + t
    else if (z <= (-7500000.0d0)) then
        tmp = t_1
    else if (z <= 5.6d-53) then
        tmp = x + (y * (t / a))
    else if (z <= 5.4d+44) then
        tmp = t_1
    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 t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -3.7e+87) {
		tmp = x + t;
	} else if (z <= -7500000.0) {
		tmp = t_1;
	} else if (z <= 5.6e-53) {
		tmp = x + (y * (t / a));
	} else if (z <= 5.4e+44) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / z))
	tmp = 0
	if z <= -3.7e+87:
		tmp = x + t
	elif z <= -7500000.0:
		tmp = t_1
	elif z <= 5.6e-53:
		tmp = x + (y * (t / a))
	elif z <= 5.4e+44:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -3.7e+87)
		tmp = Float64(x + t);
	elseif (z <= -7500000.0)
		tmp = t_1;
	elseif (z <= 5.6e-53)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 5.4e+44)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -3.7e+87)
		tmp = x + t;
	elseif (z <= -7500000.0)
		tmp = t_1;
	elseif (z <= 5.6e-53)
		tmp = x + (y * (t / a));
	elseif (z <= 5.4e+44)
		tmp = t_1;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+87], N[(x + t), $MachinePrecision], If[LessEqual[z, -7500000.0], t$95$1, If[LessEqual[z, 5.6e-53], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+44], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000003e87 or 5.4e44 < z

   1. Initial program 72.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 84.8%

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

   if -3.70000000000000003e87 < z < -7.5e6 or 5.59999999999999971e-53 < z < 5.4e44

   1. Initial program 92.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*r/ 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in a around 0 69.5%

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

       1. mul-1-neg 69.5%

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

       2. unsub-neg 69.5%

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

       3. associate-/l* 74.4%

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

   12. Simplified 74.4%

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

   if -7.5e6 < z < 5.59999999999999971e-53

   1. Initial program 96.0%

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

      1. clear-num 95.8%

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

      2. un-div-inv 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in z around 0 79.3%

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

      1. associate-*l/ 81.6%

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

      2. *-commutative 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7500000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+85}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= z -5e+85)
     (+ x t)
     (if (<= z -1600000.0)
       t_1
       (if (<= z 5e-53) (+ x (* y (/ t a))) (if (<= z 7e+43) t_1 (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -5e+85) {
		tmp = x + t;
	} else if (z <= -1600000.0) {
		tmp = t_1;
	} else if (z <= 5e-53) {
		tmp = x + (y * (t / a));
	} else if (z <= 7e+43) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (t / z))
    if (z <= (-5d+85)) then
        tmp = x + t
    else if (z <= (-1600000.0d0)) then
        tmp = t_1
    else if (z <= 5d-53) then
        tmp = x + (y * (t / a))
    else if (z <= 7d+43) then
        tmp = t_1
    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 t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -5e+85) {
		tmp = x + t;
	} else if (z <= -1600000.0) {
		tmp = t_1;
	} else if (z <= 5e-53) {
		tmp = x + (y * (t / a));
	} else if (z <= 7e+43) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if z <= -5e+85:
		tmp = x + t
	elif z <= -1600000.0:
		tmp = t_1
	elif z <= 5e-53:
		tmp = x + (y * (t / a))
	elif z <= 7e+43:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -5e+85)
		tmp = Float64(x + t);
	elseif (z <= -1600000.0)
		tmp = t_1;
	elseif (z <= 5e-53)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 7e+43)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / z));
	tmp = 0.0;
	if (z <= -5e+85)
		tmp = x + t;
	elseif (z <= -1600000.0)
		tmp = t_1;
	elseif (z <= 5e-53)
		tmp = x + (y * (t / a));
	elseif (z <= 7e+43)
		tmp = t_1;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+85], N[(x + t), $MachinePrecision], If[LessEqual[z, -1600000.0], t$95$1, If[LessEqual[z, 5e-53], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+43], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000001e85 or 7.0000000000000002e43 < z

