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

Percentage Accurate: 77.1% → 91.1%

Time: 11.2s

Alternatives: 16

Speedup: 0.8×

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: 77.1% 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: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+116}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+173}:\\ \;\;\;\;x + \left(y + \left(z - t\right) \cdot \frac{y}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+116)
   (- (+ x (* y (/ z t))) (* a (/ y t)))
   (if (<= t 2.9e+173)
     (+ x (+ y (* (- z t) (/ y (- t a)))))
     (- x (* y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+116) {
		tmp = (x + (y * (z / t))) - (a * (y / t));
	} else if (t <= 2.9e+173) {
		tmp = x + (y + ((z - t) * (y / (t - a))));
	} 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 <= (-5.2d+116)) then
        tmp = (x + (y * (z / t))) - (a * (y / t))
    else if (t <= 2.9d+173) then
        tmp = x + (y + ((z - t) * (y / (t - a))))
    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 <= -5.2e+116) {
		tmp = (x + (y * (z / t))) - (a * (y / t));
	} else if (t <= 2.9e+173) {
		tmp = x + (y + ((z - t) * (y / (t - a))));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+116:
		tmp = (x + (y * (z / t))) - (a * (y / t))
	elif t <= 2.9e+173:
		tmp = x + (y + ((z - t) * (y / (t - a))))
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+116)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) - Float64(a * Float64(y / t)));
	elseif (t <= 2.9e+173)
		tmp = Float64(x + Float64(y + Float64(Float64(z - t) * Float64(y / Float64(t - a)))));
	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 <= -5.2e+116)
		tmp = (x + (y * (z / t))) - (a * (y / t));
	elseif (t <= 2.9e+173)
		tmp = x + (y + ((z - t) * (y / (t - a))));
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+116], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+173], N[(x + N[(y + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $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 < -5.19999999999999973e116

