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

Percentage Accurate: 85.9% → 98.2%

Time: 10.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{t}{a - z}\\ t_2 := x + \frac{y \cdot t}{a - z}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ t (- a z))))) (t_2 (+ x (/ (* y t) (- a z)))))
   (if (<= z -6.8e+137)
     (+ x t)
     (if (<= z -1.35e+14)
       t_2
       (if (<= z -6.3e-25)
         t_1
         (if (<= z 2e-273)
           (+ x (/ t (/ a (- y z))))
           (if (<= z 1.1e-88) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (t / (a - z)));
	double t_2 = x + ((y * t) / (a - z));
	double tmp;
	if (z <= -6.8e+137) {
		tmp = x + t;
	} else if (z <= -1.35e+14) {
		tmp = t_2;
	} else if (z <= -6.3e-25) {
		tmp = t_1;
	} else if (z <= 2e-273) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= 1.1e-88) {
		tmp = 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 - (z * (t / (a - z)))
    t_2 = x + ((y * t) / (a - z))
    if (z <= (-6.8d+137)) then
        tmp = x + t
    else if (z <= (-1.35d+14)) then
        tmp = t_2
    else if (z <= (-6.3d-25)) then
        tmp = t_1
    else if (z <= 2d-273) then
        tmp = x + (t / (a / (y - z)))
    else if (z <= 1.1d-88) then
        tmp = 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 - (z * (t / (a - z)));
	double t_2 = x + ((y * t) / (a - z));
	double tmp;
	if (z <= -6.8e+137) {
		tmp = x + t;
	} else if (z <= -1.35e+14) {
		tmp = t_2;
	} else if (z <= -6.3e-25) {
		tmp = t_1;
	} else if (z <= 2e-273) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= 1.1e-88) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * (t / (a - z)))
	t_2 = x + ((y * t) / (a - z))
	tmp = 0
	if z <= -6.8e+137:
		tmp = x + t
	elif z <= -1.35e+14:
		tmp = t_2
	elif z <= -6.3e-25:
		tmp = t_1
	elif z <= 2e-273:
		tmp = x + (t / (a / (y - z)))
	elif z <= 1.1e-88:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(t / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y * t) / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.8e+137)
		tmp = Float64(x + t);
	elseif (z <= -1.35e+14)
		tmp = t_2;
	elseif (z <= -6.3e-25)
		tmp = t_1;
	elseif (z <= 2e-273)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	elseif (z <= 1.1e-88)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z * (t / (a - z)));
	t_2 = x + ((y * t) / (a - z));
	tmp = 0.0;
	if (z <= -6.8e+137)
		tmp = x + t;
	elseif (z <= -1.35e+14)
		tmp = t_2;
	elseif (z <= -6.3e-25)
		tmp = t_1;
	elseif (z <= 2e-273)
		tmp = x + (t / (a / (y - z)));
	elseif (z <= 1.1e-88)
		tmp = 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[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+137], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.35e+14], t$95$2, If[LessEqual[z, -6.3e-25], t$95$1, If[LessEqual[z, 2e-273], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-88], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999973e137

   1. Initial program 71.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 96.9%

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

   if -6.79999999999999973e137 < z < -1.35e14 or 2e-273 < z < 1.10000000000000002e-88

