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

Percentage Accurate: 98.0% → 98.0%

Time: 15.0s

Alternatives: 15

Speedup: 1.0×

Specification

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]

Initial Program: 98.0% 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]

Alternative 1: 98.0% 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 98.4%

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

   1. +-commutative 98.4%

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

   2. fma-def 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+111}:\\ \;\;\;\;y \cdot t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+204}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 0.1)
       (+ x (* y (/ (- t z) a)))
       (if (<= t_1 2.0)
         (- x (* y (/ (- t z) z)))
         (if (<= t_1 1e+111)
           (* y t_1)
           (if (<= t_1 1e+204)
             (- x (/ y (/ z t)))
             (/ (* y (- t)) (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 2.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (t_1 <= 1e+111) {
		tmp = y * t_1;
	} else if (t_1 <= 1e+204) {
		tmp = x - (y / (z / t));
	} else {
		tmp = (y * -t) / (z - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 0.1d0) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 2.0d0) then
        tmp = x - (y * ((t - z) / z))
    else if (t_1 <= 1d+111) then
        tmp = y * t_1
    else if (t_1 <= 1d+204) then
        tmp = x - (y / (z / t))
    else
        tmp = (y * -t) / (z - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 2.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (t_1 <= 1e+111) {
		tmp = y * t_1;
	} else if (t_1 <= 1e+204) {
		tmp = x - (y / (z / t));
	} else {
		tmp = (y * -t) / (z - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 0.1:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 2.0:
		tmp = x - (y * ((t - z) / z))
	elif t_1 <= 1e+111:
		tmp = y * t_1
	elif t_1 <= 1e+204:
		tmp = x - (y / (z / t))
	else:
		tmp = (y * -t) / (z - a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (t_1 <= 1e+111)
		tmp = Float64(y * t_1);
	elseif (t_1 <= 1e+204)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(Float64(y * Float64(-t)) / Float64(z - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 0.1)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 2.0)
		tmp = x - (y * ((t - z) / z));
	elseif (t_1 <= 1e+111)
		tmp = y * t_1;
	elseif (t_1 <= 1e+204)
		tmp = x - (y / (z / t));
	else
		tmp = (y * -t) / (z - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+111], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+204], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * (-t)), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0 76.9%

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

   4. Taylor expanded in z around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. *-commutative 68.5%

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

      3. neg-mul-1 68.5%

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

      4. distribute-rgt-neg-in 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-*r/ 77.0%

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

      3. distribute-lft-neg-in 77.0%

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

      4. cancel-sign-sub-inv 77.0%

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

   9. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. *-lft-identity 85.7%

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

      4. times-frac 97.1%

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

      5. /-rgt-identity 97.1%

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

   5. Simplified 97.1%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.9%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.99999999999999957e110

   1. Initial program 99.7%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.3%

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

      2. pow3 98.4%

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

      3. +-commutative 98.4%

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

      4. fma-udef 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in x around 0 73.4%

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

      1. pow-base-1 73.4%

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

      2. associate-*r/ 89.1%

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

      3. *-lft-identity 89.1%

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

   7. Simplified 89.1%

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

   if 9.99999999999999957e110 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.99999999999999989e203

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 75.8%

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

   4. Taylor expanded in z around 0 87.5%

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

      1. associate-*r/ 87.5%

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

      2. *-commutative 87.5%

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

      3. neg-mul-1 87.5%

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

      4. distribute-rgt-neg-in 87.5%

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

   6. Simplified 87.5%

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

      1. div-inv 87.3%

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

      2. add-sqr-sqrt 50.0%

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

      3. sqrt-unprod 26.2%

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

      4. sqr-neg 26.2%

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

      5. sqrt-unprod 12.8%

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

      6. add-sqr-sqrt 38.9%

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

      7. distribute-rgt-neg-in 38.9%

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

      8. cancel-sign-sub-inv 38.9%

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

      9. div-inv 38.9%

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

      10. associate-/l* 38.9%

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

      11. add-sqr-sqrt 12.8%

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

      12. sqrt-unprod 26.2%

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

      13. sqr-neg 26.2%

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

      14. sqrt-unprod 50.2%

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

      15. add-sqr-sqrt 87.7%

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

   8. Applied egg-rr 87.7%

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

   if 9.99999999999999989e203 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 84.3%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in t around inf 93.3%

