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

Percentage Accurate: 76.6% → 88.2%

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: 76.6% 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: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+95} \lor \neg \left(t \leq 3.2 \cdot 10^{+67}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e+95) (not (<= t 3.2e+67)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (+ (+ x y) (/ (* y (- z t)) (- t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+95) || !(t <= 3.2e+67)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + ((y * (z - t)) / (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 <= (-2d+95)) .or. (.not. (t <= 3.2d+67))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = (x + y) + ((y * (z - t)) / (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 <= -2e+95) || !(t <= 3.2e+67)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + ((y * (z - t)) / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e+95) or not (t <= 3.2e+67):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = (x + y) + ((y * (z - t)) / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e+95) || !(t <= 3.2e+67))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e+95) || ~((t <= 3.2e+67)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = (x + y) + ((y * (z - t)) / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e+95], N[Not[LessEqual[t, 3.2e+67]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000004e95 or 3.19999999999999983e67 < t

   1. Initial program 52.5%

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

   3. Taylor expanded in t around inf 78.3%

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

      1. sub-neg 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. associate-/l* 87.6%

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

      5. mul-1-neg 87.6%

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

      6. remove-double-neg 87.6%

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

      7. associate-/l* 93.7%

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

   5. Simplified 93.7%

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

   if -2.00000000000000004e95 < t < 3.19999999999999983e67

   1. Initial program 93.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+95} \lor \neg \left(t \leq 3.2 \cdot 10^{+67}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+54} \lor \neg \left(z \leq 3.8 \cdot 10^{+61}\right) \land \left(z \leq 1.2 \cdot 10^{+81} \lor \neg \left(z \leq 8.4 \cdot 10^{+175}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.6e+54)
         (and (not (<= z 3.8e+61)) (or (<= z 1.2e+81) (not (<= z 8.4e+175)))))
   (* y (/ z (- t a)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e+54) || (!(z <= 3.8e+61) && ((z <= 1.2e+81) || !(z <= 8.4e+175)))) {
		tmp = y * (z / (t - a));
	} 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 <= (-7.6d+54)) .or. (.not. (z <= 3.8d+61)) .and. (z <= 1.2d+81) .or. (.not. (z <= 8.4d+175))) then
        tmp = y * (z / (t - a))
    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 <= -7.6e+54) || (!(z <= 3.8e+61) && ((z <= 1.2e+81) || !(z <= 8.4e+175)))) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.6e+54) or (not (z <= 3.8e+61) and ((z <= 1.2e+81) or not (z <= 8.4e+175))):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.6e+54) || (!(z <= 3.8e+61) && ((z <= 1.2e+81) || !(z <= 8.4e+175))))
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.6e+54) || (~((z <= 3.8e+61)) && ((z <= 1.2e+81) || ~((z <= 8.4e+175)))))
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.6e+54], And[N[Not[LessEqual[z, 3.8e+61]], $MachinePrecision], Or[LessEqual[z, 1.2e+81], N[Not[LessEqual[z, 8.4e+175]], $MachinePrecision]]]], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000005e54 or 3.79999999999999995e61 < z < 1.19999999999999995e81 or 8.3999999999999996e175 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-neg-frac2 67.4%

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

      3. sub-neg 67.4%

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

      4. distribute-neg-in 67.4%

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

      5. remove-double-neg 67.4%

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

      6. +-commutative 67.4%

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

      7. sub-neg 67.4%

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

      8. associate-/l* 65.4%

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

   5. Simplified 65.4%

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

   if -7.6000000000000005e54 < z < 3.79999999999999995e61 or 1.19999999999999995e81 < z < 8.3999999999999996e175