   1. Initial program 72.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 84.8%

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

   if -5.0000000000000001e85 < z < -1.6e6 or 5e-53 < z < 7.0000000000000002e43

   1. Initial program 92.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*r/ 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in a around 0 74.4%

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

       1. mul-1-neg 74.4%

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

       2. distribute-neg-frac2 74.4%

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

   12. Simplified 74.4%

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

   if -1.6e6 < z < 5e-53

   1. Initial program 96.0%

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

      1. clear-num 95.8%

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

      2. un-div-inv 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in z around 0 79.3%

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

      1. associate-*l/ 81.6%

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

      2. *-commutative 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+85}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1600000:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-74)
   (+ x t)
   (if (<= z 2.4e-222)
     (* y (/ t a))
     (if (<= z 3.9e-103) x (if (<= z 4.7e-67) (/ y (/ a t)) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-74) {
		tmp = x + t;
	} else if (z <= 2.4e-222) {
		tmp = y * (t / a);
	} else if (z <= 3.9e-103) {
		tmp = x;
	} else if (z <= 4.7e-67) {
		tmp = y / (a / t);
	} 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 <= (-5.5d-74)) then
        tmp = x + t
    else if (z <= 2.4d-222) then
        tmp = y * (t / a)
    else if (z <= 3.9d-103) then
        tmp = x
    else if (z <= 4.7d-67) then
        tmp = y / (a / t)
    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 <= -5.5e-74) {
		tmp = x + t;
	} else if (z <= 2.4e-222) {
		tmp = y * (t / a);
	} else if (z <= 3.9e-103) {
		tmp = x;
	} else if (z <= 4.7e-67) {
		tmp = y / (a / t);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-74:
		tmp = x + t
	elif z <= 2.4e-222:
		tmp = y * (t / a)
	elif z <= 3.9e-103:
		tmp = x
	elif z <= 4.7e-67:
		tmp = y / (a / t)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-74)
		tmp = Float64(x + t);
	elseif (z <= 2.4e-222)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 3.9e-103)
		tmp = x;
	elseif (z <= 4.7e-67)
		tmp = Float64(y / Float64(a / t));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-74)
		tmp = x + t;
	elseif (z <= 2.4e-222)
		tmp = y * (t / a);
	elseif (z <= 3.9e-103)
		tmp = x;
	elseif (z <= 4.7e-67)
		tmp = y / (a / t);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-74], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.4e-222], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-103], x, If[LessEqual[z, 4.7e-67], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5000000000000001e-74 or 4.70000000000000004e-67 < z

   1. Initial program 79.3%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 70.1%

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

   if -5.5000000000000001e-74 < z < 2.39999999999999993e-222

   1. Initial program 98.5%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 85.8%

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

   6. Taylor expanded in y around inf 77.7%

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

   7. Taylor expanded in t around inf 52.7%

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

   if 2.39999999999999993e-222 < z < 3.9000000000000002e-103

   1. Initial program 99.9%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 57.9%

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

   if 3.9000000000000002e-103 < z < 4.70000000000000004e-67

   1. Initial program 73.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 73.5%

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

   6. Taylor expanded in y around inf 99.6%

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

   7. Taylor expanded in t around inf 72.2%

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

      1. clear-num 72.0%

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

      2. div-inv 72.4%

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

   9. Applied egg-rr 72.4%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+84} \lor \neg \left(z \leq 6.8 \cdot 10^{+113}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+84) (not (<= z 6.8e+113)))
   (+ x t)
   (- x (* y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+84) || !(z <= 6.8e+113)) {
		tmp = x + t;
	} else {
		tmp = x - (y * (t / (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 ((z <= (-4.4d+84)) .or. (.not. (z <= 6.8d+113))) then
        tmp = x + t
    else
        tmp = x - (y * (t / (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 ((z <= -4.4e+84) || !(z <= 6.8e+113)) {
		tmp = x + t;
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+84) or not (z <= 6.8e+113):
		tmp = x + t
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+84) || !(z <= 6.8e+113))
		tmp = Float64(x + t);
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e+84) || ~((z <= 6.8e+113)))
		tmp = x + t;
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e+84], N[Not[LessEqual[z, 6.8e+113]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999997e84 or 6.80000000000000038e113 < z