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

       1. mul-1-neg 93.3%

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

       2. *-commutative 93.3%

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

       3. distribute-neg-frac 93.3%

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

   11. Simplified 93.3%

       \[\leadsto \color{blue}{\frac{-y \cdot t}{z - a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+111}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+204}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 0.1)
       (+ x (* y (/ t a)))
       (if (<= t_1 2.0) (+ y x) (* y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (y * (t / a));
	} else if (t_1 <= 2.0) {
		tmp = y + x;
	} else {
		tmp = y * 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 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 0.1d0) then
        tmp = x + (y * (t / a))
    else if (t_1 <= 2.0d0) then
        tmp = y + x
    else
        tmp = y * 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 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 0.1) {
		tmp = x + (y * (t / a));
	} else if (t_1 <= 2.0) {
		tmp = y + x;
	} else {
		tmp = y * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 0.1:
		tmp = x + (y * (t / a))
	elif t_1 <= 2.0:
		tmp = y + x
	else:
		tmp = y * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 0.1)
		tmp = x + (y * (t / a));
	elseif (t_1 <= 2.0)
		tmp = y + x;
	else
		tmp = y * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(y + x), $MachinePrecision], N[(y * t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0 76.9%

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

   4. Taylor expanded in z around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. *-commutative 68.5%

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

      3. neg-mul-1 68.5%

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

      4. distribute-rgt-neg-in 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-*r/ 77.0%

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

      3. distribute-lft-neg-in 77.0%

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

      4. cancel-sign-sub-inv 77.0%

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

   9. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. *-lft-identity 78.8%

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

      4. times-frac 84.2%

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

      5. /-rgt-identity 84.2%

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

   5. Simplified 84.2%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.2%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 93.7%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 92.6%

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

      2. pow3 92.6%

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

      3. +-commutative 92.6%

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

      4. fma-udef 92.6%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. pow-base-1 77.2%

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

      2. associate-*r/ 78.0%

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

      3. *-lft-identity 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x - \frac{y \cdot t}{z - a}\\ \mathbf{if}\;t\_1 \leq -50000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 50000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (- x (/ (* y t) (- z a)))))
   (if (<= t_1 -50000000000.0)
     t_2
     (if (<= t_1 0.1)
       (+ x (* y (/ (- t z) a)))
       (if (<= t_1 50000.0) (- x (* y (/ (- t z) z))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x - ((y * t) / (z - a));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 50000.0) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    t_2 = x - ((y * t) / (z - a))
    if (t_1 <= (-50000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.1d0) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 50000.0d0) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x - ((y * t) / (z - a));
	double tmp;
	if (t_1 <= -50000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 50000.0) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	t_2 = x - ((y * t) / (z - a))
	tmp = 0
	if t_1 <= -50000000000.0:
		tmp = t_2
	elif t_1 <= 0.1:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 50000.0:
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(x - Float64(Float64(y * t) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= -50000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 50000.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	t_2 = x - ((y * t) / (z - a));
	tmp = 0.0;
	if (t_1 <= -50000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 50000.0)
		tmp = x - (y * ((t - z) / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000.0], t$95$2, If[LessEqual[t$95$1, 0.1], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 50000.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e10 or 5e4 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf 91.1%

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

      1. associate-*r/ 91.1%

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

      2. mul-1-neg 91.1%

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

      3. distribute-lft-neg-out 91.1%

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

      4. *-commutative 91.1%

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

   5. Simplified 91.1%

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

   if -5e10 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.10000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

      3. *-lft-identity 86.4%

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

      4. times-frac 98.2%

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

      5. /-rgt-identity 98.2%

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

   5. Simplified 98.2%

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

   if 0.10000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5e4

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -50000000000:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.1:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 50000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e+17)
     (- x (* t (/ y z)))
     (if (<= t_1 2.0) (+ x (* y (/ z (- z a)))) (* y t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 2.0) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = y * 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 = (z - t) / (z - a)
    if (t_1 <= (-5d+17)) then
        tmp = x - (t * (y / z))
    else if (t_1 <= 2.0d0) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = y * 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 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x - (t * (y / z));
	} else if (t_1 <= 2.0) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = y * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x - (t * (y / z))
	elif t_1 <= 2.0:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = y * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(y * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x - (t * (y / z));
	elseif (t_1 <= 2.0)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = y * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5e17