   1. Initial program 38.7%

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

      1. sub-neg 38.7%

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

      2. +-commutative 38.7%

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

      3. distribute-frac-neg 38.7%

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

      4. distribute-rgt-neg-out 38.7%

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

      5. associate-/l* 42.6%

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

      6. fma-define 42.8%

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

      7. distribute-frac-neg 42.8%

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

      8. distribute-neg-frac2 42.8%

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

      9. sub-neg 42.8%

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

      10. distribute-neg-in 42.8%

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

      11. remove-double-neg 42.8%

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

      12. +-commutative 42.8%

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

      13. sub-neg 42.8%

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

   3. Simplified 42.8%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. associate-+r+ 81.3%

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

      2. distribute-rgt1-in 81.3%

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

      3. metadata-eval 81.3%

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

      4. mul0-lft 81.3%

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

      5. associate-+r+ 81.3%

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

      6. associate-/l* 95.2%

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

      7. associate-/l* 97.6%

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

   7. Simplified 97.6%

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

   if -5.19999999999999973e116 < t < 2.90000000000000007e173

   1. Initial program 88.1%

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

      1. associate--l+ 90.3%

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

      2. +-commutative 90.3%

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

      3. associate-/l* 94.2%

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

   4. Applied egg-rr 94.2%

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

   if 2.90000000000000007e173 < t

   1. Initial program 39.9%

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

   3. Taylor expanded in y around 0 92.9%

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

   4. Taylor expanded in t around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

      3. associate-/l* 96.7%

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

      4. mul-1-neg 96.7%

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

      5. sub-neg 96.7%

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

   6. Simplified 96.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+116}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+173}:\\ \;\;\;\;x + \left(y + \left(z - t\right) \cdot \frac{y}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a - z}{t}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- a z) t)))))
   (if (<= a -9e+44)
     (+ x y)
     (if (<= a 4.05e-134)
       t_1
       (if (<= a 1.12e-114)
         (/ (* y z) (- t a))
         (if (<= a 6.4e-13) 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 <= -9e+44) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = t_1;
	} else if (a <= 1.12e-114) {
		tmp = (y * z) / (t - a);
	} else if (a <= 6.4e-13) {
		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 <= (-9d+44)) then
        tmp = x + y
    else if (a <= 4.05d-134) then
        tmp = t_1
    else if (a <= 1.12d-114) then
        tmp = (y * z) / (t - a)
    else if (a <= 6.4d-13) 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 <= -9e+44) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = t_1;
	} else if (a <= 1.12e-114) {
		tmp = (y * z) / (t - a);
	} else if (a <= 6.4e-13) {
		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 <= -9e+44:
		tmp = x + y
	elif a <= 4.05e-134:
		tmp = t_1
	elif a <= 1.12e-114:
		tmp = (y * z) / (t - a)
	elif a <= 6.4e-13:
		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 <= -9e+44)
		tmp = Float64(x + y);
	elseif (a <= 4.05e-134)
		tmp = t_1;
	elseif (a <= 1.12e-114)
		tmp = Float64(Float64(y * z) / Float64(t - a));
	elseif (a <= 6.4e-13)
		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 <= -9e+44)
		tmp = x + y;
	elseif (a <= 4.05e-134)
		tmp = t_1;
	elseif (a <= 1.12e-114)
		tmp = (y * z) / (t - a);
	elseif (a <= 6.4e-13)
		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, -9e+44], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.05e-134], t$95$1, If[LessEqual[a, 1.12e-114], N[(N[(y * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e-13], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9e44 or 6.39999999999999999e-13 < a

   1. Initial program 81.6%

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

   3. Taylor expanded in a around inf 82.4%

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

      1. +-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -9e44 < a < 4.04999999999999995e-134 or 1.11999999999999995e-114 < a < 6.39999999999999999e-13

   1. Initial program 68.2%

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

   3. Taylor expanded in y around 0 94.9%

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

   4. Taylor expanded in t around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. unsub-neg 78.8%

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

      3. associate-/l* 83.8%

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

      4. mul-1-neg 83.8%

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

      5. sub-neg 83.8%

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

   6. Simplified 83.8%

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

   if 4.04999999999999995e-134 < a < 1.11999999999999995e-114

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. +-commutative 89.8%

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

      3. distribute-frac-neg 89.8%

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

      4. distribute-rgt-neg-out 89.8%

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

      5. associate-/l* 90.0%

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

      6. fma-define 90.0%

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

      7. distribute-frac-neg 90.0%

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

      8. distribute-neg-frac2 90.0%

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

      9. sub-neg 90.0%

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

      10. distribute-neg-in 90.0%

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

      11. remove-double-neg 90.0%

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

      12. +-commutative 90.0%

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

      13. sub-neg 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around inf 80.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-13}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-285} \lor \neg \left(x \leq 7.6 \cdot 10^{-215}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.75e-151)
   x
   (if (<= x -2.4e-290)
     (* y (/ z (- t a)))
     (if (or (<= x 6.5e-285) (not (<= x 7.6e-215)))
       (+ x y)
       (* y (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.75e-151) {
		tmp = x;
	} else if (x <= -2.4e-290) {
		tmp = y * (z / (t - a));
	} else if ((x <= 6.5e-285) || !(x <= 7.6e-215)) {
		tmp = x + y;
	} else {
		tmp = y * ((z - a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.75d-151)) then
        tmp = x
    else if (x <= (-2.4d-290)) then
        tmp = y * (z / (t - a))
    else if ((x <= 6.5d-285) .or. (.not. (x <= 7.6d-215))) then
        tmp = x + y
    else
        tmp = y * ((z - a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.75e-151) {
		tmp = x;
	} else if (x <= -2.4e-290) {
		tmp = y * (z / (t - a));
	} else if ((x <= 6.5e-285) || !(x <= 7.6e-215)) {
		tmp = x + y;
	} else {
		tmp = y * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.75e-151:
		tmp = x
	elif x <= -2.4e-290:
		tmp = y * (z / (t - a))
	elif (x <= 6.5e-285) or not (x <= 7.6e-215):
		tmp = x + y
	else:
		tmp = y * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.75e-151)
		tmp = x;
	elseif (x <= -2.4e-290)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif ((x <= 6.5e-285) || !(x <= 7.6e-215))
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.75e-151)
		tmp = x;
	elseif (x <= -2.4e-290)
		tmp = y * (z / (t - a));
	elseif ((x <= 6.5e-285) || ~((x <= 7.6e-215)))
		tmp = x + y;
	else
		tmp = y * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.75e-151], x, If[LessEqual[x, -2.4e-290], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 6.5e-285], N[Not[LessEqual[x, 7.6e-215]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7499999999999999e-151

