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

Percentage Accurate: 77.0% → 88.3%

Time: 11.5s

Alternatives: 11

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-22}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+176)
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (if (<= t 3e-22)
     (- (+ x y) (* (/ y (- a t)) (- z t)))
     (- x (* y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+176) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 3e-22) {
		tmp = (x + y) - ((y / (a - t)) * (z - t));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.6d+176)) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else if (t <= 3d-22) then
        tmp = (x + y) - ((y / (a - t)) * (z - t))
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+176) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 3e-22) {
		tmp = (x + y) - ((y / (a - t)) * (z - t));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+176:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	elif t <= 3e-22:
		tmp = (x + y) - ((y / (a - t)) * (z - t))
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e+176)
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	elseif (t <= 3e-22)
		tmp = Float64(Float64(x + y) - Float64(Float64(y / Float64(a - t)) * Float64(z - t)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+176)
		tmp = (x - (a * (y / t))) + (y * (z / t));
	elseif (t <= 3e-22)
		tmp = (x + y) - ((y / (a - t)) * (z - t));
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e+176], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-22], N[(N[(x + y), $MachinePrecision] - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6000000000000005e176

   1. Initial program 46.6%

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

   3. Taylor expanded in y around 0 46.6%

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

      1. associate-*l/ 54.4%

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

   5. Simplified 54.4%

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

      1. associate-*l/ 46.6%

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

      2. associate-*r/ 57.9%

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

      3. clear-num 57.9%

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

      4. un-div-inv 58.0%

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

   7. Applied egg-rr 58.0%

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

   8. Taylor expanded in t around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. mul-1-neg 85.3%

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

      3. unsub-neg 85.3%

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

      4. associate-/l* 88.9%

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

      5. mul-1-neg 88.9%

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

      6. remove-double-neg 88.9%

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

      7. associate-/l* 89.2%

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

   10. Simplified 89.2%

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

   if -5.6000000000000005e176 < t < 2.9999999999999999e-22

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 93.2%

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

   5. Simplified 93.2%

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

   if 2.9999999999999999e-22 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. distribute-lft-out-- 79.7%

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

      3. div-sub 79.7%

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

      4. mul-1-neg 79.7%

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

      5. unsub-neg 79.7%

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

      6. *-commutative 79.7%

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

      7. distribute-lft-out-- 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 81.1%

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

      1. neg-mul-1 81.1%

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

      2. sub-neg 81.1%

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

      3. associate-*r/ 88.2%

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

   8. Simplified 88.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-22}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a - z}{t}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -380000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- a z) t)))))
   (if (<= a -1.6e+83)
     (+ x y)
     (if (<= a -380000000000.0)
       t_1
       (if (<= a -1.62e-25)
         (+ x y)
         (if (<= a -2.3e-71)
           (* z (/ y (- t a)))
           (if (<= a 8.8e+49) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (a <= -1.6e+83) {
		tmp = x + y;
	} else if (a <= -380000000000.0) {
		tmp = t_1;
	} else if (a <= -1.62e-25) {
		tmp = x + y;
	} else if (a <= -2.3e-71) {
		tmp = z * (y / (t - a));
	} else if (a <= 8.8e+49) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((a - z) / t))
    if (a <= (-1.6d+83)) then
        tmp = x + y
    else if (a <= (-380000000000.0d0)) then
        tmp = t_1
    else if (a <= (-1.62d-25)) then
        tmp = x + y
    else if (a <= (-2.3d-71)) then
        tmp = z * (y / (t - a))
    else if (a <= 8.8d+49) then
        tmp = t_1
    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 t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (a <= -1.6e+83) {
		tmp = x + y;
	} else if (a <= -380000000000.0) {
		tmp = t_1;
	} else if (a <= -1.62e-25) {
		tmp = x + y;
	} else if (a <= -2.3e-71) {
		tmp = z * (y / (t - a));
	} else if (a <= 8.8e+49) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((a - z) / t))
	tmp = 0
	if a <= -1.6e+83:
		tmp = x + y
	elif a <= -380000000000.0:
		tmp = t_1
	elif a <= -1.62e-25:
		tmp = x + y
	elif a <= -2.3e-71:
		tmp = z * (y / (t - a))
	elif a <= 8.8e+49:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -1.6e+83)
		tmp = Float64(x + y);
	elseif (a <= -380000000000.0)
		tmp = t_1;
	elseif (a <= -1.62e-25)
		tmp = Float64(x + y);
	elseif (a <= -2.3e-71)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 8.8e+49)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((a - z) / t));
	tmp = 0.0;
	if (a <= -1.6e+83)
		tmp = x + y;
	elseif (a <= -380000000000.0)
		tmp = t_1;
	elseif (a <= -1.62e-25)
		tmp = x + y;
	elseif (a <= -2.3e-71)
		tmp = z * (y / (t - a));
	elseif (a <= 8.8e+49)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+83], N[(x + y), $MachinePrecision], If[LessEqual[a, -380000000000.0], t$95$1, If[LessEqual[a, -1.62e-25], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.3e-71], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+49], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5999999999999999e83 or -3.8e11 < a < -1.62e-25 or 8.8000000000000003e49 < a