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0 76.9%

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

   4. Taylor expanded in z around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. *-commutative 68.5%

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

      3. neg-mul-1 68.5%

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

      4. distribute-rgt-neg-in 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-*r/ 77.0%

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

      3. distribute-lft-neg-in 77.0%

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

      4. cancel-sign-sub-inv 77.0%

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

   9. Simplified 77.0%

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

   if -5e17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 92.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 93.7%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 92.6%

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

      2. pow3 92.6%

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

      3. +-commutative 92.6%

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

      4. fma-udef 92.6%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. pow-base-1 77.2%

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

      2. associate-*r/ 78.0%

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

      3. *-lft-identity 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 700000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-40)
   (+ y x)
   (if (<= z 700000000.0)
     (+ x (* y (/ t a)))
     (if (or (<= z 4.7e+142) (not (<= z 1.2e+181)))
       (+ y x)
       (- x (* t (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-40) {
		tmp = y + x;
	} else if (z <= 700000000.0) {
		tmp = x + (y * (t / a));
	} else if ((z <= 4.7e+142) || !(z <= 1.2e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (t * (y / 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 <= (-9.5d-40)) then
        tmp = y + x
    else if (z <= 700000000.0d0) then
        tmp = x + (y * (t / a))
    else if ((z <= 4.7d+142) .or. (.not. (z <= 1.2d+181))) then
        tmp = y + x
    else
        tmp = x - (t * (y / 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 <= -9.5e-40) {
		tmp = y + x;
	} else if (z <= 700000000.0) {
		tmp = x + (y * (t / a));
	} else if ((z <= 4.7e+142) || !(z <= 1.2e+181)) {
		tmp = y + x;
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-40:
		tmp = y + x
	elif z <= 700000000.0:
		tmp = x + (y * (t / a))
	elif (z <= 4.7e+142) or not (z <= 1.2e+181):
		tmp = y + x
	else:
		tmp = x - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-40)
		tmp = Float64(y + x);
	elseif (z <= 700000000.0)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif ((z <= 4.7e+142) || !(z <= 1.2e+181))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-40)
		tmp = y + x;
	elseif (z <= 700000000.0)
		tmp = x + (y * (t / a));
	elseif ((z <= 4.7e+142) || ~((z <= 1.2e+181)))
		tmp = y + x;
	else
		tmp = x - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-40], N[(y + x), $MachinePrecision], If[LessEqual[z, 700000000.0], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.7e+142], N[Not[LessEqual[z, 1.2e+181]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000006e-40 or 7e8 < z < 4.7e142 or 1.20000000000000001e181 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -9.5000000000000006e-40 < z < 7e8

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. *-lft-identity 71.8%

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

      4. times-frac 73.7%

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

      5. /-rgt-identity 73.7%

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

   5. Simplified 73.7%

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

   if 4.7e142 < z < 1.20000000000000001e181

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 83.6%

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

   4. Taylor expanded in z around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. *-commutative 70.3%

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

      3. neg-mul-1 70.3%

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

      4. distribute-rgt-neg-in 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 86.6%

