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

Percentage Accurate: 98.0% → 98.2%

Time: 11.1s

Alternatives: 17

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: 98.2% 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]

Derivation

1. Initial program 98.8%

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

   1. clear-num 98.8%

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

   2. un-div-inv 98.8%

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

4. Applied egg-rr 98.8%

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

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -5e-8)
     (+ x (/ (* y t) (- a z)))
     (if (<= t_1 4e-6)
       (+ x (* y (/ (- t z) a)))
       (if (<= t_1 1000000.0)
         (- x (* y (/ (- t z) z)))
         (+ x (* y (/ t (- a z)))))))))

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-8) {
		tmp = x + ((y * t) / (a - z));
	} else if (t_1 <= 4e-6) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 1000000.0) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if (t_1 <= (-5d-8)) then
        tmp = x + ((y * t) / (a - z))
    else if (t_1 <= 4d-6) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 1000000.0d0) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = x + (y * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e-8) {
		tmp = x + ((y * t) / (a - z));
	} else if (t_1 <= 4e-6) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 1000000.0) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -5e-8:
		tmp = x + ((y * t) / (a - z))
	elif t_1 <= 4e-6:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 1000000.0:
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = x + (y * (t / (a - z)))
	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-8)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (t_1 <= 4e-6)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 1000000.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	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-8)
		tmp = x + ((y * t) / (a - z));
	elseif (t_1 <= 4e-6)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 1000000.0)
		tmp = x - (y * ((t - z) / z));
	else
		tmp = x + (y * (t / (a - z)));
	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-8], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-6], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.9999999999999998e-8

   1. Initial program 97.3%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in t around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. associate-/l* 91.9%

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

      3. distribute-lft-neg-out 91.9%

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

      4. *-commutative 91.9%

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

   7. Simplified 91.9%

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

      1. *-commutative 91.9%

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

      2. add-sqr-sqrt 51.7%

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

      3. sqrt-unprod 50.8%

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

      4. sqr-neg 50.8%

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

      5. sqrt-unprod 17.7%

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

      6. add-sqr-sqrt 27.9%

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

      7. cancel-sign-sub-inv 27.9%

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

      8. *-commutative 27.9%

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

      9. associate-*l/ 27.9%

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

      10. add-sqr-sqrt 17.7%

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

      11. sqrt-unprod 50.9%

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

      12. sqr-neg 50.9%

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

      13. sqrt-unprod 54.1%

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

      14. add-sqr-sqrt 99.1%

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

   9. Applied egg-rr 99.1%

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

   if -4.9999999999999998e-8 < (/.f64 (-.f64 z t) (-.f64 z a)) < 3.99999999999999982e-6

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in a around inf 85.5%

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

      1. +-commutative 85.5%

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

      2. mul-1-neg 85.5%

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

      3. associate-/l* 97.7%

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

      4. distribute-rgt-neg-in 97.7%

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

      5. distribute-frac-neg 97.7%

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

      6. neg-sub0 97.7%

         \[\leadsto y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{a} + x \]

      7. sub-neg 97.7%

         \[\leadsto y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{a} + x \]

      8. +-commutative 97.7%

         \[\leadsto y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{a} + x \]

      9. associate--r+ 97.7%

         \[\leadsto y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{a} + x \]

      10. neg-sub0 97.7%

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

      11. remove-double-neg 97.7%

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

   7. Simplified 97.7%

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

   if 3.99999999999999982e-6 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e6

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.4%

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

   if 1e6 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. mul-1-neg 90.1%

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

      3. distribute-lft-neg-out 90.1%

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

      4. *-commutative 90.1%

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

      5. *-lft-identity 90.1%

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

      6. times-frac 96.7%

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

      7. /-rgt-identity 96.7%

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

      8. distribute-neg-frac 96.7%

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

      9. distribute-neg-frac2 96.7%

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

      10. neg-sub0 96.7%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 96.7%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 96.7%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 96.7%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 96.7%