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 84.1%

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

      1. +-commutative 84.1%

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

   5. Simplified 84.1%

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

   if -1.5999999999999999e83 < a < -3.8e11 or -2.2999999999999998e-71 < a < 8.8000000000000003e49

   1. Initial program 74.5%

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

   3. Taylor expanded in t around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. distribute-lft-out-- 79.1%

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

      3. div-sub 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. *-commutative 80.0%

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

      7. distribute-lft-out-- 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in t around inf 80.0%

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

      1. neg-mul-1 80.0%

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

      2. sub-neg 80.0%

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

      3. associate-*r/ 78.8%

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

   8. Simplified 78.8%

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

   if -1.62e-25 < a < -2.2999999999999998e-71

   1. Initial program 51.9%

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

      1. sub-neg 51.9%

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

      2. +-commutative 51.9%

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

      3. distribute-frac-neg 51.9%

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

      4. distribute-rgt-neg-out 51.9%

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

      5. associate-/l* 52.0%

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

      6. fma-define 51.4%

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

      7. distribute-frac-neg 51.4%

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

      8. distribute-neg-frac2 51.4%

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

      9. sub-neg 51.4%

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

      10. distribute-neg-in 51.4%

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

      11. remove-double-neg 51.4%

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

      12. +-commutative 51.4%

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

      13. sub-neg 51.4%

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

   3. Simplified 51.4%

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

   5. Taylor expanded in z around inf 68.1%

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

      1. clear-num 67.8%

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

      2. inv-pow 67.8%

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

   7. Applied egg-rr 67.8%

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

      1. unpow-1 67.8%

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

   9. Simplified 67.8%

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

       1. clear-num 68.1%

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

       2. *-commutative 68.1%

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

       3. associate-*r/ 68.1%

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

       4. *-commutative 68.1%

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

   11. Applied egg-rr 68.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -380000000000:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -22000000000:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.25e+83)
   (+ x y)
   (if (<= a -22000000000.0)
     (- x (* y (/ (- a z) t)))
     (if (<= a -8.8e-26)
       (+ x y)
       (if (<= a -2.3e-71)
         (* z (/ y (- t a)))
         (if (<= a 4e+48) (+ x (/ (* y (- z a)) t)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.25e+83) {
		tmp = x + y;
	} else if (a <= -22000000000.0) {
		tmp = x - (y * ((a - z) / t));
	} else if (a <= -8.8e-26) {
		tmp = x + y;
	} else if (a <= -2.3e-71) {
		tmp = z * (y / (t - a));
	} else if (a <= 4e+48) {
		tmp = x + ((y * (z - a)) / t);
	} 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 (a <= (-3.25d+83)) then
        tmp = x + y
    else if (a <= (-22000000000.0d0)) then
        tmp = x - (y * ((a - z) / t))
    else if (a <= (-8.8d-26)) then
        tmp = x + y
    else if (a <= (-2.3d-71)) then
        tmp = z * (y / (t - a))
    else if (a <= 4d+48) then
        tmp = x + ((y * (z - a)) / t)
    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 (a <= -3.25e+83) {
		tmp = x + y;
	} else if (a <= -22000000000.0) {
		tmp = x - (y * ((a - z) / t));
	} else if (a <= -8.8e-26) {
		tmp = x + y;
	} else if (a <= -2.3e-71) {
		tmp = z * (y / (t - a));
	} else if (a <= 4e+48) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.25e+83:
		tmp = x + y
	elif a <= -22000000000.0:
		tmp = x - (y * ((a - z) / t))
	elif a <= -8.8e-26:
		tmp = x + y
	elif a <= -2.3e-71:
		tmp = z * (y / (t - a))
	elif a <= 4e+48:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.25e+83)
		tmp = Float64(x + y);
	elseif (a <= -22000000000.0)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (a <= -8.8e-26)
		tmp = Float64(x + y);
	elseif (a <= -2.3e-71)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 4e+48)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.25e+83)
		tmp = x + y;
	elseif (a <= -22000000000.0)
		tmp = x - (y * ((a - z) / t));
	elseif (a <= -8.8e-26)
		tmp = x + y;
	elseif (a <= -2.3e-71)
		tmp = z * (y / (t - a));
	elseif (a <= 4e+48)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.25e+83], N[(x + y), $MachinePrecision], If[LessEqual[a, -22000000000.0], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.8e-26], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.3e-71], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+48], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2500000000000001e83 or -2.2e10 < a < -8.8000000000000003e-26 or 4.00000000000000018e48 < a