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

      3. distribute-lft-neg-in 86.6%

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

      4. cancel-sign-sub-inv 86.6%

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

   9. Simplified 86.6%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 700000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+164}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+303}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))))
   (if (<= t -2.6e+184)
     t_1
     (if (<= t 4.8e+164)
       (+ y x)
       (if (<= t 3e+226)
         t_1
         (if (<= t 1.4e+303) (/ t (/ a y)) (* y (- (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double tmp;
	if (t <= -2.6e+184) {
		tmp = t_1;
	} else if (t <= 4.8e+164) {
		tmp = y + x;
	} else if (t <= 3e+226) {
		tmp = t_1;
	} else if (t <= 1.4e+303) {
		tmp = t / (a / y);
	} else {
		tmp = y * -(t / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - (t / z))
    if (t <= (-2.6d+184)) then
        tmp = t_1
    else if (t <= 4.8d+164) then
        tmp = y + x
    else if (t <= 3d+226) then
        tmp = t_1
    else if (t <= 1.4d+303) then
        tmp = t / (a / y)
    else
        tmp = y * -(t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double tmp;
	if (t <= -2.6e+184) {
		tmp = t_1;
	} else if (t <= 4.8e+164) {
		tmp = y + x;
	} else if (t <= 3e+226) {
		tmp = t_1;
	} else if (t <= 1.4e+303) {
		tmp = t / (a / y);
	} else {
		tmp = y * -(t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	tmp = 0
	if t <= -2.6e+184:
		tmp = t_1
	elif t <= 4.8e+164:
		tmp = y + x
	elif t <= 3e+226:
		tmp = t_1
	elif t <= 1.4e+303:
		tmp = t / (a / y)
	else:
		tmp = y * -(t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (t <= -2.6e+184)
		tmp = t_1;
	elseif (t <= 4.8e+164)
		tmp = Float64(y + x);
	elseif (t <= 3e+226)
		tmp = t_1;
	elseif (t <= 1.4e+303)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = Float64(y * Float64(-Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (t / z));
	tmp = 0.0;
	if (t <= -2.6e+184)
		tmp = t_1;
	elseif (t <= 4.8e+164)
		tmp = y + x;
	elseif (t <= 3e+226)
		tmp = t_1;
	elseif (t <= 1.4e+303)
		tmp = t / (a / y);
	else
		tmp = y * -(t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+184], t$95$1, If[LessEqual[t, 4.8e+164], N[(y + x), $MachinePrecision], If[LessEqual[t, 3e+226], t$95$1, If[LessEqual[t, 1.4e+303], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.59999999999999993e184 or 4.80000000000000021e164 < t < 2.99999999999999975e226

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 77.9%

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

   4. Taylor expanded in y around inf 61.0%

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

   if -2.59999999999999993e184 < t < 4.80000000000000021e164

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 71.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

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

   5. Simplified 71.8%

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

   if 2.99999999999999975e226 < t < 1.39999999999999988e303

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

      3. *-lft-identity 67.5%

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

      4. times-frac 73.5%

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

      5. /-rgt-identity 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in x around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. associate-*r/ 54.2%

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

      3. *-commutative 54.2%

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

      4. distribute-rgt-neg-out 54.2%

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

   8. Simplified 54.2%

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

   9. Taylor expanded in z around 0 48.6%

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

       1. associate-/l* 61.0%

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

   11. Simplified 61.0%

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

   if 1.39999999999999988e303 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in x around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. associate-/l* 100.0%

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

       3. associate-/r/ 100.0%

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

       4. distribute-rgt-neg-in 100.0%

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

   12. Simplified 100.0%

       \[\leadsto \color{blue}{\frac{t}{z} \cdot \left(-y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+164}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+303}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{t}{\frac{z}{y}}\\ \mathbf{if}\;t \leq -3.35 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (/ t (/ z y)))))
   (if (<= t -3.35e+184)
     t_1
     (if (<= t 1.9e+182)
       (+ y x)
       (if (<= t 1.12e+223) t_1 (if (<= t 6.5e+226) x (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t / (z / y));
	double tmp;
	if (t <= -3.35e+184) {
		tmp = t_1;
	} else if (t <= 1.9e+182) {
		tmp = y + x;
	} else if (t <= 1.12e+223) {
		tmp = t_1;
	} else if (t <= 6.5e+226) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(t / (z / y))
    if (t <= (-3.35d+184)) then
        tmp = t_1
    else if (t <= 1.9d+182) then
        tmp = y + x
    else if (t <= 1.12d+223) then
        tmp = t_1
    else if (t <= 6.5d+226) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t / (z / y));
	double tmp;
	if (t <= -3.35e+184) {
		tmp = t_1;
	} else if (t <= 1.9e+182) {
		tmp = y + x;
	} else if (t <= 1.12e+223) {
		tmp = t_1;
	} else if (t <= 6.5e+226) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(t / (z / y))
	tmp = 0
	if t <= -3.35e+184:
		tmp = t_1
	elif t <= 1.9e+182:
		tmp = y + x
	elif t <= 1.12e+223:
		tmp = t_1
	elif t <= 6.5e+226:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(t / Float64(z / y)))
	tmp = 0.0
	if (t <= -3.35e+184)
		tmp = t_1;
	elseif (t <= 1.9e+182)
		tmp = Float64(y + x);
	elseif (t <= 1.12e+223)
		tmp = t_1;
	elseif (t <= 6.5e+226)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(t / (z / y));
	tmp = 0.0;
	if (t <= -3.35e+184)
		tmp = t_1;
	elseif (t <= 1.9e+182)
		tmp = y + x;
	elseif (t <= 1.12e+223)
		tmp = t_1;
	elseif (t <= 6.5e+226)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t, -3.35e+184], t$95$1, If[LessEqual[t, 1.9e+182], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.12e+223], t$95$1, If[LessEqual[t, 6.5e+226], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.35e184 or 1.90000000000000006e182 < t < 1.1200000000000001e223