   1. Initial program 67.8%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 88.0%

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

   if -4.3999999999999997e84 < z < 6.80000000000000038e113

   1. Initial program 95.5%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in y around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*r/ 83.9%

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

   9. Simplified 83.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+84} \lor \neg \left(z \leq 6.8 \cdot 10^{+113}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+86} \lor \neg \left(z \leq 2.2 \cdot 10^{+110}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+86) (not (<= z 2.2e+110)))
   (+ x t)
   (- x (/ y (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+86) || !(z <= 2.2e+110)) {
		tmp = x + t;
	} else {
		tmp = x - (y / ((z - a) / 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 <= (-1.85d+86)) .or. (.not. (z <= 2.2d+110))) then
        tmp = x + t
    else
        tmp = x - (y / ((z - a) / 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 <= -1.85e+86) || !(z <= 2.2e+110)) {
		tmp = x + t;
	} else {
		tmp = x - (y / ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+86) or not (z <= 2.2e+110):
		tmp = x + t
	else:
		tmp = x - (y / ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+86) || !(z <= 2.2e+110))
		tmp = Float64(x + t);
	else
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+86) || ~((z <= 2.2e+110)))
		tmp = x + t;
	else
		tmp = x - (y / ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+86], N[Not[LessEqual[z, 2.2e+110]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999996e86 or 2.19999999999999992e110 < z

   1. Initial program 67.8%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 88.0%

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

   if -1.84999999999999996e86 < z < 2.19999999999999992e110

   1. Initial program 95.5%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in y around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*r/ 83.9%

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

   9. Simplified 83.9%

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

       1. clear-num 83.9%

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

       2. un-div-inv 84.3%

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

   11. Applied egg-rr 84.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+86} \lor \neg \left(z \leq 2.2 \cdot 10^{+110}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e-96)
   (- x (* y (/ t (- z a))))
   (if (<= y 5.4e+72) (+ x (* t (/ z (- z a)))) (- x (/ y (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e-96) {
		tmp = x - (y * (t / (z - a)));
	} else if (y <= 5.4e+72) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x - (y / ((z - a) / 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 (y <= (-1.05d-96)) then
        tmp = x - (y * (t / (z - a)))
    else if (y <= 5.4d+72) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = x - (y / ((z - a) / 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 (y <= -1.05e-96) {
		tmp = x - (y * (t / (z - a)));
	} else if (y <= 5.4e+72) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x - (y / ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e-96:
		tmp = x - (y * (t / (z - a)))
	elif y <= 5.4e+72:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x - (y / ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e-96)
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	elseif (y <= 5.4e+72)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e-96)
		tmp = x - (y * (t / (z - a)));
	elseif (y <= 5.4e+72)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x - (y / ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e-96], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+72], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000001e-96

   1. Initial program 84.7%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

      1. clear-num 97.7%

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

      2. un-div-inv 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r/ 85.4%

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

   9. Simplified 85.4%

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

   if -1.05000000000000001e-96 < y < 5.4000000000000001e72

   1. Initial program 86.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around 0 78.0%

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

      1. mul-1-neg 78.0%

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

      2. unsub-neg 78.0%

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

      3. associate-/l* 90.5%

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

   7. Simplified 90.5%

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

   if 5.4000000000000001e72 < y

   1. Initial program 86.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-*r/ 91.0%

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

   9. Simplified 91.0%

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

       1. clear-num 90.9%

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

       2. un-div-inv 91.0%

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

   11. Applied egg-rr 91.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12.5 \lor \neg \left(z \leq 5600000000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -12.5) (not (<= z 5600000000000.0)))
   (+ x t)
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -12.5) || !(z <= 5600000000000.0)) {
		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 <= (-12.5d0)) .or. (.not. (z <= 5600000000000.0d0))) 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 <= -12.5) || !(z <= 5600000000000.0)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -12.5) or not (z <= 5600000000000.0):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -12.5) || !(z <= 5600000000000.0))
		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 <= -12.5) || ~((z <= 5600000000000.0)))
		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, -12.5], N[Not[LessEqual[z, 5600000000000.0]], $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 < -12.5 or 5.6e12 < z

