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

Percentage Accurate: 85.4% → 98.4%

Time: 10.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. +-commutative 85.4%

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

   2. associate-*r/ 98.8%

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

   3. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+143}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+143)
   (+ y x)
   (if (<= z -2.15e-36)
     (- x (/ y (/ z t)))
     (if (<= z 1e-13)
       (+ x (* y (/ t a)))
       (if (<= z 2.9e+59)
         (+ y x)
         (if (<= z 7e+125) (+ x (* t (/ y a))) (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+143) {
		tmp = y + x;
	} else if (z <= -2.15e-36) {
		tmp = x - (y / (z / t));
	} else if (z <= 1e-13) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.9e+59) {
		tmp = y + x;
	} else if (z <= 7e+125) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 <= (-1d+143)) then
        tmp = y + x
    else if (z <= (-2.15d-36)) then
        tmp = x - (y / (z / t))
    else if (z <= 1d-13) then
        tmp = x + (y * (t / a))
    else if (z <= 2.9d+59) then
        tmp = y + x
    else if (z <= 7d+125) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 <= -1e+143) {
		tmp = y + x;
	} else if (z <= -2.15e-36) {
		tmp = x - (y / (z / t));
	} else if (z <= 1e-13) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.9e+59) {
		tmp = y + x;
	} else if (z <= 7e+125) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+143:
		tmp = y + x
	elif z <= -2.15e-36:
		tmp = x - (y / (z / t))
	elif z <= 1e-13:
		tmp = x + (y * (t / a))
	elif z <= 2.9e+59:
		tmp = y + x
	elif z <= 7e+125:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+143)
		tmp = Float64(y + x);
	elseif (z <= -2.15e-36)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= 1e-13)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.9e+59)
		tmp = Float64(y + x);
	elseif (z <= 7e+125)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+143)
		tmp = y + x;
	elseif (z <= -2.15e-36)
		tmp = x - (y / (z / t));
	elseif (z <= 1e-13)
		tmp = x + (y * (t / a));
	elseif (z <= 2.9e+59)
		tmp = y + x;
	elseif (z <= 7e+125)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+143], N[(y + x), $MachinePrecision], If[LessEqual[z, -2.15e-36], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-13], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+59], N[(y + x), $MachinePrecision], If[LessEqual[z, 7e+125], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1e143 or 1e-13 < z < 2.89999999999999991e59 or 7.00000000000000023e125 < z

   1. Initial program 68.0%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around inf 87.1%

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

   if -1e143 < z < -2.1500000000000001e-36

   1. Initial program 90.1%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 83.1%

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

      1. associate-*r/ 83.1%

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

      2. mul-1-neg 83.1%

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

      3. distribute-rgt-neg-out 83.1%

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

      4. associate-*l/ 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in z around inf 77.9%

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

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. unsub-neg 77.9%

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

      4. associate-/l* 80.3%

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

   9. Simplified 80.3%

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

   if -2.1500000000000001e-36 < z < 1e-13

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-*r/ 97.5%

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

      3. fma-def 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in z around 0 76.7%

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

   if 2.89999999999999991e59 < z < 7.00000000000000023e125

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-*r/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*r/ 87.7%