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf 71.7%

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

   if -2.7499999999999999e-151 < x < -2.4000000000000001e-290

   1. Initial program 77.9%

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

      1. sub-neg 77.9%

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

      2. +-commutative 77.9%

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

      3. distribute-frac-neg 77.9%

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

      4. distribute-rgt-neg-out 77.9%

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

      5. associate-/l* 67.2%

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

      6. fma-define 67.2%

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

      7. distribute-frac-neg 67.2%

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

      8. distribute-neg-frac2 67.2%

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

      9. sub-neg 67.2%

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

      10. distribute-neg-in 67.2%

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

      11. remove-double-neg 67.2%

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

      12. +-commutative 67.2%

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

      13. sub-neg 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate-/l* 67.1%

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

   7. Simplified 67.1%

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

   if -2.4000000000000001e-290 < x < 6.5e-285 or 7.59999999999999954e-215 < x

   1. Initial program 80.8%

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

   3. Taylor expanded in a around inf 67.3%

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

      1. +-commutative 67.3%

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

   5. Simplified 67.3%

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

   if 6.5e-285 < x < 7.59999999999999954e-215

   1. Initial program 45.6%

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

      1. sub-neg 45.6%

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

      2. +-commutative 45.6%

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

      3. distribute-frac-neg 45.6%

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

      4. distribute-rgt-neg-out 45.6%

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

      5. associate-/l* 45.9%

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

      6. fma-define 45.6%

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

      7. distribute-frac-neg 45.6%

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

      8. distribute-neg-frac2 45.6%

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

      9. sub-neg 45.6%

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

      10. distribute-neg-in 45.6%

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

      11. remove-double-neg 45.6%

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

      12. +-commutative 45.6%

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

      13. sub-neg 45.6%

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

   3. Simplified 45.6%

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

   5. Taylor expanded in t around inf 57.4%

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

      1. associate-+r+ 69.4%

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

      2. distribute-rgt1-in 69.4%

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

      3. metadata-eval 69.4%

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

      4. mul0-lft 69.4%

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

      5. associate-+r+ 69.4%

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

      6. associate-/l* 75.4%

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

      7. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around inf 58.0%

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

      1. div-sub 58.0%

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

   10. Simplified 58.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-285} \lor \neg \left(x \leq 7.6 \cdot 10^{-215}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-96}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= a -3.4e+41)
     (+ x y)
     (if (<= a 4.05e-134)
       t_1
       (if (<= a 2.25e-96)
         (/ (* y z) (- t a))
         (if (<= a 9.5e+81) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (a <= -3.4e+41) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = t_1;
	} else if (a <= 2.25e-96) {
		tmp = (y * z) / (t - a);
	} else if (a <= 9.5e+81) {
		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 * (z / t))
    if (a <= (-3.4d+41)) then
        tmp = x + y
    else if (a <= 4.05d-134) then
        tmp = t_1
    else if (a <= 2.25d-96) then
        tmp = (y * z) / (t - a)
    else if (a <= 9.5d+81) 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 * (z / t));
	double tmp;
	if (a <= -3.4e+41) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = t_1;
	} else if (a <= 2.25e-96) {
		tmp = (y * z) / (t - a);
	} else if (a <= 9.5e+81) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / t))
	tmp = 0
	if a <= -3.4e+41:
		tmp = x + y
	elif a <= 4.05e-134:
		tmp = t_1
	elif a <= 2.25e-96:
		tmp = (y * z) / (t - a)
	elif a <= 9.5e+81:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (a <= -3.4e+41)
		tmp = Float64(x + y);
	elseif (a <= 4.05e-134)
		tmp = t_1;
	elseif (a <= 2.25e-96)
		tmp = Float64(Float64(y * z) / Float64(t - a));
	elseif (a <= 9.5e+81)
		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 * (z / t));
	tmp = 0.0;
	if (a <= -3.4e+41)
		tmp = x + y;
	elseif (a <= 4.05e-134)
		tmp = t_1;
	elseif (a <= 2.25e-96)
		tmp = (y * z) / (t - a);
	elseif (a <= 9.5e+81)
		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[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+41], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.05e-134], t$95$1, If[LessEqual[a, 2.25e-96], N[(N[(y * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+81], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.39999999999999998e41 or 9.50000000000000083e81 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 85.4%