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 84.1%

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

      1. +-commutative 84.1%

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

   5. Simplified 84.1%

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

   if -3.2500000000000001e83 < a < -2.2e10

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. distribute-lft-out-- 81.6%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. *-commutative 81.6%

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

      7. distribute-lft-out-- 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in t around inf 81.6%

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

      1. neg-mul-1 81.6%

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

      2. sub-neg 81.6%

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

      3. associate-*r/ 81.8%

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

   8. Simplified 81.8%

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

   if -8.8000000000000003e-26 < a < -2.2999999999999998e-71

   1. Initial program 51.9%

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

      1. sub-neg 51.9%

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

      2. +-commutative 51.9%

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

      3. distribute-frac-neg 51.9%

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

      4. distribute-rgt-neg-out 51.9%

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

      5. associate-/l* 52.0%

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

      6. fma-define 51.4%

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

      7. distribute-frac-neg 51.4%

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

      8. distribute-neg-frac2 51.4%

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

      9. sub-neg 51.4%

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

      10. distribute-neg-in 51.4%

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

      11. remove-double-neg 51.4%

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

      12. +-commutative 51.4%

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

      13. sub-neg 51.4%

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

   3. Simplified 51.4%

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

   5. Taylor expanded in z around inf 68.1%

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

      1. clear-num 67.8%

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

      2. inv-pow 67.8%

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

   7. Applied egg-rr 67.8%

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

      1. unpow-1 67.8%

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

   9. Simplified 67.8%

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

       1. clear-num 68.1%

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

       2. *-commutative 68.1%

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

       3. associate-*r/ 68.1%

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

       4. *-commutative 68.1%

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

   11. Applied egg-rr 68.1%

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

   if -2.2999999999999998e-71 < a < 4.00000000000000018e48

   1. Initial program 74.7%

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

   3. Taylor expanded in t around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. distribute-lft-out-- 78.8%

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

      3. div-sub 79.8%

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

      4. mul-1-neg 79.8%

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

      5. unsub-neg 79.8%

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

      6. *-commutative 79.8%

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

      7. distribute-lft-out-- 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -22000000000:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a \cdot y}{t}\\ \mathbf{if}\;a \leq -2 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* a y) t))))
   (if (<= a -2e-26)
     (+ x y)
     (if (<= a 8.2e-74)
       t_1
       (if (<= a 3.5e-31)
         (* z (/ y (- t a)))
         (if (<= a 5.2e+47) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((a * y) / t);
	double tmp;
	if (a <= -2e-26) {
		tmp = x + y;
	} else if (a <= 8.2e-74) {
		tmp = t_1;
	} else if (a <= 3.5e-31) {
		tmp = z * (y / (t - a));
	} else if (a <= 5.2e+47) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - ((a * y) / t)
    if (a <= (-2d-26)) then
        tmp = x + y
    else if (a <= 8.2d-74) then
        tmp = t_1
    else if (a <= 3.5d-31) then
        tmp = z * (y / (t - a))
    else if (a <= 5.2d+47) then
        tmp = t_1
    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 t_1 = x - ((a * y) / t);
	double tmp;
	if (a <= -2e-26) {
		tmp = x + y;
	} else if (a <= 8.2e-74) {
		tmp = t_1;
	} else if (a <= 3.5e-31) {
		tmp = z * (y / (t - a));
	} else if (a <= 5.2e+47) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((a * y) / t)
	tmp = 0
	if a <= -2e-26:
		tmp = x + y
	elif a <= 8.2e-74:
		tmp = t_1
	elif a <= 3.5e-31:
		tmp = z * (y / (t - a))
	elif a <= 5.2e+47:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(a * y) / t))
	tmp = 0.0
	if (a <= -2e-26)
		tmp = Float64(x + y);
	elseif (a <= 8.2e-74)
		tmp = t_1;
	elseif (a <= 3.5e-31)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 5.2e+47)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((a * y) / t);
	tmp = 0.0;
	if (a <= -2e-26)
		tmp = x + y;
	elseif (a <= 8.2e-74)
		tmp = t_1;
	elseif (a <= 3.5e-31)
		tmp = z * (y / (t - a));
	elseif (a <= 5.2e+47)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e-26], N[(x + y), $MachinePrecision], If[LessEqual[a, 8.2e-74], t$95$1, If[LessEqual[a, 3.5e-31], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+47], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0000000000000001e-26 or 5.20000000000000007e47 < a