   1. Initial program 90.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 88.6%

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

   if -1.35e14 < z < -6.29999999999999961e-25 or 1.10000000000000002e-88 < z

   1. Initial program 87.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

      4. associate-/l* 92.8%

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

      5. associate-/r/ 89.6%

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

   6. Simplified 89.6%

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

   if -6.29999999999999961e-25 < z < 2e-273

   1. Initial program 87.4%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in a around inf 82.4%

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

      1. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-25}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 3: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+65}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e+65)
   (+ x t)
   (if (<= z 1.9e-273)
     (+ x (/ y (/ a t)))
     (if (<= z 4.6e-17) (+ x (/ (* y t) (- a z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+65) {
		tmp = x + t;
	} else if (z <= 1.9e-273) {
		tmp = x + (y / (a / t));
	} else if (z <= 4.6e-17) {
		tmp = x + ((y * t) / (a - z));
	} 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 <= (-3.15d+65)) then
        tmp = x + t
    else if (z <= 1.9d-273) then
        tmp = x + (y / (a / t))
    else if (z <= 4.6d-17) then
        tmp = x + ((y * t) / (a - z))
    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 <= -3.15e+65) {
		tmp = x + t;
	} else if (z <= 1.9e-273) {
		tmp = x + (y / (a / t));
	} else if (z <= 4.6e-17) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e+65:
		tmp = x + t
	elif z <= 1.9e-273:
		tmp = x + (y / (a / t))
	elif z <= 4.6e-17:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e+65)
		tmp = Float64(x + t);
	elseif (z <= 1.9e-273)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4.6e-17)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.15e+65)
		tmp = x + t;
	elseif (z <= 1.9e-273)
		tmp = x + (y / (a / t));
	elseif (z <= 4.6e-17)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e+65], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.9e-273], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-17], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.14999999999999999e65 or 4.60000000000000018e-17 < z

   1. Initial program 79.2%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 88.1%

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

   if -3.14999999999999999e65 < z < 1.9000000000000002e-273

   1. Initial program 86.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around 0 74.8%

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

      1. associate-/l* 85.5%

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

   6. Simplified 85.5%

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

   if 1.9000000000000002e-273 < z < 4.60000000000000018e-17

   1. Initial program 98.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around inf 88.4%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+65}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4: 79.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-273}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+64)
   (+ x t)
   (if (<= z 1.58e-273)
     (+ x (* (- y z) (/ t a)))
     (if (<= z 2.15e-16) (+ x (/ (* y t) (- a z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+64) {
		tmp = x + t;
	} else if (z <= 1.58e-273) {
		tmp = x + ((y - z) * (t / a));
	} else if (z <= 2.15e-16) {
		tmp = x + ((y * t) / (a - z));
	} 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 <= (-4.5d+64)) then
        tmp = x + t
    else if (z <= 1.58d-273) then
        tmp = x + ((y - z) * (t / a))
    else if (z <= 2.15d-16) then
        tmp = x + ((y * t) / (a - z))
    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 <= -4.5e+64) {
		tmp = x + t;
	} else if (z <= 1.58e-273) {
		tmp = x + ((y - z) * (t / a));
	} else if (z <= 2.15e-16) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+64:
		tmp = x + t
	elif z <= 1.58e-273:
		tmp = x + ((y - z) * (t / a))
	elif z <= 2.15e-16:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+64)
		tmp = Float64(x + t);
	elseif (z <= 1.58e-273)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	elseif (z <= 2.15e-16)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+64)
		tmp = x + t;
	elseif (z <= 1.58e-273)
		tmp = x + ((y - z) * (t / a));
	elseif (z <= 2.15e-16)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+64], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.58e-273], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-16], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999973e64 or 2.1499999999999999e-16 < z

   1. Initial program 79.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 88.3%

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

   if -4.49999999999999973e64 < z < 1.57999999999999994e-273

   1. Initial program 86.3%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around inf 74.9%

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

      1. associate-/l* 86.5%

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

      2. associate-/r/ 86.5%

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

   6. Simplified 86.5%

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

   if 1.57999999999999994e-273 < z < 2.1499999999999999e-16

   1. Initial program 98.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around inf 88.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-273}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+63)
   (+ x t)
   (if (<= z 1.7e-273)
     (+ x (/ t (/ a (- y z))))
     (if (<= z 3.8e-16) (+ x (/ (* y t) (- a z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+63) {
		tmp = x + t;
	} else if (z <= 1.7e-273) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= 3.8e-16) {
		tmp = x + ((y * t) / (a - z));
	} 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 <= (-6d+63)) then
        tmp = x + t
    else if (z <= 1.7d-273) then
        tmp = x + (t / (a / (y - z)))
    else if (z <= 3.8d-16) then
        tmp = x + ((y * t) / (a - z))
    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 <= -6e+63) {
		tmp = x + t;
	} else if (z <= 1.7e-273) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= 3.8e-16) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+63:
		tmp = x + t
	elif z <= 1.7e-273:
		tmp = x + (t / (a / (y - z)))
	elif z <= 3.8e-16:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+63)
		tmp = Float64(x + t);
	elseif (z <= 1.7e-273)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	elseif (z <= 3.8e-16)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+63)
		tmp = x + t;
	elseif (z <= 1.7e-273)
		tmp = x + (t / (a / (y - z)));
	elseif (z <= 3.8e-16)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+63], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.7e-273], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-16], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999998e63 or 3.80000000000000012e-16 < z