   1. Initial program 95.2%

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

   3. Taylor expanded in a around 0 77.6%

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

   4. Taylor expanded in z around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. *-commutative 61.7%

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

      3. neg-mul-1 61.7%

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

      4. distribute-rgt-neg-in 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in x around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-*r/ 71.6%

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

      3. distribute-lft-neg-in 71.6%

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

      4. cancel-sign-sub-inv 71.6%

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

   9. Simplified 71.6%

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

   10. Taylor expanded in x around 0 51.0%

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

       1. mul-1-neg 51.0%

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

       2. associate-/l* 58.4%

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

       3. distribute-neg-frac 58.4%

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

   12. Simplified 58.4%

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

   if -3.35e184 < t < 1.90000000000000006e182

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 70.9%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 70.9%

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

   5. Simplified 70.9%

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

   if 1.1200000000000001e223 < t < 6.49999999999999955e226

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if 6.49999999999999955e226 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. *-lft-identity 63.3%

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

      4. times-frac 68.9%

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

      5. /-rgt-identity 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. associate-*r/ 50.9%

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

      3. *-commutative 50.9%

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

      4. distribute-rgt-neg-out 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in z around 0 45.6%

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

       1. associate-/l* 57.2%

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

   11. Simplified 57.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{+184}:\\ \;\;\;\;-\frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+223}:\\ \;\;\;\;-\frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-41} \lor \neg \left(z \leq 2.3 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-41) (not (<= z 2.3e+25))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-41) || !(z <= 2.3e+25)) {
		tmp = y + x;
	} 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 <= (-7.2d-41)) .or. (.not. (z <= 2.3d+25))) then
        tmp = y + x
    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 <= -7.2e-41) || !(z <= 2.3e+25)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-41) or not (z <= 2.3e+25):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-41) || !(z <= 2.3e+25))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-41) || ~((z <= 2.3e+25)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-41], N[Not[LessEqual[z, 2.3e+25]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e-41 or 2.2999999999999998e25 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 76.3%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -7.2e-41 < z < 2.2999999999999998e25

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 71.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-41} \lor \neg \left(z \leq 2.3 \cdot 10^{+25}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-40} \lor \neg \left(z \leq 130\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e-40) (not (<= z 130.0))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-40) || !(z <= 130.0)) {
		tmp = y + x;
	} 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 <= (-9d-40)) .or. (.not. (z <= 130.0d0))) then
        tmp = y + x
    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 <= -9e-40) || !(z <= 130.0)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e-40) or not (z <= 130.0):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e-40) || !(z <= 130.0))
		tmp = Float64(y + x);
	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 <= -9e-40) || ~((z <= 130.0)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e-40], N[Not[LessEqual[z, 130.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000002e-40 or 130 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.9%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -9.0000000000000002e-40 < z < 130

