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

Percentage Accurate: 86.0% → 98.1%

Time: 10.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.0% 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: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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 y around 0 85.9%

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

   1. associate-*r/ 85.9%

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

   2. mul-1-neg 85.9%

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

   3. distribute-rgt-neg-out 85.9%

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

   4. associate-*l/ 86.5%

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

   5. associate-*l/ 93.1%

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

   6. distribute-lft-out 95.0%

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

   7. +-commutative 95.0%

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

   8. sub-neg 95.0%

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

   9. associate-*l/ 86.7%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

8. Final simplification 98.8%

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

Alternative 2: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+169)
   (+ x t)
   (if (<= z 5.5e-55)
     (+ x (* t (/ y a)))
     (if (<= z 8.8e+73) (- x (/ t (/ z y))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+169) {
		tmp = x + t;
	} else if (z <= 5.5e-55) {
		tmp = x + (t * (y / a));
	} else if (z <= 8.8e+73) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.6d+169)) then
        tmp = x + t
    else if (z <= 5.5d-55) then
        tmp = x + (t * (y / a))
    else if (z <= 8.8d+73) then
        tmp = x - (t / (z / y))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+169) {
		tmp = x + t;
	} else if (z <= 5.5e-55) {
		tmp = x + (t * (y / a));
	} else if (z <= 8.8e+73) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+169:
		tmp = x + t
	elif z <= 5.5e-55:
		tmp = x + (t * (y / a))
	elif z <= 8.8e+73:
		tmp = x - (t / (z / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+169)
		tmp = Float64(x + t);
	elseif (z <= 5.5e-55)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 8.8e+73)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+169)
		tmp = x + t;
	elseif (z <= 5.5e-55)
		tmp = x + (t * (y / a));
	elseif (z <= 8.8e+73)
		tmp = x - (t / (z / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+169], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.5e-55], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+73], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999994e169 or 8.8e73 < z

   1. Initial program 72.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 81.0%

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

   if -6.5999999999999994e169 < z < 5.4999999999999999e-55

   1. Initial program 92.8%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 83.3%

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

      1. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in a around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-/l* 75.9%

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

   10. Simplified 75.9%

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

   if 5.4999999999999999e-55 < z < 8.8e73

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

      3. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. un-div-inv 80.3%

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

   9. Applied egg-rr 80.3%

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

   10. Taylor expanded in z around 0 78.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+76}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+169)
   (+ x t)
   (if (<= z 5.5e-55)
     (+ x (* t (/ y a)))
     (if (<= z 4.1e+76) (- x (* t (/ y z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+169) {
		tmp = x + t;
	} else if (z <= 5.5e-55) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.1e+76) {
		tmp = x - (t * (y / 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 <= (-6.6d+169)) then
        tmp = x + t
    else if (z <= 5.5d-55) then
        tmp = x + (t * (y / a))
    else if (z <= 4.1d+76) then
        tmp = x - (t * (y / 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 <= -6.6e+169) {
		tmp = x + t;
	} else if (z <= 5.5e-55) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.1e+76) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+169:
		tmp = x + t
	elif z <= 5.5e-55:
		tmp = x + (t * (y / a))
	elif z <= 4.1e+76:
		tmp = x - (t * (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+169)
		tmp = Float64(x + t);
	elseif (z <= 5.5e-55)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 4.1e+76)
		tmp = Float64(x - Float64(t * Float64(y / 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 <= -6.6e+169)
		tmp = x + t;
	elseif (z <= 5.5e-55)
		tmp = x + (t * (y / a));
	elseif (z <= 4.1e+76)
		tmp = x - (t * (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+169], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.5e-55], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+76], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999994e169 or 4.0999999999999998e76 < z

   1. Initial program 72.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 81.0%

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

   if -6.5999999999999994e169 < z < 5.4999999999999999e-55

   1. Initial program 92.8%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 83.3%

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

      1. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in a around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-/l* 75.9%