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

      15. remove-double-neg 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 1000000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x + y \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -2000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (+ x (* y (/ t (- a z))))))
   (if (<= t_1 -2000000000.0)
     t_2
     (if (<= t_1 4e-6)
       (+ x (* y (/ (- t z) a)))
       (if (<= t_1 1000000.0) (- 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 / (a - z)));
	double tmp;
	if (t_1 <= -2000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 4e-6) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 1000000.0) {
		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 / (a - z)))
    if (t_1 <= (-2000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 4d-6) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 1000000.0d0) 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 / (a - z)));
	double tmp;
	if (t_1 <= -2000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 4e-6) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 1000000.0) {
		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 / (a - z)))
	tmp = 0
	if t_1 <= -2000000000.0:
		tmp = t_2
	elif t_1 <= 4e-6:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 1000000.0:
		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(y * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2000000000.0)
		tmp = t_2;
	elseif (t_1 <= 4e-6)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 1000000.0)
		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 / (a - z)));
	tmp = 0.0;
	if (t_1 <= -2000000000.0)
		tmp = t_2;
	elseif (t_1 <= 4e-6)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 1000000.0)
		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[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2000000000.0], t$95$2, If[LessEqual[t$95$1, 4e-6], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], 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)) < -2e9 or 1e6 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 94.6%

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

      1. associate-*r/ 94.6%

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

      2. mul-1-neg 94.6%

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

      3. distribute-lft-neg-out 94.6%

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

      4. *-commutative 94.6%

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

      5. *-lft-identity 94.6%

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

      6. times-frac 96.5%

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

      7. /-rgt-identity 96.5%

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

      8. distribute-neg-frac 96.5%

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

      9. distribute-neg-frac2 96.5%

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

      10. neg-sub0 96.5%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 96.5%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 96.5%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 96.5%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 96.5%

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

      15. remove-double-neg 96.5%

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

   5. Simplified 96.5%

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

   if -2e9 < (/.f64 (-.f64 z t) (-.f64 z a)) < 3.99999999999999982e-6

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in a around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. associate-/l* 97.8%

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

      4. distribute-rgt-neg-in 97.8%

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

      5. distribute-frac-neg 97.8%

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

      6. neg-sub0 97.8%

         \[\leadsto y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{a} + x \]

      7. sub-neg 97.8%

         \[\leadsto y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{a} + x \]

      8. +-commutative 97.8%

         \[\leadsto y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{a} + x \]

      9. associate--r+ 97.8%

         \[\leadsto y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{a} + x \]

      10. neg-sub0 97.8%

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

      11. remove-double-neg 97.8%

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

   7. Simplified 97.8%

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

   if 3.99999999999999982e-6 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e6

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -2000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 1000000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x + y \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 1000000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (+ x (* y (/ t (- a z))))))
   (if (<= t_1 -5e-8)
     t_2
     (if (<= t_1 4e-6)
       (- x (* y (/ z a)))
       (if (<= t_1 1000000.0) (- 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 / (a - z)));
	double tmp;
	if (t_1 <= -5e-8) {
		tmp = t_2;
	} else if (t_1 <= 4e-6) {
		tmp = x - (y * (z / a));
	} else if (t_1 <= 1000000.0) {
		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 / (a - z)))
    if (t_1 <= (-5d-8)) then
        tmp = t_2
    else if (t_1 <= 4d-6) then
        tmp = x - (y * (z / a))
    else if (t_1 <= 1000000.0d0) 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 / (a - z)));
	double tmp;
	if (t_1 <= -5e-8) {
		tmp = t_2;
	} else if (t_1 <= 4e-6) {
		tmp = x - (y * (z / a));
	} else if (t_1 <= 1000000.0) {
		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 / (a - z)))
	tmp = 0
	if t_1 <= -5e-8:
		tmp = t_2
	elif t_1 <= 4e-6:
		tmp = x - (y * (z / a))
	elif t_1 <= 1000000.0:
		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(y * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-8)
		tmp = t_2;
	elseif (t_1 <= 4e-6)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (t_1 <= 1000000.0)
		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 / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-8)
		tmp = t_2;
	elseif (t_1 <= 4e-6)
		tmp = x - (y * (z / a));
	elseif (t_1 <= 1000000.0)
		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[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-8], t$95$2, If[LessEqual[t$95$1, 4e-6], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000.0], 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)) < -4.9999999999999998e-8 or 1e6 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 94.7%