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. *-lft-identity 71.8%

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

      4. times-frac 73.7%

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

      5. /-rgt-identity 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-40} \lor \neg \left(z \leq 130\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+246} \lor \neg \left(t \leq 2.8 \cdot 10^{+226}\right):\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.6e+246) (not (<= t 2.8e+226))) (/ t (/ a y)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e+246) || !(t <= 2.8e+226)) {
		tmp = t / (a / y);
	} 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 ((t <= (-3.6d+246)) .or. (.not. (t <= 2.8d+226))) then
        tmp = t / (a / y)
    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 ((t <= -3.6e+246) || !(t <= 2.8e+226)) {
		tmp = t / (a / y);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.6e+246) or not (t <= 2.8e+226):
		tmp = t / (a / y)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.6e+246) || !(t <= 2.8e+226))
		tmp = Float64(t / Float64(a / y));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.6e+246) || ~((t <= 2.8e+226)))
		tmp = t / (a / y);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.6e+246], N[Not[LessEqual[t, 2.8e+226]], $MachinePrecision]], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e246 or 2.8000000000000003e226 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

      3. *-lft-identity 71.1%

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

      4. times-frac 73.4%

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

      5. /-rgt-identity 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in x around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-*r/ 58.5%

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

      3. *-commutative 58.5%

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

      4. distribute-rgt-neg-out 58.5%

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

   8. Simplified 58.5%

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

   9. Taylor expanded in z around 0 56.4%

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

       1. associate-/l* 63.6%

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

   11. Simplified 63.6%

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

   if -3.6e246 < t < 2.8000000000000003e226

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+246} \lor \neg \left(t \leq 2.8 \cdot 10^{+226}\right):\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+225}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+184)
   (* y (- (/ t z)))
   (if (<= t 5.5e+225) (+ y x) (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+184) {
		tmp = y * -(t / z);
	} else if (t <= 5.5e+225) {
		tmp = y + x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.2d+184)) then
        tmp = y * -(t / z)
    else if (t <= 5.5d+225) then
        tmp = y + x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+184) {
		tmp = y * -(t / z);
	} else if (t <= 5.5e+225) {
		tmp = y + x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+184:
		tmp = y * -(t / z)
	elif t <= 5.5e+225:
		tmp = y + x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+184)
		tmp = Float64(y * Float64(-Float64(t / z)));
	elseif (t <= 5.5e+225)
		tmp = Float64(y + x);
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+184)
		tmp = y * -(t / z);
	elseif (t <= 5.5e+225)
		tmp = y + x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+184], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 5.5e+225], N[(y + x), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e184

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 76.0%

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

   4. Taylor expanded in z around 0 62.4%

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

      1. associate-*r/ 62.4%

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

      2. *-commutative 62.4%

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

      3. neg-mul-1 62.4%

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

      4. distribute-rgt-neg-in 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in x around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. associate-*r/ 69.2%

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

      3. distribute-lft-neg-in 69.2%

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

      4. cancel-sign-sub-inv 69.2%

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

   9. Simplified 69.2%

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

   10. Taylor expanded in x around 0 48.7%

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

       1. mul-1-neg 48.7%

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

       2. associate-/l* 55.5%

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

       3. associate-/r/ 55.1%

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

       4. distribute-rgt-neg-in 55.1%

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

   12. Simplified 55.1%

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

   if -4.2e184 < t < 5.49999999999999985e225

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 68.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 68.7%

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

   5. Simplified 68.7%

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

   if 5.49999999999999985e225 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. *-lft-identity 63.3%

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

      4. times-frac 68.9%

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

      5. /-rgt-identity 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. associate-*r/ 50.9%

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

      3. *-commutative 50.9%

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

      4. distribute-rgt-neg-out 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in z around 0 45.6%

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

       1. associate-/l* 57.2%

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

   11. Simplified 57.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+225}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.0% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 14: 60.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in z around inf 61.6%

   \[\leadsto \color{blue}{x + y} \]
4. Step-by-step derivation

   1. +-commutative 61.6%

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

5. Simplified 61.6%

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

6. Final simplification 61.6%

   \[\leadsto y + x \]
7. Add Preprocessing

Alternative 15: 49.9% 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 98.4%

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

3. Taylor expanded in x around inf 47.1%

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

4. Final simplification 47.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% 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 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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