   1. Initial program 74.7%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 77.3%

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

   if -12.5 < z < 5.6e12

   1. Initial program 95.8%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. clear-num 96.3%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in z around 0 76.0%

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

      1. associate-*l/ 78.7%

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

      2. *-commutative 78.7%

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

   9. Simplified 78.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.5 \lor \neg \left(z \leq 5600000000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-74} \lor \neg \left(z \leq 2.4 \cdot 10^{-256}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e-74) (not (<= z 2.4e-256))) (+ x t) (* y (/ t a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-74) || !(z <= 2.4e-256)) {
		tmp = x + t;
	} else {
		tmp = 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 <= (-4.5d-74)) .or. (.not. (z <= 2.4d-256))) then
        tmp = x + t
    else
        tmp = 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 <= -4.5e-74) || !(z <= 2.4e-256)) {
		tmp = x + t;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e-74) or not (z <= 2.4e-256):
		tmp = x + t
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e-74) || !(z <= 2.4e-256))
		tmp = Float64(x + t);
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e-74) || ~((z <= 2.4e-256)))
		tmp = x + t;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e-74], N[Not[LessEqual[z, 2.4e-256]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999999e-74 or 2.3999999999999999e-256 < z

   1. Initial program 82.0%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 65.3%

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

   if -4.4999999999999999e-74 < z < 2.3999999999999999e-256

   1. Initial program 98.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 86.0%

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

   6. Taylor expanded in y around inf 80.1%

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

   7. Taylor expanded in t around inf 54.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-74} \lor \neg \left(z \leq 2.4 \cdot 10^{-256}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-171} \lor \neg \left(z \leq 2.5 \cdot 10^{-220}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e-171) (not (<= z 2.5e-220))) (+ x t) (/ (* y t) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e-171) || !(z <= 2.5e-220)) {
		tmp = x + t;
	} else {
		tmp = (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 <= (-1.1d-171)) .or. (.not. (z <= 2.5d-220))) then
        tmp = x + t
    else
        tmp = (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 <= -1.1e-171) || !(z <= 2.5e-220)) {
		tmp = x + t;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e-171) or not (z <= 2.5e-220):
		tmp = x + t
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e-171) || !(z <= 2.5e-220))
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e-171) || ~((z <= 2.5e-220)))
		tmp = x + t;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e-171], N[Not[LessEqual[z, 2.5e-220]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001e-171 or 2.5000000000000001e-220 < z

   1. Initial program 82.6%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 63.9%

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

   if -1.1000000000000001e-171 < z < 2.5000000000000001e-220

   1. Initial program 99.8%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 91.7%

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

   6. Taylor expanded in y around inf 84.4%

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

   7. Taylor expanded in t around inf 56.7%

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

      1. associate-*r/ 58.4%

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

   9. Applied egg-rr 58.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-171} \lor \neg \left(z \leq 2.5 \cdot 10^{-220}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+16}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e+117) x (if (<= a 4e+16) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+117) {
		tmp = x;
	} else if (a <= 4e+16) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d+117)) then
        tmp = x
    else if (a <= 4d+16) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+117) {
		tmp = x;
	} else if (a <= 4e+16) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e+117:
		tmp = x
	elif a <= 4e+16:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e+117)
		tmp = x;
	elseif (a <= 4e+16)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e+117)
		tmp = x;
	elseif (a <= 4e+16)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e+117], x, If[LessEqual[a, 4e+16], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8999999999999999e117 or 4e16 < a

   1. Initial program 86.4%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 62.0%

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

   if -3.8999999999999999e117 < a < 4e16

   1. Initial program 85.8%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 59.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+16}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 13: 51.2% 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 86.0%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in x around inf 45.2%

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

6. Final simplification 45.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% 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 2024071 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (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))))