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

      1. associate-*r/ 94.7%

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

      2. mul-1-neg 94.7%

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

      3. distribute-lft-neg-out 94.7%

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

      4. *-commutative 94.7%

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

      5. *-lft-identity 94.7%

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

      6. times-frac 96.6%

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

      7. /-rgt-identity 96.6%

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

      8. distribute-neg-frac 96.6%

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

      9. distribute-neg-frac2 96.6%

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

      10. neg-sub0 96.6%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 96.6%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 96.6%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 96.6%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 96.6%

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

      15. remove-double-neg 96.6%

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

   5. Simplified 96.6%

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

   if -4.9999999999999998e-8 < (/.f64 (-.f64 z t) (-.f64 z a)) < 3.99999999999999982e-6

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-/l* 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in z around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 86.0%

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

   10. Simplified 86.0%

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

   if 3.99999999999999982e-6 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e6

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 99.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 1000000:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x + y \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 1.00001:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (+ x (* y (/ t (- a z))))))
   (if (<= t_1 -5e-8)
     t_2
     (if (<= t_1 4e-6)
       (- x (* y (/ z a)))
       (if (<= t_1 1.00001) (+ x y) 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 / (a - z)));
	double tmp;
	if (t_1 <= -5e-8) {
		tmp = t_2;
	} else if (t_1 <= 4e-6) {
		tmp = x - (y * (z / a));
	} else if (t_1 <= 1.00001) {
		tmp = x + y;
	} 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 / (a - z)))
    if (t_1 <= (-5d-8)) then
        tmp = t_2
    else if (t_1 <= 4d-6) then
        tmp = x - (y * (z / a))
    else if (t_1 <= 1.00001d0) then
        tmp = x + y
    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 / (a - z)));
	double tmp;
	if (t_1 <= -5e-8) {
		tmp = t_2;
	} else if (t_1 <= 4e-6) {
		tmp = x - (y * (z / a));
	} else if (t_1 <= 1.00001) {
		tmp = x + y;
	} 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 / (a - z)))
	tmp = 0
	if t_1 <= -5e-8:
		tmp = t_2
	elif t_1 <= 4e-6:
		tmp = x - (y * (z / a))
	elif t_1 <= 1.00001:
		tmp = x + y
	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(y * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-8)
		tmp = t_2;
	elseif (t_1 <= 4e-6)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (t_1 <= 1.00001)
		tmp = Float64(x + y);
	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 / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-8)
		tmp = t_2;
	elseif (t_1 <= 4e-6)
		tmp = x - (y * (z / a));
	elseif (t_1 <= 1.00001)
		tmp = x + y;
	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[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-8], t$95$2, If[LessEqual[t$95$1, 4e-6], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.00001], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.9999999999999998e-8 or 1.0000100000000001 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 94.3%

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

      1. associate-*r/ 94.3%

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

      2. mul-1-neg 94.3%

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

      3. distribute-lft-neg-out 94.3%

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

      4. *-commutative 94.3%

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

      5. *-lft-identity 94.3%

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

      6. times-frac 96.1%

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

      7. /-rgt-identity 96.1%

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

      8. distribute-neg-frac 96.1%

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

      9. distribute-neg-frac2 96.1%

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

      10. neg-sub0 96.1%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 96.1%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 96.1%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 96.1%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 96.1%

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

      15. remove-double-neg 96.1%

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

   5. Simplified 96.1%

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

   if -4.9999999999999998e-8 < (/.f64 (-.f64 z t) (-.f64 z a)) < 3.99999999999999982e-6

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-/l* 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in z around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 86.0%

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

   10. Simplified 86.0%

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

   if 3.99999999999999982e-6 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1.0000100000000001