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 69.0%

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

      1. +-commutative 69.0%

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

   5. Simplified 69.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+54} \lor \neg \left(z \leq 3.8 \cdot 10^{+61}\right) \land \left(z \leq 1.2 \cdot 10^{+81} \lor \neg \left(z \leq 8.4 \cdot 10^{+175}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+55} \lor \neg \left(z \leq 1.25 \cdot 10^{+67} \lor \neg \left(z \leq 6.5 \cdot 10^{+80}\right) \land z \leq 2.65 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+55)
         (not
          (or (<= z 1.25e+67) (and (not (<= z 6.5e+80)) (<= z 2.65e+175)))))
   (* y (/ z t))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+55) || !((z <= 1.25e+67) || (!(z <= 6.5e+80) && (z <= 2.65e+175)))) {
		tmp = y * (z / 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 ((z <= (-7.2d+55)) .or. (.not. (z <= 1.25d+67) .or. (.not. (z <= 6.5d+80)) .and. (z <= 2.65d+175))) then
        tmp = y * (z / 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 ((z <= -7.2e+55) || !((z <= 1.25e+67) || (!(z <= 6.5e+80) && (z <= 2.65e+175)))) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+55) or not ((z <= 1.25e+67) or (not (z <= 6.5e+80) and (z <= 2.65e+175))):
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+55) || !((z <= 1.25e+67) || (!(z <= 6.5e+80) && (z <= 2.65e+175))))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e+55) || ~(((z <= 1.25e+67) || (~((z <= 6.5e+80)) && (z <= 2.65e+175)))))
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+55], N[Not[Or[LessEqual[z, 1.25e+67], And[N[Not[LessEqual[z, 6.5e+80]], $MachinePrecision], LessEqual[z, 2.65e+175]]]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999975e55 or 1.24999999999999994e67 < z < 6.4999999999999998e80 or 2.65000000000000006e175 < z

   1. Initial program 80.9%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. distribute-neg-frac2 66.7%

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

      3. sub-neg 66.7%

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

      4. distribute-neg-in 66.7%

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

      5. remove-double-neg 66.7%

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

      6. +-commutative 66.7%

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

      7. sub-neg 66.7%

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

      8. associate-/l* 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in t around inf 50.4%

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

      1. associate-*r/ 51.4%

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

   8. Simplified 51.4%

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

   if -7.19999999999999975e55 < z < 1.24999999999999994e67 or 6.4999999999999998e80 < z < 2.65000000000000006e175

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

   5. Simplified 68.3%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+55} \lor \neg \left(z \leq 1.25 \cdot 10^{+67} \lor \neg \left(z \leq 6.5 \cdot 10^{+80}\right) \land z \leq 2.65 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+162}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= z -1.8e+57)
     t_1
     (if (<= z 1.25e+67)
       (+ x y)
       (if (<= z 2.1e+81) t_1 (if (<= z 1.45e+162) (+ x y) (/ (* y z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -1.8e+57) {
		tmp = t_1;
	} else if (z <= 1.25e+67) {
		tmp = x + y;
	} else if (z <= 2.1e+81) {
		tmp = t_1;
	} else if (z <= 1.45e+162) {
		tmp = x + y;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (z <= (-1.8d+57)) then
        tmp = t_1
    else if (z <= 1.25d+67) then
        tmp = x + y
    else if (z <= 2.1d+81) then
        tmp = t_1
    else if (z <= 1.45d+162) then
        tmp = x + y
    else
        tmp = (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 t_1 = y * (z / t);
	double tmp;
	if (z <= -1.8e+57) {
		tmp = t_1;
	} else if (z <= 1.25e+67) {
		tmp = x + y;
	} else if (z <= 2.1e+81) {
		tmp = t_1;
	} else if (z <= 1.45e+162) {
		tmp = x + y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	tmp = 0
	if z <= -1.8e+57:
		tmp = t_1
	elif z <= 1.25e+67:
		tmp = x + y
	elif z <= 2.1e+81:
		tmp = t_1
	elif z <= 1.45e+162:
		tmp = x + y
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (z <= -1.8e+57)
		tmp = t_1;
	elseif (z <= 1.25e+67)
		tmp = Float64(x + y);
	elseif (z <= 2.1e+81)
		tmp = t_1;
	elseif (z <= 1.45e+162)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (z <= -1.8e+57)
		tmp = t_1;
	elseif (z <= 1.25e+67)
		tmp = x + y;
	elseif (z <= 2.1e+81)
		tmp = t_1;
	elseif (z <= 1.45e+162)
		tmp = x + y;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+57], t$95$1, If[LessEqual[z, 1.25e+67], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.1e+81], t$95$1, If[LessEqual[z, 1.45e+162], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e57 or 1.24999999999999994e67 < z < 2.0999999999999999e81