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

   10. Simplified 75.9%

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

   if 5.4999999999999999e-55 < z < 4.0999999999999998e76

   1. Initial program 91.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 79.6%

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

      1. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in a around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

      3. associate-/l* 78.6%

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

   10. Simplified 78.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+76}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.16 \cdot 10^{-103} \lor \neg \left(y \leq 5.6 \cdot 10^{-75}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.16e-103) (not (<= y 5.6e-75)))
   (+ x (* t (/ y (- a z))))
   (+ x (/ t (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.16e-103) || !(y <= 5.6e-75)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.16d-103)) .or. (.not. (y <= 5.6d-75))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.16e-103) || !(y <= 5.6e-75)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.16e-103) or not (y <= 5.6e-75):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.16e-103) || !(y <= 5.6e-75))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.16e-103) || ~((y <= 5.6e-75)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.16e-103], N[Not[LessEqual[y, 5.6e-75]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1599999999999999e-103 or 5.59999999999999996e-75 < y

   1. Initial program 83.2%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around inf 81.1%

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

      1. associate-/l* 88.0%

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

   7. Simplified 88.0%

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

   if -2.1599999999999999e-103 < y < 5.59999999999999996e-75

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 90.7%

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

      3. fma-define 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

      3. associate-/l* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-/r/ 89.1%

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

   7. Simplified 89.1%

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

      1. associate-/r/ 96.2%

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

   9. Applied egg-rr 96.2%

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

       1. *-commutative 96.2%

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

       2. clear-num 96.2%

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

       3. un-div-inv 96.3%

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

   11. Applied egg-rr 96.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.16 \cdot 10^{-103} \lor \neg \left(y \leq 5.6 \cdot 10^{-75}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-103} \lor \neg \left(y \leq 6 \cdot 10^{-71}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.6e-103) (not (<= y 6e-71)))
   (+ x (* t (/ y (- a z))))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.6e-103) || !(y <= 6e-71)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.6d-103)) .or. (.not. (y <= 6d-71))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.6e-103) || !(y <= 6e-71)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.6e-103) or not (y <= 6e-71):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.6e-103) || !(y <= 6e-71))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.6e-103) || ~((y <= 6e-71)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.6e-103], N[Not[LessEqual[y, 6e-71]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6000000000000001e-103 or 6.0000000000000003e-71 < y

   1. Initial program 83.2%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around inf 81.1%

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

      1. associate-/l* 88.0%

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

   7. Simplified 88.0%

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

   if -4.6000000000000001e-103 < y < 6.0000000000000003e-71

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 90.7%

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

      3. fma-define 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

      3. associate-/l* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-/r/ 89.1%

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

   7. Simplified 89.1%

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

      1. associate-/r/ 96.2%

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

   9. Applied egg-rr 96.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-103} \lor \neg \left(y \leq 6 \cdot 10^{-71}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169} \lor \neg \left(z \leq 8.2 \cdot 10^{-38}\right):\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e+169) (not (<= z 8.2e-38)))
   (- x (* t (/ (- y z) z)))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+169) || !(z <= 8.2e-38)) {
		tmp = x - (t * ((y - z) / z));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.6d+169)) .or. (.not. (z <= 8.2d-38))) then
        tmp = x - (t * ((y - z) / z))
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+169) || !(z <= 8.2e-38)) {
		tmp = x - (t * ((y - z) / z));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e+169) or not (z <= 8.2e-38):
		tmp = x - (t * ((y - z) / z))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e+169) || !(z <= 8.2e-38))
		tmp = Float64(x - Float64(t * Float64(Float64(y - z) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.6e+169) || ~((z <= 8.2e-38)))
		tmp = x - (t * ((y - z) / z));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e+169], N[Not[LessEqual[z, 8.2e-38]], $MachinePrecision]], N[(x - N[(t * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999994e169 or 8.1999999999999996e-38 < z

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. associate-/l* 95.4%

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

      3. fma-define 95.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   3. Simplified 95.4%