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 1.00001:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot t\_1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -4e-8)
     (* y t_1)
     (if (<= t_1 4e-6)
       (- x (* y (/ z a)))
       (if (<= t_1 5e+35) (+ x y) (* y (/ t (- a z))))))))

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 <= -4e-8) {
		tmp = y * t_1;
	} else if (t_1 <= 4e-6) {
		tmp = x - (y * (z / a));
	} else if (t_1 <= 5e+35) {
		tmp = x + y;
	} else {
		tmp = y * (t / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if (t_1 <= (-4d-8)) then
        tmp = y * t_1
    else if (t_1 <= 4d-6) then
        tmp = x - (y * (z / a))
    else if (t_1 <= 5d+35) then
        tmp = x + y
    else
        tmp = y * (t / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -4e-8) {
		tmp = y * t_1;
	} else if (t_1 <= 4e-6) {
		tmp = x - (y * (z / a));
	} else if (t_1 <= 5e+35) {
		tmp = x + y;
	} else {
		tmp = y * (t / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -4e-8:
		tmp = y * t_1
	elif t_1 <= 4e-6:
		tmp = x - (y * (z / a))
	elif t_1 <= 5e+35:
		tmp = x + y
	else:
		tmp = y * (t / (a - z))
	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 <= -4e-8)
		tmp = Float64(y * t_1);
	elseif (t_1 <= 4e-6)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (t_1 <= 5e+35)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(t / Float64(a - z)));
	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 <= -4e-8)
		tmp = y * t_1;
	elseif (t_1 <= 4e-6)
		tmp = x - (y * (z / a));
	elseif (t_1 <= 5e+35)
		tmp = x + y;
	else
		tmp = y * (t / (a - z));
	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, -4e-8], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 4e-6], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+35], N[(x + y), $MachinePrecision], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.0000000000000001e-8

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-define 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 88.7%

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

      1. associate--l+ 88.7%

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

      2. div-sub 88.7%

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

   7. Simplified 88.7%

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

   8. Taylor expanded in x around 0 71.5%

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

      1. div-sub 71.5%

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

   10. Simplified 71.5%

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

   if -4.0000000000000001e-8 < (/.f64 (-.f64 z t) (-.f64 z a)) < 3.99999999999999982e-6

   1. Initial program 98.9%

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

      1. +-commutative 98.9%

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

      2. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. associate-/l* 86.3%

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

   10. Simplified 86.3%

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

   if 3.99999999999999982e-6 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.00000000000000021e35

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 96.8%

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

      1. +-commutative 96.8%

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

   7. Simplified 96.8%

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

   if 5.00000000000000021e35 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. fma-define 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around inf 83.3%

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

      1. associate--l+ 83.3%

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

      2. div-sub 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in x around 0 67.5%

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

      1. div-sub 67.5%

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

   10. Simplified 67.5%

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

   11. Taylor expanded in t around inf 62.1%

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

       1. associate-*r/ 91.8%

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

       2. mul-1-neg 91.8%

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

       3. distribute-lft-neg-out 91.8%

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

       4. *-commutative 91.8%

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

       5. *-lft-identity 91.8%

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

       6. times-frac 97.2%

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

       7. /-rgt-identity 97.2%

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

       8. distribute-neg-frac 97.2%

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

       9. distribute-neg-frac2 97.2%

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

       10. neg-sub0 97.2%

           \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

       11. sub-neg 97.2%

           \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

       12. +-commutative 97.2%

           \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

       13. associate--r+ 97.2%

           \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

       14. neg-sub0 97.2%

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

       15. remove-double-neg 97.2%

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

   13. Simplified 67.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-8} \lor \neg \left(t\_1 \leq 1.00001\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (or (<= t_1 -5e-8) (not (<= t_1 1.00001)))
     (+ x (* y (/ t (- a z))))
     (+ x (* y (/ z (- 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-8) || !(t_1 <= 1.00001)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    if ((t_1 <= (-5d-8)) .or. (.not. (t_1 <= 1.00001d0))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if ((t_1 <= -5e-8) || !(t_1 <= 1.00001)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if (t_1 <= -5e-8) or not (t_1 <= 1.00001):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (y * (z / (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-8) || !(t_1 <= 1.00001))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / 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-8) || ~((t_1 <= 1.00001)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (y * (z / (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[Or[LessEqual[t$95$1, -5e-8], N[Not[LessEqual[t$95$1, 1.00001]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.9999999999999998e-8 or 1.0000100000000001 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 94.3%