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-neg-frac2 58.7%

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

      3. sub-neg 58.7%

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

      4. distribute-neg-in 58.7%

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

      5. remove-double-neg 58.7%

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

      6. +-commutative 58.7%

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

      7. sub-neg 58.7%

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

      8. associate-/l* 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around inf 44.6%

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

      1. associate-*r/ 50.5%

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

   8. Simplified 50.5%

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

   if -1.8000000000000001e57 < z < 1.24999999999999994e67 or 2.0999999999999999e81 < z < 1.45000000000000003e162

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 68.5%

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

      1. +-commutative 68.5%

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

   5. Simplified 68.5%

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

   if 1.45000000000000003e162 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-neg-frac2 83.5%

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

      3. sub-neg 83.5%

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

      4. distribute-neg-in 83.5%

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

      5. remove-double-neg 83.5%

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

      6. +-commutative 83.5%

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

      7. sub-neg 83.5%

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

      8. associate-/l* 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in t around inf 63.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+162}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+152}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= z -1.7e+57)
     t_1
     (if (<= z 1.12e+67)
       (+ x y)
       (if (<= z 8.5e+80) t_1 (if (<= z 8.5e+152) (+ x y) (* (/ y t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -1.7e+57) {
		tmp = t_1;
	} else if (z <= 1.12e+67) {
		tmp = x + y;
	} else if (z <= 8.5e+80) {
		tmp = t_1;
	} else if (z <= 8.5e+152) {
		tmp = x + y;
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (z <= (-1.7d+57)) then
        tmp = t_1
    else if (z <= 1.12d+67) then
        tmp = x + y
    else if (z <= 8.5d+80) then
        tmp = t_1
    else if (z <= 8.5d+152) then
        tmp = x + y
    else
        tmp = (y / t) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -1.7e+57) {
		tmp = t_1;
	} else if (z <= 1.12e+67) {
		tmp = x + y;
	} else if (z <= 8.5e+80) {
		tmp = t_1;
	} else if (z <= 8.5e+152) {
		tmp = x + y;
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	tmp = 0
	if z <= -1.7e+57:
		tmp = t_1
	elif z <= 1.12e+67:
		tmp = x + y
	elif z <= 8.5e+80:
		tmp = t_1
	elif z <= 8.5e+152:
		tmp = x + y
	else:
		tmp = (y / t) * z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (z <= -1.7e+57)
		tmp = t_1;
	elseif (z <= 1.12e+67)
		tmp = Float64(x + y);
	elseif (z <= 8.5e+80)
		tmp = t_1;
	elseif (z <= 8.5e+152)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (z <= -1.7e+57)
		tmp = t_1;
	elseif (z <= 1.12e+67)
		tmp = x + y;
	elseif (z <= 8.5e+80)
		tmp = t_1;
	elseif (z <= 8.5e+152)
		tmp = x + y;
	else
		tmp = (y / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+57], t$95$1, If[LessEqual[z, 1.12e+67], N[(x + y), $MachinePrecision], If[LessEqual[z, 8.5e+80], t$95$1, If[LessEqual[z, 8.5e+152], N[(x + y), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999996e57 or 1.12e67 < z < 8.50000000000000007e80

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-neg-frac2 58.7%

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

      3. sub-neg 58.7%

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

      4. distribute-neg-in 58.7%

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

      5. remove-double-neg 58.7%

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

      6. +-commutative 58.7%

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

      7. sub-neg 58.7%

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

      8. associate-/l* 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around inf 44.6%

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

      1. associate-*r/ 50.5%

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

   8. Simplified 50.5%

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

   if -1.69999999999999996e57 < z < 1.12e67 or 8.50000000000000007e80 < z < 8.4999999999999993e152