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 80.0%

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

      1. +-commutative 80.0%

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

   5. Simplified 80.0%

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

   if -2.0000000000000001e-26 < a < 8.20000000000000063e-74 or 3.49999999999999985e-31 < a < 5.20000000000000007e47

   1. Initial program 71.5%

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

   3. Taylor expanded in t around inf 80.3%

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

      1. associate--l+ 80.3%

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

      2. distribute-lft-out-- 80.3%

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

      3. div-sub 80.5%

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

      4. mul-1-neg 80.5%

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

      5. unsub-neg 80.5%

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

      6. *-commutative 80.5%

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

      7. distribute-lft-out-- 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf 61.0%

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

      1. *-commutative 61.0%

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

   8. Simplified 61.0%

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

   if 8.20000000000000063e-74 < a < 3.49999999999999985e-31

   1. Initial program 90.8%

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

      1. sub-neg 90.8%

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

      2. +-commutative 90.8%

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

      3. distribute-frac-neg 90.8%

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

      4. distribute-rgt-neg-out 90.8%

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

      5. associate-/l* 91.0%

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

      6. fma-define 91.5%

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

      7. distribute-frac-neg 91.5%

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

      8. distribute-neg-frac2 91.5%

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

      9. sub-neg 91.5%

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

      10. distribute-neg-in 91.5%

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

      11. remove-double-neg 91.5%

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

      12. +-commutative 91.5%

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

      13. sub-neg 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around inf 72.7%

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

      1. clear-num 72.6%

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

      2. inv-pow 72.6%

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

   7. Applied egg-rr 72.6%

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

      1. unpow-1 72.6%

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

   9. Simplified 72.6%

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

       1. clear-num 72.7%

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

       2. *-commutative 72.7%

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

       3. associate-*r/ 72.9%

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

       4. *-commutative 72.9%

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

   11. Applied egg-rr 72.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+47}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+177} \lor \neg \left(t \leq 2.7 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e+177) (not (<= t 2.7e-22)))
   (- x (* y (/ (- a z) t)))
   (+ (+ x y) (* y (/ z (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+177) || !(t <= 2.7e-22)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) + (y * (z / (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 ((t <= (-1.25d+177)) .or. (.not. (t <= 2.7d-22))) then
        tmp = x - (y * ((a - z) / t))
    else
        tmp = (x + y) + (y * (z / (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 ((t <= -1.25e+177) || !(t <= 2.7e-22)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) + (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.25e+177) or not (t <= 2.7e-22):
		tmp = x - (y * ((a - z) / t))
	else:
		tmp = (x + y) + (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e+177) || !(t <= 2.7e-22))
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(y * Float64(z / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.25e+177) || ~((t <= 2.7e-22)))
		tmp = x - (y * ((a - z) / t));
	else
		tmp = (x + y) + (y * (z / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e+177], N[Not[LessEqual[t, 2.7e-22]], $MachinePrecision]], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2500000000000001e177 or 2.7000000000000002e-22 < t

   1. Initial program 57.5%

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

   3. Taylor expanded in t around inf 81.3%

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

      1. associate--l+ 81.3%

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

      2. distribute-lft-out-- 81.3%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. *-commutative 81.3%

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

      7. distribute-lft-out-- 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in t around inf 82.4%