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

   5. Taylor expanded in a around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

      3. associate-/l* 90.8%

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

   7. Simplified 90.8%

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

   if -6.5999999999999994e169 < z < 8.1999999999999996e-38

   1. Initial program 92.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around inf 82.8%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169} \lor \neg \left(z \leq 8.2 \cdot 10^{-38}\right):\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+261} \lor \neg \left(z \leq 2.5 \cdot 10^{+79}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+261) (not (<= z 2.5e+79)))
   (+ x t)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+261) || !(z <= 2.5e+79)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.1d+261)) .or. (.not. (z <= 2.5d+79))) then
        tmp = x + t
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+261) || !(z <= 2.5e+79)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+261) or not (z <= 2.5e+79):
		tmp = x + t
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+261) || !(z <= 2.5e+79))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+261) || ~((z <= 2.5e+79)))
		tmp = x + t;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+261], N[Not[LessEqual[z, 2.5e+79]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999992e261 or 2.5e79 < z

   1. Initial program 73.7%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around inf 84.1%

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

   if -1.09999999999999992e261 < z < 2.5e79

   1. Initial program 90.1%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 80.5%

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

      1. associate-/l* 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+261} \lor \neg \left(z \leq 2.5 \cdot 10^{+79}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169} \lor \neg \left(z \leq 4.2 \cdot 10^{-55}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e+169) (not (<= z 4.2e-55))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+169) || !(z <= 4.2e-55)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.6d+169)) .or. (.not. (z <= 4.2d-55))) then
        tmp = x + t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+169) || !(z <= 4.2e-55)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e+169) or not (z <= 4.2e-55):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e+169) || !(z <= 4.2e-55))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.6e+169) || ~((z <= 4.2e-55)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e+169], N[Not[LessEqual[z, 4.2e-55]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999994e169 or 4.2000000000000003e-55 < z

   1. Initial program 76.1%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 75.3%

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

   if -6.5999999999999994e169 < z < 4.2000000000000003e-55

   1. Initial program 93.3%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 83.8%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in a around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 75.7%

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

   10. Simplified 75.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169} \lor \neg \left(z \leq 4.2 \cdot 10^{-55}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169} \lor \neg \left(z \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e+169) (not (<= z 5e-55))) (+ x t) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+169) || !(z <= 5e-55)) {
		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 <= (-6.6d+169)) .or. (.not. (z <= 5d-55))) 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 <= -6.6e+169) || !(z <= 5e-55)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e+169) or not (z <= 5e-55):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e+169) || !(z <= 5e-55))
		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 <= -6.6e+169) || ~((z <= 5e-55)))
		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, -6.6e+169], N[Not[LessEqual[z, 5e-55]], $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 < -6.5999999999999994e169 or 5.0000000000000002e-55 < z

   1. Initial program 76.1%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 75.3%

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

   if -6.5999999999999994e169 < z < 5.0000000000000002e-55

   1. Initial program 93.3%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+169} \lor \neg \left(z \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+91} \lor \neg \left(z \leq -1.7 \cdot 10^{-226}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+91) (not (<= z -1.7e-226))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+91) || !(z <= -1.7e-226)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.5d+91)) .or. (.not. (z <= (-1.7d-226)))) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+91) || !(z <= -1.7e-226)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+91) or not (z <= -1.7e-226):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+91) || !(z <= -1.7e-226))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+91) || ~((z <= -1.7e-226)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+91], N[Not[LessEqual[z, -1.7e-226]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000003e91 or -1.70000000000000004e-226 < z

   1. Initial program 83.8%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 60.7%

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

   if -1.50000000000000003e91 < z < -1.70000000000000004e-226

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-/l* 93.9%

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

      3. fma-define 94.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 51.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+91} \lor \neg \left(z \leq -1.7 \cdot 10^{-226}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% 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 86.7%

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

   1. +-commutative 86.7%

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

   2. associate-/l* 95.0%

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

   3. fma-define 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]

3. Simplified 95.0%

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

5. Taylor expanded in t around 0 50.9%

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

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(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))))