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

   8. Simplified 87.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+143}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -3.45 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-132}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 6.5128 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -3.45e-48)
     t_1
     (if (<= z 5.1e-132)
       (+ x (* y (/ t a)))
       (if (<= z 1.75e-47)
         (+ x (/ y (/ (- z a) z)))
         (if (<= z 6.5128e-45) (+ x (* t (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -3.45e-48) {
		tmp = t_1;
	} else if (z <= 5.1e-132) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.75e-47) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 6.5128e-45) {
		tmp = x + (t * (y / a));
	} 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 / (z - t)))
    if (z <= (-3.45d-48)) then
        tmp = t_1
    else if (z <= 5.1d-132) then
        tmp = x + (y * (t / a))
    else if (z <= 1.75d-47) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= 6.5128d-45) then
        tmp = x + (t * (y / a))
    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 / (z - t)));
	double tmp;
	if (z <= -3.45e-48) {
		tmp = t_1;
	} else if (z <= 5.1e-132) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.75e-47) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= 6.5128e-45) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -3.45e-48:
		tmp = t_1
	elif z <= 5.1e-132:
		tmp = x + (y * (t / a))
	elif z <= 1.75e-47:
		tmp = x + (y / ((z - a) / z))
	elif z <= 6.5128e-45:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -3.45e-48)
		tmp = t_1;
	elseif (z <= 5.1e-132)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.75e-47)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= 6.5128e-45)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -3.45e-48)
		tmp = t_1;
	elseif (z <= 5.1e-132)
		tmp = x + (y * (t / a));
	elseif (z <= 1.75e-47)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= 6.5128e-45)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.45e-48], t$95$1, If[LessEqual[z, 5.1e-132], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-47], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5128e-45], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.45000000000000009e-48 or 6.5128000000000001e-45 < z

   1. Initial program 75.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 89.7%

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

   if -3.45000000000000009e-48 < z < 5.10000000000000005e-132

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate-*r/ 97.7%

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

      3. fma-def 97.7%

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

   3. Simplified 97.7%

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

      1. fma-udef 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in z around 0 82.2%

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

   if 5.10000000000000005e-132 < z < 1.7499999999999999e-47

   1. Initial program 99.7%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around 0 81.6%

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

   if 1.7499999999999999e-47 < z < 6.5128000000000001e-45

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*r/ 99.5%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in z around 0 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r/ 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-132}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 6.5128 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 4: 75.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-12} \lor \neg \left(z \leq 5.4 \cdot 10^{+57}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e-47)
   (+ y x)
   (if (or (<= z 1.85e-12) (and (not (<= z 5.4e+57)) (<= z 7e+125)))
     (+ x (* t (/ y a)))
     (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e-47) {
		tmp = y + x;
	} else if ((z <= 1.85e-12) || (!(z <= 5.4e+57) && (z <= 7e+125))) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.7d-47)) then
        tmp = y + x
    else if ((z <= 1.85d-12) .or. (.not. (z <= 5.4d+57)) .and. (z <= 7d+125)) then
        tmp = x + (t * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e-47) {
		tmp = y + x;
	} else if ((z <= 1.85e-12) || (!(z <= 5.4e+57) && (z <= 7e+125))) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.7e-47:
		tmp = y + x
	elif (z <= 1.85e-12) or (not (z <= 5.4e+57) and (z <= 7e+125)):
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e-47)
		tmp = Float64(y + x);
	elseif ((z <= 1.85e-12) || (!(z <= 5.4e+57) && (z <= 7e+125)))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.7e-47)
		tmp = y + x;
	elseif ((z <= 1.85e-12) || (~((z <= 5.4e+57)) && (z <= 7e+125)))
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e-47], N[(y + x), $MachinePrecision], If[Or[LessEqual[z, 1.85e-12], And[N[Not[LessEqual[z, 5.4e+57]], $MachinePrecision], LessEqual[z, 7e+125]]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e-47 or 1.84999999999999999e-12 < z < 5.3999999999999997e57 or 7.00000000000000023e125 < z

   1. Initial program 74.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 80.7%

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

   if -3.7e-47 < z < 1.84999999999999999e-12 or 5.3999999999999997e57 < z < 7.00000000000000023e125