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

      1. +-commutative 85.4%

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

   5. Simplified 85.4%

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

   if -3.39999999999999998e41 < a < 4.04999999999999995e-134 or 2.25e-96 < a < 9.50000000000000083e81

   1. Initial program 68.7%

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

   3. Taylor expanded in y around 0 96.6%

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

   4. Taylor expanded in a around 0 77.0%

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

      1. associate-*r/ 81.6%

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

   6. Simplified 81.6%

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

   if 4.04999999999999995e-134 < a < 2.25e-96

   1. Initial program 85.7%

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

      1. sub-neg 85.7%

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

      2. +-commutative 85.7%

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

      3. distribute-frac-neg 85.7%

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

      4. distribute-rgt-neg-out 85.7%

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

      5. associate-/l* 86.2%

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

      6. fma-define 86.2%

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

      7. distribute-frac-neg 86.2%

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

      8. distribute-neg-frac2 86.2%

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

      9. sub-neg 86.2%

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

      10. distribute-neg-in 86.2%

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

      11. remove-double-neg 86.2%

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

      12. +-commutative 86.2%

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

      13. sub-neg 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around inf 67.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-96}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-96}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e-67)
   (+ x y)
   (if (<= a 4.05e-134)
     x
     (if (<= a 2.35e-96) (/ (* y (- z)) a) (if (<= a 4.2e-83) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-67) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = x;
	} else if (a <= 2.35e-96) {
		tmp = (y * -z) / a;
	} else if (a <= 4.2e-83) {
		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 (a <= (-3d-67)) then
        tmp = x + y
    else if (a <= 4.05d-134) then
        tmp = x
    else if (a <= 2.35d-96) then
        tmp = (y * -z) / a
    else if (a <= 4.2d-83) 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 (a <= -3e-67) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = x;
	} else if (a <= 2.35e-96) {
		tmp = (y * -z) / a;
	} else if (a <= 4.2e-83) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e-67:
		tmp = x + y
	elif a <= 4.05e-134:
		tmp = x
	elif a <= 2.35e-96:
		tmp = (y * -z) / a
	elif a <= 4.2e-83:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e-67)
		tmp = Float64(x + y);
	elseif (a <= 4.05e-134)
		tmp = x;
	elseif (a <= 2.35e-96)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (a <= 4.2e-83)
		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 (a <= -3e-67)
		tmp = x + y;
	elseif (a <= 4.05e-134)
		tmp = x;
	elseif (a <= 2.35e-96)
		tmp = (y * -z) / a;
	elseif (a <= 4.2e-83)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e-67], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.05e-134], x, If[LessEqual[a, 2.35e-96], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 4.2e-83], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.00000000000000032e-67 or 4.1999999999999998e-83 < a

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf 73.1%

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

      1. +-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -3.00000000000000032e-67 < a < 4.04999999999999995e-134 or 2.3499999999999999e-96 < a < 4.1999999999999998e-83