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 68.5%

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

      1. +-commutative 68.5%

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

   5. Simplified 68.5%

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

   if 8.4999999999999993e152 < z

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. +-commutative 93.5%

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

      3. distribute-frac-neg 93.5%

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

      4. distribute-rgt-neg-out 93.5%

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

      5. associate-/l* 90.1%

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

      6. fma-define 90.1%

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

      7. distribute-frac-neg 90.1%

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

      8. distribute-neg-frac2 90.1%

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

      9. sub-neg 90.1%

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

      10. distribute-neg-in 90.1%

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

      11. remove-double-neg 90.1%

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

      12. +-commutative 90.1%

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

      13. sub-neg 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in a around 0 70.1%

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

   6. Taylor expanded in y around 0 70.1%

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

   7. Taylor expanded in x around 0 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*r/ 57.0%

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

   9. Simplified 57.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+152}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+96} \lor \neg \left(t \leq 9.2 \cdot 10^{+54}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+96) (not (<= t 9.2e+54)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (+ (+ x y) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+96) || !(t <= 9.2e+54)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + ((z - t) * (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 ((t <= (-2.1d+96)) .or. (.not. (t <= 9.2d+54))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = (x + y) + ((z - t) * (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 ((t <= -2.1e+96) || !(t <= 9.2e+54)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+96) or not (t <= 9.2e+54):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+96) || !(t <= 9.2e+54))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+96) || ~((t <= 9.2e+54)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+96], N[Not[LessEqual[t, 9.2e+54]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1000000000000001e96 or 9.19999999999999977e54 < t

   1. Initial program 54.5%

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

   3. Taylor expanded in t around inf 79.2%

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

      1. sub-neg 79.2%

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

      2. mul-1-neg 79.2%

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

      3. unsub-neg 79.2%

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

      4. associate-/l* 88.1%

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

      5. mul-1-neg 88.1%

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

      6. remove-double-neg 88.1%

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

      7. associate-/l* 94.0%

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

   5. Simplified 94.0%

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

   if -2.1000000000000001e96 < t < 9.19999999999999977e54

   1. Initial program 93.7%

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

      1. associate-/l* 92.8%

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

      2. *-commutative 92.8%

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

   4. Applied egg-rr 92.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+96} \lor \neg \left(t \leq 9.2 \cdot 10^{+54}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-5} \lor \neg \left(a \leq 1.8 \cdot 10^{-86}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - a \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.3e-5) (not (<= a 1.8e-86)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (- (* y z) (* a y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.3e-5) || !(a <= 1.8e-86)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (((y * z) - (a * y)) / 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 <= (-5.3d-5)) .or. (.not. (a <= 1.8d-86))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + (((y * z) - (a * y)) / 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 <= -5.3e-5) || !(a <= 1.8e-86)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (((y * z) - (a * y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.3e-5) or not (a <= 1.8e-86):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + (((y * z) - (a * y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.3e-5) || !(a <= 1.8e-86))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y * z) - Float64(a * y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.3e-5) || ~((a <= 1.8e-86)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + (((y * z) - (a * y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.3e-5], N[Not[LessEqual[a, 1.8e-86]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y * z), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.3000000000000001e-5 or 1.79999999999999983e-86 < a

   1. Initial program 80.4%

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

   3. Taylor expanded in t around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   if -5.3000000000000001e-5 < a < 1.79999999999999983e-86

   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 t around -inf 85.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-5} \lor \neg \left(a \leq 1.8 \cdot 10^{-86}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - a \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{-24} \lor \neg \left(a \leq 1.5 \cdot 10^{-87}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.15e-24) (not (<= a 1.5e-87)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.15e-24) || !(a <= 1.5e-87)) {
		tmp = (x + y) - (y * (z / a));
	} 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 <= (-3.15d-24)) .or. (.not. (a <= 1.5d-87))) then
        tmp = (x + y) - (y * (z / a))
    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 <= -3.15e-24) || !(a <= 1.5e-87)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.15e-24) or not (a <= 1.5e-87):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.15e-24) || !(a <= 1.5e-87))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	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 <= -3.15e-24) || ~((a <= 1.5e-87)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.15e-24], N[Not[LessEqual[a, 1.5e-87]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1499999999999999e-24 or 1.50000000000000008e-87 < a