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

      1. neg-mul-1 82.4%

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

      2. sub-neg 82.4%

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

      3. associate-*r/ 87.5%

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

   8. Simplified 87.5%

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

   if -1.2500000000000001e177 < t < 2.7000000000000002e-22

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 88.4%

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

      1. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+177} \lor \neg \left(t \leq 2.7 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176} \lor \neg \left(t \leq 3 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y}{\frac{t - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.6e+176) (not (<= t 3e-22)))
   (- x (* y (/ (- a z) t)))
   (+ (+ x y) (/ y (/ (- t a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.6e+176) || !(t <= 3e-22)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) + (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) :: tmp
    if ((t <= (-5.6d+176)) .or. (.not. (t <= 3d-22))) then
        tmp = x - (y * ((a - z) / t))
    else
        tmp = (x + y) + (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 tmp;
	if ((t <= -5.6e+176) || !(t <= 3e-22)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) + (y / ((t - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.6e+176) or not (t <= 3e-22):
		tmp = x - (y * ((a - z) / t))
	else:
		tmp = (x + y) + (y / ((t - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.6e+176) || !(t <= 3e-22))
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(y / Float64(Float64(t - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.6e+176) || ~((t <= 3e-22)))
		tmp = x - (y * ((a - z) / t));
	else
		tmp = (x + y) + (y / ((t - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.6e+176], N[Not[LessEqual[t, 3e-22]], $MachinePrecision]], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.6000000000000005e176 or 2.9999999999999999e-22 < t

   1. Initial program 57.5%

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

   3. Taylor expanded in t around inf 81.3%

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

      1. associate--l+ 81.3%

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

      2. distribute-lft-out-- 81.3%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. *-commutative 81.3%

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

      7. distribute-lft-out-- 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in t around inf 82.4%

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

      1. neg-mul-1 82.4%

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

      2. sub-neg 82.4%

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

      3. associate-*r/ 87.5%

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

   8. Simplified 87.5%

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

   if -5.6000000000000005e176 < t < 2.9999999999999999e-22

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 93.2%

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

   5. Simplified 93.2%

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

      1. associate-*l/ 88.3%

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

      2. associate-*r/ 93.1%

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

      3. clear-num 93.1%

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

      4. un-div-inv 93.2%

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

   7. Applied egg-rr 93.2%

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

   8. Taylor expanded in z around inf 92.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176} \lor \neg \left(t \leq 3 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y}{\frac{t - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-22}:\\ \;\;\;\;\left(x + y\right) + \frac{y}{\frac{t - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+177)
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (if (<= t 1.95e-22)
     (+ (+ x y) (/ y (/ (- t a) z)))
     (- x (* y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+177) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 1.95e-22) {
		tmp = (x + y) + (y / ((t - a) / z));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+177)) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else if (t <= 1.95d-22) then
        tmp = (x + y) + (y / ((t - a) / z))
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+177) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 1.95e-22) {
		tmp = (x + y) + (y / ((t - a) / z));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+177:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	elif t <= 1.95e-22:
		tmp = (x + y) + (y / ((t - a) / z))
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+177)
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	elseif (t <= 1.95e-22)
		tmp = Float64(Float64(x + y) + Float64(y / Float64(Float64(t - a) / z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+177)
		tmp = (x - (a * (y / t))) + (y * (z / t));
	elseif (t <= 1.95e-22)
		tmp = (x + y) + (y / ((t - a) / z));
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+177], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-22], N[(N[(x + y), $MachinePrecision] + N[(y / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.80000000000000002e177

   1. Initial program 46.6%

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

   3. Taylor expanded in y around 0 46.6%

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

      1. associate-*l/ 54.4%

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

   5. Simplified 54.4%

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

      1. associate-*l/ 46.6%

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

      2. associate-*r/ 57.9%

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

      3. clear-num 57.9%

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

      4. un-div-inv 58.0%

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

   7. Applied egg-rr 58.0%

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

   8. Taylor expanded in t around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. mul-1-neg 85.3%

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

      3. unsub-neg 85.3%

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

      4. associate-/l* 88.9%

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

      5. mul-1-neg 88.9%

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

      6. remove-double-neg 88.9%

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

      7. associate-/l* 89.2%

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

   10. Simplified 89.2%

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

   if -2.80000000000000002e177 < t < 1.94999999999999999e-22

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 93.2%

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

   5. Simplified 93.2%

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

      1. associate-*l/ 88.3%

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

      2. associate-*r/ 93.1%

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

      3. clear-num 93.1%

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

      4. un-div-inv 93.2%

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

   7. Applied egg-rr 93.2%

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

   8. Taylor expanded in z around inf 92.6%

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

   if 1.94999999999999999e-22 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. distribute-lft-out-- 79.7%

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

      3. div-sub 79.7%

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

      4. mul-1-neg 79.7%

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

      5. unsub-neg 79.7%

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

      6. *-commutative 79.7%

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

      7. distribute-lft-out-- 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 81.1%