   1. Initial program 79.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 88.3%

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

   if -5.99999999999999998e63 < z < 1.69999999999999996e-273

   1. Initial program 86.3%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around inf 74.9%

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

      1. associate-/l* 86.5%

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

   6. Simplified 86.5%

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

   if 1.69999999999999996e-273 < z < 3.80000000000000012e-16

   1. Initial program 98.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around inf 88.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e-18)
   (- x (/ t (/ z (- y z))))
   (if (<= z 1.82e-273)
     (+ x (/ t (/ a (- y z))))
     (if (<= z 1.85e-89)
       (+ x (/ (* y t) (- a z)))
       (- x (* z (/ t (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-18) {
		tmp = x - (t / (z / (y - z)));
	} else if (z <= 1.82e-273) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= 1.85e-89) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x - (z * (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 <= (-2.6d-18)) then
        tmp = x - (t / (z / (y - z)))
    else if (z <= 1.82d-273) then
        tmp = x + (t / (a / (y - z)))
    else if (z <= 1.85d-89) then
        tmp = x + ((y * t) / (a - z))
    else
        tmp = x - (z * (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 <= -2.6e-18) {
		tmp = x - (t / (z / (y - z)));
	} else if (z <= 1.82e-273) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= 1.85e-89) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e-18:
		tmp = x - (t / (z / (y - z)))
	elif z <= 1.82e-273:
		tmp = x + (t / (a / (y - z)))
	elif z <= 1.85e-89:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e-18)
		tmp = Float64(x - Float64(t / Float64(z / Float64(y - z))));
	elseif (z <= 1.82e-273)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	elseif (z <= 1.85e-89)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e-18)
		tmp = x - (t / (z / (y - z)));
	elseif (z <= 1.82e-273)
		tmp = x + (t / (a / (y - z)));
	elseif (z <= 1.85e-89)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e-18], N[(x - N[(t / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.82e-273], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-89], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e-18

   1. Initial program 77.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   if -2.6e-18 < z < 1.81999999999999997e-273

   1. Initial program 87.4%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in a around inf 82.4%

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

      1. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

   if 1.81999999999999997e-273 < z < 1.8499999999999999e-89

   1. Initial program 97.7%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 93.1%

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

   if 1.8499999999999999e-89 < z

   1. Initial program 86.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 93.0%

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

      5. associate-/r/ 89.6%

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

   6. Simplified 89.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 7: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+65}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e+65) (+ x t) (if (<= z 6.4e-62) (+ x (* y (/ t a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+65) {
		tmp = x + t;
	} else if (z <= 6.4e-62) {
		tmp = x + (y * (t / 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 <= (-3.15d+65)) then
        tmp = x + t
    else if (z <= 6.4d-62) then
        tmp = x + (y * (t / 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 <= -3.15e+65) {
		tmp = x + t;
	} else if (z <= 6.4e-62) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e+65:
		tmp = x + t
	elif z <= 6.4e-62:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e+65)
		tmp = Float64(x + t);
	elseif (z <= 6.4e-62)
		tmp = Float64(x + Float64(y * Float64(t / 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 <= -3.15e+65)
		tmp = x + t;
	elseif (z <= 6.4e-62)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e+65], N[(x + t), $MachinePrecision], If[LessEqual[z, 6.4e-62], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.14999999999999999e65 or 6.40000000000000043e-62 < z

   1. Initial program 81.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 85.5%

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

   if -3.14999999999999999e65 < z < 6.40000000000000043e-62

   1. Initial program 90.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 76.1%

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

      1. associate-/l* 82.7%

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

      2. div-inv 82.7%

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

      3. clear-num 82.7%

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

   6. Applied egg-rr 82.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+65}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 8: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+65}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e+65) (+ x t) (if (<= z 6.2e-58) (+ x (/ y (/ a t))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+65) {
		tmp = x + t;
	} else if (z <= 6.2e-58) {
		tmp = x + (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 <= (-3.15d+65)) then
        tmp = x + t
    else if (z <= 6.2d-58) then
        tmp = x + (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 <= -3.15e+65) {
		tmp = x + t;
	} else if (z <= 6.2e-58) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e+65:
		tmp = x + t
	elif z <= 6.2e-58:
		tmp = x + (y / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e+65)
		tmp = Float64(x + t);
	elseif (z <= 6.2e-58)
		tmp = Float64(x + 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 <= -3.15e+65)
		tmp = x + t;
	elseif (z <= 6.2e-58)
		tmp = x + (y / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e+65], N[(x + t), $MachinePrecision], If[LessEqual[z, 6.2e-58], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.14999999999999999e65 or 6.1999999999999998e-58 < z