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. associate-*r/ 97.6%

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

      3. fma-def 97.7%

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

   3. Simplified 97.7%

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

      1. fma-udef 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in z around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r/ 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-12} \lor \neg \left(z \leq 5.4 \cdot 10^{+57}\right) \land z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-48}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e-48)
   (+ y x)
   (if (<= z 9e-15)
     (+ x (* y (/ t a)))
     (if (<= z 2.9e+59)
       (+ y x)
       (if (<= z 7e+125) (+ x (* t (/ y a))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e-48) {
		tmp = y + x;
	} else if (z <= 9e-15) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.9e+59) {
		tmp = y + x;
	} else if (z <= 7e+125) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 <= (-7d-48)) then
        tmp = y + x
    else if (z <= 9d-15) then
        tmp = x + (y * (t / a))
    else if (z <= 2.9d+59) then
        tmp = y + x
    else if (z <= 7d+125) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 <= -7e-48) {
		tmp = y + x;
	} else if (z <= 9e-15) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.9e+59) {
		tmp = y + x;
	} else if (z <= 7e+125) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e-48:
		tmp = y + x
	elif z <= 9e-15:
		tmp = x + (y * (t / a))
	elif z <= 2.9e+59:
		tmp = y + x
	elif z <= 7e+125:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e-48)
		tmp = Float64(y + x);
	elseif (z <= 9e-15)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.9e+59)
		tmp = Float64(y + x);
	elseif (z <= 7e+125)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e-48)
		tmp = y + x;
	elseif (z <= 9e-15)
		tmp = x + (y * (t / a));
	elseif (z <= 2.9e+59)
		tmp = y + x;
	elseif (z <= 7e+125)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e-48], N[(y + x), $MachinePrecision], If[LessEqual[z, 9e-15], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+59], N[(y + x), $MachinePrecision], If[LessEqual[z, 7e+125], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999982e-48 or 8.9999999999999995e-15 < z < 2.89999999999999991e59 or 7.00000000000000023e125 < z

   1. Initial program 74.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 80.7%

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

   if -6.99999999999999982e-48 < z < 8.9999999999999995e-15

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-*r/ 97.5%

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

      3. fma-def 97.5%

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

   3. Simplified 97.5%

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

      1. fma-udef 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in z around 0 77.2%

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

   if 2.89999999999999991e59 < z < 7.00000000000000023e125

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-*r/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*r/ 87.7%

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

   8. Simplified 87.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-48}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-48} \lor \neg \left(z \leq 3.1 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.9e-48) (not (<= z 3.1e-14)))
   (+ x (/ y (/ z (- z t))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.9e-48) || !(z <= 3.1e-14)) {
		tmp = x + (y / (z / (z - 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 <= (-4.9d-48)) .or. (.not. (z <= 3.1d-14))) then
        tmp = x + (y / (z / (z - 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 <= -4.9e-48) || !(z <= 3.1e-14)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.9e-48) or not (z <= 3.1e-14):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.9e-48) || !(z <= 3.1e-14))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - 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 <= -4.9e-48) || ~((z <= 3.1e-14)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.9e-48], N[Not[LessEqual[z, 3.1e-14]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9000000000000002e-48 or 3.10000000000000004e-14 < z

   1. Initial program 74.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.6%

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

   if -4.9000000000000002e-48 < z < 3.10000000000000004e-14

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-*r/ 97.5%

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

      3. fma-def 97.5%

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

   3. Simplified 97.5%

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

      1. fma-udef 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in z around 0 77.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-48} \lor \neg \left(z \leq 3.1 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 7: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+44} \lor \neg \left(t \leq 4600000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.4e+44) (not (<= t 4600000000.0)))
   (- x (* t (/ y (- z a))))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.4e+44) || !(t <= 4600000000.0)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((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 ((t <= (-4.4d+44)) .or. (.not. (t <= 4600000000.0d0))) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (y / ((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 ((t <= -4.4e+44) || !(t <= 4600000000.0)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.4e+44) or not (t <= 4600000000.0):
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.4e+44) || !(t <= 4600000000.0))
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.4e+44) || ~((t <= 4600000000.0)))
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.4e+44], N[Not[LessEqual[t, 4600000000.0]], $MachinePrecision]], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.39999999999999991e44 or 4.6e9 < t