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

      1. associate-*r/ 94.3%

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

      2. mul-1-neg 94.3%

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

      3. distribute-lft-neg-out 94.3%

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

      4. *-commutative 94.3%

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

      5. *-lft-identity 94.3%

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

      6. times-frac 96.1%

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

      7. /-rgt-identity 96.1%

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

      8. distribute-neg-frac 96.1%

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

      9. distribute-neg-frac2 96.1%

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

      10. neg-sub0 96.1%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 96.1%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 96.1%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 96.1%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 96.1%

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

      15. remove-double-neg 96.1%

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

   5. Simplified 96.1%

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

   if -4.9999999999999998e-8 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1.0000100000000001

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 92.5%

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

   7. Simplified 92.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-8} \lor \neg \left(\frac{z - t}{z - a} \leq 1.00001\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-19}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+82}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-15)
   (+ x y)
   (if (<= z 1.1e-19)
     (+ x (* t (/ y a)))
     (if (<= z 3.2e+82) (- x (* t (/ y z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-15) {
		tmp = x + y;
	} else if (z <= 1.1e-19) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.2e+82) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + 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 (z <= (-5.5d-15)) then
        tmp = x + y
    else if (z <= 1.1d-19) then
        tmp = x + (t * (y / a))
    else if (z <= 3.2d+82) then
        tmp = x - (t * (y / z))
    else
        tmp = x + 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 (z <= -5.5e-15) {
		tmp = x + y;
	} else if (z <= 1.1e-19) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.2e+82) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-15:
		tmp = x + y
	elif z <= 1.1e-19:
		tmp = x + (t * (y / a))
	elif z <= 3.2e+82:
		tmp = x - (t * (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-15)
		tmp = Float64(x + y);
	elseif (z <= 1.1e-19)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.2e+82)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-15)
		tmp = x + y;
	elseif (z <= 1.1e-19)
		tmp = x + (t * (y / a));
	elseif (z <= 3.2e+82)
		tmp = x - (t * (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-15], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.1e-19], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+82], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e-15 or 3.19999999999999975e82 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.9%

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

      1. +-commutative 78.9%

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

   7. Simplified 78.9%

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

   if -5.5000000000000002e-15 < z < 1.0999999999999999e-19

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if 1.0999999999999999e-19 < z < 3.19999999999999975e82

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.6%

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

      1. associate-*r/ 80.6%

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

      2. mul-1-neg 80.6%

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

      3. distribute-lft-neg-out 80.6%

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

      4. *-commutative 80.6%

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

      5. *-lft-identity 80.6%

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

      6. times-frac 89.2%

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

      7. /-rgt-identity 89.2%

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

      8. distribute-neg-frac 89.2%

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

      9. distribute-neg-frac2 89.2%

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

      10. neg-sub0 89.2%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 89.2%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 89.2%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 89.2%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 89.2%

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

      15. remove-double-neg 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in a around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. unsub-neg 80.2%

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

      3. associate-/l* 81.4%

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

   8. Simplified 81.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-19}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+82}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-15} \lor \neg \left(z \leq 1.9 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e-15) (not (<= z 1.9e+79))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e-15) || !(z <= 1.9e+79)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4d-15)) .or. (.not. (z <= 1.9d+79))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e-15) || !(z <= 1.9e+79)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e-15) or not (z <= 1.9e+79):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e-15) || !(z <= 1.9e+79))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e-15) || ~((z <= 1.9e+79)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e-15], N[Not[LessEqual[z, 1.9e+79]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000003e-15 or 1.9000000000000001e79 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -4.0000000000000003e-15 < z < 1.9000000000000001e79