   1. Initial program 65.6%

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

   3. Taylor expanded in x around inf 58.5%

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

   if 4.04999999999999995e-134 < a < 2.3499999999999999e-96

   1. Initial program 85.7%

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

      1. sub-neg 85.7%

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

      2. +-commutative 85.7%

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

      3. distribute-frac-neg 85.7%

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

      4. distribute-rgt-neg-out 85.7%

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

      5. associate-/l* 86.2%

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

      6. fma-define 86.2%

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

      7. distribute-frac-neg 86.2%

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

      8. distribute-neg-frac2 86.2%

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

      9. sub-neg 86.2%

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

      10. distribute-neg-in 86.2%

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

      11. remove-double-neg 86.2%

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

      12. +-commutative 86.2%

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

      13. sub-neg 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around inf 67.4%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. associate-*r* 46.6%

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

      3. neg-mul-1 46.6%

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

   8. Simplified 46.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-96}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.7e-67)
   (+ x y)
   (if (<= a 4.05e-134)
     x
     (if (<= a 2.35e-96) (* z (/ (- y) a)) (if (<= a 1.45e-85) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e-67) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = x;
	} else if (a <= 2.35e-96) {
		tmp = z * (-y / a);
	} else if (a <= 1.45e-85) {
		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 (a <= (-5.7d-67)) then
        tmp = x + y
    else if (a <= 4.05d-134) then
        tmp = x
    else if (a <= 2.35d-96) then
        tmp = z * (-y / a)
    else if (a <= 1.45d-85) 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 (a <= -5.7e-67) {
		tmp = x + y;
	} else if (a <= 4.05e-134) {
		tmp = x;
	} else if (a <= 2.35e-96) {
		tmp = z * (-y / a);
	} else if (a <= 1.45e-85) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.7e-67:
		tmp = x + y
	elif a <= 4.05e-134:
		tmp = x
	elif a <= 2.35e-96:
		tmp = z * (-y / a)
	elif a <= 1.45e-85:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.7e-67)
		tmp = Float64(x + y);
	elseif (a <= 4.05e-134)
		tmp = x;
	elseif (a <= 2.35e-96)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (a <= 1.45e-85)
		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 (a <= -5.7e-67)
		tmp = x + y;
	elseif (a <= 4.05e-134)
		tmp = x;
	elseif (a <= 2.35e-96)
		tmp = z * (-y / a);
	elseif (a <= 1.45e-85)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.7e-67], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.05e-134], x, If[LessEqual[a, 2.35e-96], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-85], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.7000000000000002e-67 or 1.4500000000000001e-85 < a

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf 73.1%

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

      1. +-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -5.7000000000000002e-67 < a < 4.04999999999999995e-134 or 2.3499999999999999e-96 < a < 1.4500000000000001e-85

   1. Initial program 65.6%

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

   3. Taylor expanded in x around inf 58.5%

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

   if 4.04999999999999995e-134 < a < 2.3499999999999999e-96

   1. Initial program 85.7%

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

      1. sub-neg 85.7%

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

      2. +-commutative 85.7%

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

      3. distribute-frac-neg 85.7%

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

      4. distribute-rgt-neg-out 85.7%

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

      5. associate-/l* 86.2%

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

      6. fma-define 86.2%

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

      7. distribute-frac-neg 86.2%

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

      8. distribute-neg-frac2 86.2%

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

      9. sub-neg 86.2%

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

      10. distribute-neg-in 86.2%

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

      11. remove-double-neg 86.2%

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

      12. +-commutative 86.2%

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

      13. sub-neg 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around inf 67.4%