   1. Initial program 87.6%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. distribute-rgt-neg-out 83.8%

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

      4. associate-*l/ 87.2%

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

   6. Simplified 87.2%

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

   7. Taylor expanded in x around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-*r/ 87.2%

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

      5. sub-neg 87.2%

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

   9. Simplified 87.2%

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

   if -4.39999999999999991e44 < t < 4.6e9

   1. Initial program 83.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 95.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+44} \lor \neg \left(t \leq 4600000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 8: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+40)
   (- x (* t (/ y (- z a))))
   (if (<= t 6.2e+17) (+ x (/ y (/ (- z a) z))) (+ x (/ y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+40) {
		tmp = x - (t * (y / (z - a)));
	} else if (t <= 6.2e+17) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y / ((a - z) / 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 (t <= (-1.15d+40)) then
        tmp = x - (t * (y / (z - a)))
    else if (t <= 6.2d+17) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x + (y / ((a - z) / 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 (t <= -1.15e+40) {
		tmp = x - (t * (y / (z - a)));
	} else if (t <= 6.2e+17) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+40:
		tmp = x - (t * (y / (z - a)))
	elif t <= 6.2e+17:
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+40)
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	elseif (t <= 6.2e+17)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+40)
		tmp = x - (t * (y / (z - a)));
	elseif (t <= 6.2e+17)
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+40], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+17], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.14999999999999997e40

   1. Initial program 90.6%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 83.6%

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

      1. associate-*r/ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. distribute-rgt-neg-out 83.6%

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

      4. associate-*l/ 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. *-commutative 83.6%

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

      4. associate-*r/ 86.1%

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

      5. sub-neg 86.1%

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

   9. Simplified 86.1%

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

   if -1.14999999999999997e40 < t < 6.2e17

   1. Initial program 83.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 95.6%

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

   if 6.2e17 < t

   1. Initial program 85.7%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 90.7%

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

      1. associate-*r/ 90.7%

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

      2. neg-mul-1 90.7%

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

      3. sub-neg 90.7%

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

      4. mul-1-neg 90.7%

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

      5. distribute-neg-in 90.7%

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

      6. mul-1-neg 90.7%

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

      7. remove-double-neg 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 9: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. associate-*l/ 95.3%

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

3. Simplified 95.3%

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

4. Final simplification 95.3%

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

Alternative 10: 98.4% accurate, 1.0× speedup

Math

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

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(y / Float64(Float64(z - a) / Float64(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[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.4%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 11: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. +-commutative 85.4%

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

   2. associate-*r/ 98.8%

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

   3. fma-def 98.8%

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

3. Simplified 98.8%

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

   1. fma-udef 98.8%

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

5. Applied egg-rr 98.8%

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

6. Final simplification 98.8%

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

Alternative 12: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+116}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+175) x (if (<= a 1.65e+116) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+175) {
		tmp = x;
	} else if (a <= 1.65e+116) {
		tmp = y + x;
	} 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 <= (-8.5d+175)) then
        tmp = x
    else if (a <= 1.65d+116) then
        tmp = y + x
    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 <= -8.5e+175) {
		tmp = x;
	} else if (a <= 1.65e+116) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e+175:
		tmp = x
	elif a <= 1.65e+116:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e+175)
		tmp = x;
	elseif (a <= 1.65e+116)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e+175)
		tmp = x;
	elseif (a <= 1.65e+116)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e+175], x, If[LessEqual[a, 1.65e+116], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000034e175 or 1.6499999999999999e116 < a

   1. Initial program 87.4%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 74.4%

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

   if -8.50000000000000034e175 < a < 1.6499999999999999e116

   1. Initial program 84.7%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around inf 64.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+116}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 50.9% 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 85.4%

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

   1. associate-*l/ 95.3%

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

3. Simplified 95.3%

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

4. Taylor expanded in x around inf 48.8%

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

5. Final simplification 48.8%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

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(y / Float64(Float64(z - a) / Float64(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[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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