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-define 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-15} \lor \neg \left(z \leq 1.9 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16} \lor \neg \left(z \leq 1.9 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e-16) (not (<= z 1.9e+79))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e-16) || !(z <= 1.9e+79)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d-16)) .or. (.not. (z <= 1.9d+79))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e-16) || !(z <= 1.9e+79)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e-16) or not (z <= 1.9e+79):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e-16) || !(z <= 1.9e+79))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e-16) || ~((z <= 1.9e+79)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e-16], N[Not[LessEqual[z, 1.9e+79]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e-16 or 1.9000000000000001e79 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -8.5000000000000001e-16 < z < 1.9000000000000001e79

   1. Initial program 98.0%

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

      1. clear-num 98.0%

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

      2. un-div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in z around 0 75.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16} \lor \neg \left(z \leq 1.9 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-16} \lor \neg \left(z \leq 7.6 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e-16) (not (<= z 7.6e+79))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-16) || !(z <= 7.6e+79)) {
		tmp = x + y;
	} 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-16)) .or. (.not. (z <= 7.6d+79))) then
        tmp = x + y
    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-16) || !(z <= 7.6e+79)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e-16) or not (z <= 7.6e+79):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e-16) || !(z <= 7.6e+79))
		tmp = Float64(x + y);
	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-16) || ~((z <= 7.6e+79)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e-16], N[Not[LessEqual[z, 7.6e+79]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000003e-16 or 7.6000000000000005e79 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -9.0000000000000003e-16 < z < 7.6000000000000005e79

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 75.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-16} \lor \neg \left(z \leq 7.6 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+71} \lor \neg \left(y \leq 6.8 \cdot 10^{+221}\right):\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.2e+71) (not (<= y 6.8e+221))) (* y (/ t (- a z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+71) || !(y <= 6.8e+221)) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x + 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 ((y <= (-8.2d+71)) .or. (.not. (y <= 6.8d+221))) then
        tmp = y * (t / (a - z))
    else
        tmp = x + 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 ((y <= -8.2e+71) || !(y <= 6.8e+221)) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.2e+71) or not (y <= 6.8e+221):
		tmp = y * (t / (a - z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.2e+71) || !(y <= 6.8e+221))
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.2e+71) || ~((y <= 6.8e+221)))
		tmp = y * (t / (a - z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.2e+71], N[Not[LessEqual[y, 6.8e+221]], $MachinePrecision]], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000004e71 or 6.7999999999999997e221 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. div-sub 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 83.1%

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

      1. div-sub 83.1%

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

   10. Simplified 83.1%

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

   11. Taylor expanded in t around inf 39.2%

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

       1. associate-*r/ 51.7%

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

       2. mul-1-neg 51.7%

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

       3. distribute-lft-neg-out 51.7%

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

       4. *-commutative 51.7%

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

       5. *-lft-identity 51.7%

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

       6. times-frac 67.1%

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

       7. /-rgt-identity 67.1%

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

       8. distribute-neg-frac 67.1%

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

       9. distribute-neg-frac2 67.1%

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

       10. neg-sub0 67.1%

           \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

       11. sub-neg 67.1%

           \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

       12. +-commutative 67.1%

           \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

       13. associate--r+ 67.1%

           \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

       14. neg-sub0 67.1%

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

       15. remove-double-neg 67.1%

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

   13. Simplified 51.4%

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

   if -8.2000000000000004e71 < y < 6.7999999999999997e221

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 70.3%

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

      1. +-commutative 70.3%

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

   7. Simplified 70.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+71} \lor \neg \left(y \leq 6.8 \cdot 10^{+221}\right):\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+207}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e+72)
   (* y (/ t (- a z)))
   (if (<= y 1.7e+207) (+ x y) (* y (/ (- z t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+72) {
		tmp = y * (t / (a - z));
	} else if (y <= 1.7e+207) {
		tmp = x + y;
	} else {
		tmp = y * ((z - 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) :: tmp
    if (y <= (-1.2d+72)) then
        tmp = y * (t / (a - z))
    else if (y <= 1.7d+207) then
        tmp = x + y
    else
        tmp = y * ((z - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+72) {
		tmp = y * (t / (a - z));
	} else if (y <= 1.7e+207) {
		tmp = x + y;
	} else {
		tmp = y * ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e+72:
		tmp = y * (t / (a - z))
	elif y <= 1.7e+207:
		tmp = x + y
	else:
		tmp = y * ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e+72)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= 1.7e+207)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(z - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.2e+72)
		tmp = y * (t / (a - z));
	elseif (y <= 1.7e+207)
		tmp = x + y;
	else
		tmp = y * ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e+72], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+207], N[(x + y), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.20000000000000005e72