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

      1. neg-mul-1 81.1%

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

      2. sub-neg 81.1%

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

      3. associate-*r/ 88.2%

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

   8. Simplified 88.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-22}:\\ \;\;\;\;\left(x + y\right) + \frac{y}{\frac{t - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+36} \lor \neg \left(t \leq 4.9 \cdot 10^{-23}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e+36) (not (<= t 4.9e-23)))
   (- x (* y (/ (- a z) t)))
   (- (+ x y) (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+36) || !(t <= 4.9e-23)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.7d+36)) .or. (.not. (t <= 4.9d-23))) then
        tmp = x - (y * ((a - z) / t))
    else
        tmp = (x + y) - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+36) || !(t <= 4.9e-23)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.7e+36) or not (t <= 4.9e-23):
		tmp = x - (y * ((a - z) / t))
	else:
		tmp = (x + y) - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e+36) || !(t <= 4.9e-23))
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.7e+36) || ~((t <= 4.9e-23)))
		tmp = x - (y * ((a - z) / t));
	else
		tmp = (x + y) - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.7e+36], N[Not[LessEqual[t, 4.9e-23]], $MachinePrecision]], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e36 or 4.8999999999999998e-23 < t

   1. Initial program 59.0%

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

   3. Taylor expanded in t around inf 77.0%

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

      1. associate--l+ 77.0%

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

      2. distribute-lft-out-- 77.0%

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

      3. div-sub 77.0%

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

      4. mul-1-neg 77.0%

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

      5. unsub-neg 77.0%

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

      6. *-commutative 77.0%

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

      7. distribute-lft-out-- 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in t around inf 78.0%

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

      1. neg-mul-1 78.0%

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

      2. sub-neg 78.0%

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

      3. associate-*r/ 81.9%

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

   8. Simplified 81.9%

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

   if -1.6999999999999999e36 < t < 4.8999999999999998e-23

   1. Initial program 93.4%

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

   3. Taylor expanded in y around 0 93.4%

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

      1. associate-*l/ 96.3%

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

   5. Simplified 96.3%

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

      1. associate-*l/ 93.4%

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

      2. associate-*r/ 95.6%

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

      3. clear-num 95.6%

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

      4. un-div-inv 95.6%

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

   7. Applied egg-rr 95.6%

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

   8. Taylor expanded in t around 0 87.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+36} \lor \neg \left(t \leq 4.9 \cdot 10^{-23}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0205 \lor \neg \left(a \leq 4.8 \cdot 10^{+48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.0205) (not (<= a 4.8e+48))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.0205) || !(a <= 4.8e+48)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.0205d0)) .or. (.not. (a <= 4.8d+48))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.0205) || !(a <= 4.8e+48)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.0205) or not (a <= 4.8e+48):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.0205) || !(a <= 4.8e+48))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.0205) || ~((a <= 4.8e+48)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.0205], N[Not[LessEqual[a, 4.8e+48]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.0205000000000000009 or 4.8000000000000002e48 < a

   1. Initial program 80.2%

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

   3. Taylor expanded in a around inf 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

   if -0.0205000000000000009 < a < 4.8000000000000002e48

   1. Initial program 73.5%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. distribute-lft-out-- 76.3%

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

      3. div-sub 77.3%

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

      4. mul-1-neg 77.3%

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

      5. unsub-neg 77.3%

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

      6. *-commutative 77.3%

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

      7. distribute-lft-out-- 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around 0 74.8%

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

      1. associate-*r* 74.8%

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

      2. neg-mul-1 74.8%

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

      3. *-commutative 74.8%

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

   8. Simplified 74.8%

      \[\leadsto x - \frac{\color{blue}{z \cdot \left(-y\right)}}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0205 \lor \neg \left(a \leq 4.8 \cdot 10^{+48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -1.05e+203) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+203) {
		tmp = x;
	} 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 (t <= (-1.05d+203)) then
        tmp = x
    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 (t <= -1.05e+203) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+203:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+203)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+203)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+203], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999992e203

   1. Initial program 50.2%

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

   3. Taylor expanded in x around inf 73.3%

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

   if -1.04999999999999992e203 < t

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 63.7%

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

      1. +-commutative 63.7%

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

   5. Simplified 63.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.6% accurate, 13.0× 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 76.9%

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

3. Taylor expanded in x around inf 50.6%

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

4. Final simplification 50.6%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024082 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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