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

   6. Taylor expanded in t around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. associate-*r* 46.6%

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

      3. neg-mul-1 46.6%

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

   8. Simplified 46.6%

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

   9. Taylor expanded in y around 0 46.6%

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

       1. mul-1-neg 46.6%

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

       2. *-commutative 46.6%

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

       3. associate-*r/ 46.5%

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

       4. *-commutative 46.5%

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

       5. distribute-rgt-neg-in 46.5%

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

   11. Simplified 46.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+119} \lor \neg \left(t \leq 4.9 \cdot 10^{+173}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(z - t\right) \cdot \frac{y}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+119) (not (<= t 4.9e+173)))
   (- x (* y (/ (- a 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 <= -2.5e+119) || !(t <= 4.9e+173)) {
		tmp = x - (y * ((a - 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 <= (-2.5d+119)) .or. (.not. (t <= 4.9d+173))) then
        tmp = x - (y * ((a - 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 <= -2.5e+119) || !(t <= 4.9e+173)) {
		tmp = x - (y * ((a - 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 <= -2.5e+119) or not (t <= 4.9e+173):
		tmp = x - (y * ((a - 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 <= -2.5e+119) || !(t <= 4.9e+173))
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(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 <= -2.5e+119) || ~((t <= 4.9e+173)))
		tmp = x - (y * ((a - 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, -2.5e+119], N[Not[LessEqual[t, 4.9e+173]], $MachinePrecision]], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5e119 or 4.9000000000000001e173 < t

   1. Initial program 39.2%

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

   3. Taylor expanded in y around 0 92.9%

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

   4. Taylor expanded in t around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

      3. associate-/l* 95.8%

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

      4. mul-1-neg 95.8%

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

      5. sub-neg 95.8%

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

   6. Simplified 95.8%

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

   if -2.5e119 < t < 4.9000000000000001e173

   1. Initial program 88.1%

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

      1. associate--l+ 90.3%

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

      2. +-commutative 90.3%

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

      3. associate-/l* 94.2%

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

   4. Applied egg-rr 94.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+119} \lor \neg \left(t \leq 4.9 \cdot 10^{+173}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(z - t\right) \cdot \frac{y}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+43} \lor \neg \left(a \leq 4.8 \cdot 10^{+80}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e+43) (not (<= a 4.8e+80)))
   (- (+ x y) (* y (/ z a)))
   (+ x (* z (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+43) || !(a <= 4.8e+80)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (z * (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 ((a <= (-1.9d+43)) .or. (.not. (a <= 4.8d+80))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + (z * (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 ((a <= -1.9e+43) || !(a <= 4.8e+80)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (z * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e+43) or not (a <= 4.8e+80):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + (z * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e+43) || !(a <= 4.8e+80))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e+43) || ~((a <= 4.8e+80)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + (z * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e+43], N[Not[LessEqual[a, 4.8e+80]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.90000000000000004e43 or 4.79999999999999958e80 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-/l* 91.7%

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

   5. Simplified 91.7%

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

   if -1.90000000000000004e43 < a < 4.79999999999999958e80

   1. Initial program 70.2%

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

   3. Taylor expanded in y around 0 93.4%

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

      1. add-cube-cbrt 92.9%

         \[\leadsto x + y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \color{blue}{\left(\sqrt[3]{\frac{z}{a - t}} \cdot \sqrt[3]{\frac{z}{a - t}}\right) \cdot \sqrt[3]{\frac{z}{a - t}}}\right) \]

      2. pow3 93.0%

         \[\leadsto x + y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \color{blue}{{\left(\sqrt[3]{\frac{z}{a - t}}\right)}^{3}}\right) \]

   5. Applied egg-rr 93.0%

      \[\leadsto x + y \cdot \left(\left(1 + \frac{t}{a - t}\right) - \color{blue}{{\left(\sqrt[3]{\frac{z}{a - t}}\right)}^{3}}\right) \]