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. div-sub 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 79.8%

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

      1. div-sub 79.8%

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

   10. Simplified 79.8%

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

   11. Taylor expanded in t around inf 36.2%

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

       1. associate-*r/ 50.3%

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

       2. mul-1-neg 50.3%

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

       3. distribute-lft-neg-out 50.3%

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

       4. *-commutative 50.3%

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

       5. *-lft-identity 50.3%

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

       6. times-frac 68.7%

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

       7. /-rgt-identity 68.7%

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

       8. distribute-neg-frac 68.7%

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

       9. distribute-neg-frac2 68.7%

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

       10. neg-sub0 68.7%

           \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

       11. sub-neg 68.7%

           \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

       12. +-commutative 68.7%

           \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

       13. associate--r+ 68.7%

           \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

       14. neg-sub0 68.7%

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

       15. remove-double-neg 68.7%

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

   13. Simplified 50.3%

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

   if -1.20000000000000005e72 < y < 1.6999999999999999e207

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 71.0%

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

      1. +-commutative 71.0%

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

   7. Simplified 71.0%

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

   if 1.6999999999999999e207 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 82.2%

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

      1. div-sub 82.2%

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

   10. Simplified 82.2%

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

   11. Taylor expanded in a around 0 61.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+207}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e+46) x (if (<= a 3.7e+98) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+46) {
		tmp = x;
	} else if (a <= 3.7e+98) {
		tmp = x + y;
	} 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 <= (-6.8d+46)) then
        tmp = x
    else if (a <= 3.7d+98) then
        tmp = x + y
    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 <= -6.8e+46) {
		tmp = x;
	} else if (a <= 3.7e+98) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e+46:
		tmp = x
	elif a <= 3.7e+98:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e+46)
		tmp = x;
	elseif (a <= 3.7e+98)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e+46)
		tmp = x;
	elseif (a <= 3.7e+98)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e+46], x, If[LessEqual[a, 3.7e+98], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.7999999999999996e46 or 3.6999999999999999e98 < a

   1. Initial program 98.9%

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

      1. +-commutative 98.9%

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

      2. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around 0 64.3%

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

   if -6.7999999999999996e46 < a < 3.6999999999999999e98

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 65.7%

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

      1. +-commutative 65.7%

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

   7. Simplified 65.7%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.2e-270) x (if (<= x 1.2e-145) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.2e-270) {
		tmp = x;
	} else if (x <= 1.2e-145) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.2d-270)) then
        tmp = x
    else if (x <= 1.2d-145) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.2e-270) {
		tmp = x;
	} else if (x <= 1.2e-145) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.2e-270:
		tmp = x
	elif x <= 1.2e-145:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.2e-270)
		tmp = x;
	elseif (x <= 1.2e-145)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.2e-270)
		tmp = x;
	elseif (x <= 1.2e-145)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.2e-270], x, If[LessEqual[x, 1.2e-145], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e-270 or 1.20000000000000008e-145 < x

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 63.5%

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

   if -6.2e-270 < x < 1.20000000000000008e-145

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. fma-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 97.5%

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

      1. associate--l+ 97.5%

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

      2. div-sub 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 91.9%

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

      1. div-sub 91.9%

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

   10. Simplified 91.9%

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

   11. Taylor expanded in z around inf 36.0%

       \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 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 98.8%

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

Alternative 17: 50.8% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. +-commutative 98.8%

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

   2. fma-define 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. Add Preprocessing

5. Taylor expanded in y around 0 54.6%

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

Developer Target 1: 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 2024170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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