   1. Initial program 81.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 85.5%

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

   if -3.14999999999999999e65 < z < 6.1999999999999998e-58

   1. Initial program 90.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 76.1%

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

      1. associate-/l* 82.7%

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

   6. Simplified 82.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+65}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+162}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+184) x (if (<= a 1.05e+162) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+184) {
		tmp = x;
	} else if (a <= 1.05e+162) {
		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 <= (-5d+184)) then
        tmp = x
    else if (a <= 1.05d+162) 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 <= -5e+184) {
		tmp = x;
	} else if (a <= 1.05e+162) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+184:
		tmp = x
	elif a <= 1.05e+162:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+184)
		tmp = x;
	elseif (a <= 1.05e+162)
		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 <= -5e+184)
		tmp = x;
	elseif (a <= 1.05e+162)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+184], x, If[LessEqual[a, 1.05e+162], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.9999999999999999e184 or 1.05e162 < a

   1. Initial program 79.0%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 74.6%

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

   if -4.9999999999999999e184 < a < 1.05e162

   1. Initial program 88.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around inf 63.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+162}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 52.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.2e-91) x (if (<= x 2.1e-69) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.2e-91) {
		tmp = x;
	} else if (x <= 2.1e-69) {
		tmp = 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 (x <= (-7.2d-91)) then
        tmp = x
    else if (x <= 2.1d-69) then
        tmp = 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 (x <= -7.2e-91) {
		tmp = x;
	} else if (x <= 2.1e-69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.2e-91:
		tmp = x
	elif x <= 2.1e-69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.2e-91)
		tmp = x;
	elseif (x <= 2.1e-69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.2e-91)
		tmp = x;
	elseif (x <= 2.1e-69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.2e-91], x, If[LessEqual[x, 2.1e-69], t, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000001e-91 or 2.1e-69 < x

   1. Initial program 88.0%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around inf 71.1%

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

   if -7.2000000000000001e-91 < x < 2.1e-69

   1. Initial program 83.9%

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

      1. add-cube-cbrt 96.6%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\frac{y - z}{a - z} \cdot t} \cdot \sqrt[3]{\frac{y - z}{a - z} \cdot t}\right) \cdot \sqrt[3]{\frac{y - z}{a - z} \cdot t}} \]

      2. pow3 96.7%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\frac{y - z}{a - z} \cdot t}\right)}^{3}} \]

   5. Applied egg-rr 96.7%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\frac{y - z}{a - z} \cdot t}\right)}^{3}} \]

   6. Taylor expanded in x around 0 61.7%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{t \cdot \left(y - z\right)}{a - z}} \]
   7. Step-by-step derivation

      1. pow-base-1 61.7%

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

      2. associate-*r/ 61.7%

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

      3. *-lft-identity 61.7%

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

      4. associate-*r/ 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in z around inf 37.6%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 18.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

   1. add-cube-cbrt 97.7%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\frac{y - z}{a - z} \cdot t} \cdot \sqrt[3]{\frac{y - z}{a - z} \cdot t}\right) \cdot \sqrt[3]{\frac{y - z}{a - z} \cdot t}} \]

   2. pow3 97.7%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\frac{y - z}{a - z} \cdot t}\right)}^{3}} \]

5. Applied egg-rr 97.7%

   \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\frac{y - z}{a - z} \cdot t}\right)}^{3}} \]

6. Taylor expanded in x around 0 40.2%

   \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{t \cdot \left(y - z\right)}{a - z}} \]
7. Step-by-step derivation

   1. pow-base-1 40.2%

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

   2. associate-*r/ 40.2%

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

   3. *-lft-identity 40.2%

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

   4. associate-*r/ 47.9%

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

8. Simplified 47.9%

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

9. Taylor expanded in z around inf 19.6%

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

10. Final simplification 19.6%

    \[\leadsto t \]

Developer target: 99.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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))))