   6. Taylor expanded in z around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. *-commutative 86.3%

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

      3. remove-double-neg 86.3%

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

      4. neg-mul-1 86.3%

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

      5. times-frac 89.3%

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

      6. metadata-eval 89.3%

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

      7. distribute-neg-frac2 89.3%

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

      8. /-rgt-identity 89.3%

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

      9. distribute-neg-frac2 89.3%

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

      10. mul-1-neg 89.3%

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

      11. distribute-lft-neg-out 89.3%

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

      12. remove-double-neg 89.3%

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

      13. mul-1-neg 89.3%

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

      14. distribute-frac-neg 89.3%

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

   8. Simplified 89.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+43} \lor \neg \left(a \leq 4.8 \cdot 10^{+80}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+20} \lor \neg \left(t \leq 1.8 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+20) (not (<= t 1.8e-22)))
   (- x (* y (/ (- a z) t)))
   (- (+ x y) (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+20) || !(t <= 1.8e-22)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) - (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.4d+20)) .or. (.not. (t <= 1.8d-22))) then
        tmp = x - (y * ((a - z) / t))
    else
        tmp = (x + y) - (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+20) || !(t <= 1.8e-22)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+20) or not (t <= 1.8e-22):
		tmp = x - (y * ((a - z) / t))
	else:
		tmp = (x + y) - (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+20) || !(t <= 1.8e-22))
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+20) || ~((t <= 1.8e-22)))
		tmp = x - (y * ((a - z) / t));
	else
		tmp = (x + y) - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+20], N[Not[LessEqual[t, 1.8e-22]], $MachinePrecision]], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e20 or 1.7999999999999999e-22 < t

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0 94.1%

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

   4. Taylor expanded in t around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

      3. associate-/l* 84.9%

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

      4. mul-1-neg 84.9%

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

      5. sub-neg 84.9%

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

   6. Simplified 84.9%

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

   if -1.4e20 < t < 1.7999999999999999e-22

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in y around 0 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*r/ 87.5%

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

   8. Simplified 87.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+20} \lor \neg \left(t \leq 1.8 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+20} \lor \neg \left(t \leq 4.4 \cdot 10^{-20}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.15e+20) (not (<= t 4.4e-20)))
   (- x (* y (/ (- a z) t)))
   (- (+ x y) (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.15e+20) || !(t <= 4.4e-20)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) - ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.15d+20)) .or. (.not. (t <= 4.4d-20))) then
        tmp = x - (y * ((a - z) / t))
    else
        tmp = (x + y) - ((y * z) / 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 <= -2.15e+20) || !(t <= 4.4e-20)) {
		tmp = x - (y * ((a - z) / t));
	} else {
		tmp = (x + y) - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.15e+20) or not (t <= 4.4e-20):
		tmp = x - (y * ((a - z) / t))
	else:
		tmp = (x + y) - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.15e+20) || !(t <= 4.4e-20))
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.15e+20) || ~((t <= 4.4e-20)))
		tmp = x - (y * ((a - z) / t));
	else
		tmp = (x + y) - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.15e+20], N[Not[LessEqual[t, 4.4e-20]], $MachinePrecision]], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15e20 or 4.39999999999999982e-20 < t

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0 94.1%

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

   4. Taylor expanded in t around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

      3. associate-/l* 84.9%

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

      4. mul-1-neg 84.9%

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

      5. sub-neg 84.9%

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

   6. Simplified 84.9%

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

   if -2.15e20 < t < 4.39999999999999982e-20

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0 86.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+20} \lor \neg \left(t \leq 4.4 \cdot 10^{-20}\right):\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+42} \lor \neg \left(a \leq 1.7 \cdot 10^{+81}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.9e+42) (not (<= a 1.7e+81))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e+42) || !(a <= 1.7e+81)) {
		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 <= (-2.9d+42)) .or. (.not. (a <= 1.7d+81))) 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 <= -2.9e+42) || !(a <= 1.7e+81)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.9e+42) or not (a <= 1.7e+81):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.9e+42) || !(a <= 1.7e+81))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.9e+42) || ~((a <= 1.7e+81)))
		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, -2.9e+42], N[Not[LessEqual[a, 1.7e+81]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.89999999999999981e42 or 1.70000000000000001e81 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 85.4%