   1. Initial program 80.1%

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

   3. Taylor expanded in t around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   if -3.1499999999999999e-24 < a < 1.50000000000000008e-87

   1. Initial program 77.2%

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

      1. sub-neg 77.2%

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

      2. +-commutative 77.2%

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

      3. distribute-frac-neg 77.2%

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

      4. distribute-rgt-neg-out 77.2%

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

      5. associate-/l* 72.6%

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

      6. fma-define 72.8%

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

      7. distribute-frac-neg 72.8%

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

      8. distribute-neg-frac2 72.8%

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

      9. sub-neg 72.8%

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

      10. distribute-neg-in 72.8%

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

      11. remove-double-neg 72.8%

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

      12. +-commutative 72.8%

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

      13. sub-neg 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in a around 0 71.8%

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

   6. Taylor expanded in y around 0 85.5%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{-24} \lor \neg \left(a \leq 1.5 \cdot 10^{-87}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+129} \lor \neg \left(a \leq 1.4 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.6e+129) (not (<= a 1.4e+49))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.6e+129) || !(a <= 1.4e+49)) {
		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 <= (-9.6d+129)) .or. (.not. (a <= 1.4d+49))) 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 <= -9.6e+129) || !(a <= 1.4e+49)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.6e+129) or not (a <= 1.4e+49):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.6e+129) || !(a <= 1.4e+49))
		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 <= -9.6e+129) || ~((a <= 1.4e+49)))
		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, -9.6e+129], N[Not[LessEqual[a, 1.4e+49]], $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 < -9.5999999999999995e129 or 1.3999999999999999e49 < a

   1. Initial program 84.1%

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

   3. Taylor expanded in a around inf 87.9%

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

      1. +-commutative 87.9%

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

   5. Simplified 87.9%

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

   if -9.5999999999999995e129 < a < 1.3999999999999999e49

   1. Initial program 76.2%

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

      1. sub-neg 76.2%

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

      2. +-commutative 76.2%

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

      3. distribute-frac-neg 76.2%

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

      4. distribute-rgt-neg-out 76.2%

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

      5. associate-/l* 73.6%

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

      6. fma-define 73.7%

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

      7. distribute-frac-neg 73.7%

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

      8. distribute-neg-frac2 73.7%

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

      9. sub-neg 73.7%

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

      10. distribute-neg-in 73.7%

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

      11. remove-double-neg 73.7%

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

      12. +-commutative 73.7%

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

      13. sub-neg 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in a around 0 61.6%

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

   6. Taylor expanded in y around 0 74.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+129} \lor \neg \left(a \leq 1.4 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-223} \lor \neg \left(a \leq 2.7 \cdot 10^{-23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.15e-223) (not (<= a 2.7e-23))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.15e-223) || !(a <= 2.7e-23)) {
		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 <= (-2.15d-223)) .or. (.not. (a <= 2.7d-23))) 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 <= -2.15e-223) || !(a <= 2.7e-23)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.15e-223) or not (a <= 2.7e-23):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.15e-223) || !(a <= 2.7e-23))
		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 <= -2.15e-223) || ~((a <= 2.7e-23)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.15e-223], N[Not[LessEqual[a, 2.7e-23]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.15e-223 or 2.69999999999999985e-23 < a

   1. Initial program 82.6%

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

   3. Taylor expanded in a around inf 64.3%

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

      1. +-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -2.15e-223 < a < 2.69999999999999985e-23

   1. Initial program 71.3%

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

   3. Taylor expanded in x around inf 41.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-223} \lor \neg \left(a \leq 2.7 \cdot 10^{-23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.9% 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 78.8%

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

3. Taylor expanded in x around inf 43.5%

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

Developer target: 88.3% 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 2024110 
(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))))