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

      1. +-commutative 85.4%

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

   5. Simplified 85.4%

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

   if -2.89999999999999981e42 < a < 1.70000000000000001e81

   1. Initial program 70.2%

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

   3. Taylor expanded in y around 0 93.4%

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

   4. Taylor expanded in a around 0 73.3%

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

      1. associate-*r/ 77.2%

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

   6. Simplified 77.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+42} \lor \neg \left(a \leq 1.7 \cdot 10^{+81}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.5e-152) x (if (<= x -4.5e-291) (* y (/ z (- t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.5e-152) {
		tmp = x;
	} else if (x <= -4.5e-291) {
		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 (x <= (-6.5d-152)) then
        tmp = x
    else if (x <= (-4.5d-291)) 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 (x <= -6.5e-152) {
		tmp = x;
	} else if (x <= -4.5e-291) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.5e-152:
		tmp = x
	elif x <= -4.5e-291:
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.5e-152)
		tmp = x;
	elseif (x <= -4.5e-291)
		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 (x <= -6.5e-152)
		tmp = x;
	elseif (x <= -4.5e-291)
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.5e-152], x, If[LessEqual[x, -4.5e-291], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5000000000000001e-152

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf 71.7%

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

   if -6.5000000000000001e-152 < x < -4.49999999999999974e-291

   1. Initial program 77.9%

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

      1. sub-neg 77.9%

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

      2. +-commutative 77.9%

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

      3. distribute-frac-neg 77.9%

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

      4. distribute-rgt-neg-out 77.9%

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

      5. associate-/l* 67.2%

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

      6. fma-define 67.2%

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

      7. distribute-frac-neg 67.2%

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

      8. distribute-neg-frac2 67.2%

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

      9. sub-neg 67.2%

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

      10. distribute-neg-in 67.2%

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

      11. remove-double-neg 67.2%

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

      12. +-commutative 67.2%

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

      13. sub-neg 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate-/l* 67.1%

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

   7. Simplified 67.1%

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

   if -4.49999999999999974e-291 < x

   1. Initial program 76.0%

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

   3. Taylor expanded in a around inf 61.0%

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

      1. +-commutative 61.0%

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

   5. Simplified 61.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (- (+ (/ t (- a t)) 1.0) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (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 * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
}

Python

def code(x, y, z, t, a):
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in y around 0 93.9%

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

4. Final simplification 93.9%

   \[\leadsto x + y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \]
5. Add Preprocessing

Alternative 14: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-67} \lor \neg \left(a \leq 6.2 \cdot 10^{-80}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e-67) (not (<= a 6.2e-80))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-67) || !(a <= 6.2e-80)) {
		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 <= (-1.35d-67)) .or. (.not. (a <= 6.2d-80))) 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 <= -1.35e-67) || !(a <= 6.2e-80)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e-67) or not (a <= 6.2e-80):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e-67) || !(a <= 6.2e-80))
		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 <= -1.35e-67) || ~((a <= 6.2e-80)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.35e-67], N[Not[LessEqual[a, 6.2e-80]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.35000000000000008e-67 or 6.20000000000000032e-80 < a

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf 73.1%

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

      1. +-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -1.35000000000000008e-67 < a < 6.20000000000000032e-80

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf 53.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-67} \lor \neg \left(a \leq 6.2 \cdot 10^{-80}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.0% 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 74.9%

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

3. Taylor expanded in x around inf 51.2%

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

Alternative 16: 2.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in x around 0 37.6%

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

   1. associate-*r/ 40.1%

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

5. Simplified 40.1%

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

6. Taylor expanded in z around 0 17.8%

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

   1. sub-neg 17.8%

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

   2. mul-1-neg 17.8%

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

   3. remove-double-neg 17.8%

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

8. Simplified 17.8%

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

9. Taylor expanded in t around inf 2.6%

   \[\leadsto \color{blue}{y + -1 \cdot y} \]
10. Step-by-step derivation

    1. distribute-rgt1-in 2.6%

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

    2. metadata-eval 2.6%

       \[\leadsto \color{blue}{0} \cdot y \]

    3. mul0-lft 2.6%

       \[\leadsto \color{blue}{0} \]

11. Simplified 2.6%

    \[\leadsto \color{blue}{0} \]
12. Add Preprocessing

Developer target: 88.1% 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 2024085 
(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))))