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

Percentage Accurate: 76.6% → 91.6%

Time: 10.7s

Alternatives: 12

Speedup: 1.0×

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: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-100} \lor \neg \left(a \leq 5.5 \cdot 10^{-101}\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.8e-100) (not (<= a 5.5e-101)))
   (+ x (fma (/ (- t z) (- a t)) y y))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.8e-100) || !(a <= 5.5e-101)) {
		tmp = x + fma(((t - z) / (a - t)), y, y);
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.8e-100) || !(a <= 5.5e-101))
		tmp = Float64(x + fma(Float64(Float64(t - z) / Float64(a - t)), y, y));
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.8e-100], N[Not[LessEqual[a, 5.5e-101]], $MachinePrecision]], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.79999999999999953e-100 or 5.49999999999999973e-101 < a

   1. Initial program 86.8%

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

      1. associate--l+ 89.1%

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

      2. sub-neg 89.1%

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

      3. +-commutative 89.1%

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

      4. associate-/l* 90.7%

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

      5. distribute-neg-frac 90.7%

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

      6. associate-/r/ 95.0%

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

      7. fma-def 95.0%

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

      8. sub-neg 95.0%

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

      9. +-commutative 95.0%

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

      10. distribute-neg-in 95.0%

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

      11. unsub-neg 95.0%

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

      12. remove-double-neg 95.0%

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

   3. Simplified 95.0%

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

   if -6.79999999999999953e-100 < a < 5.49999999999999973e-101

   1. Initial program 70.0%

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

      1. associate--l+ 76.5%

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

      2. sub-neg 76.5%

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

      3. +-commutative 76.5%

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

      4. associate-/l* 80.8%

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

      5. distribute-neg-frac 80.8%

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

      6. associate-/r/ 80.8%

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

      7. fma-def 80.8%

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

      8. sub-neg 80.8%

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

      9. +-commutative 80.8%

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

      10. distribute-neg-in 80.8%

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

      11. unsub-neg 80.8%

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

      12. remove-double-neg 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in z around inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r/ 93.9%

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

      4. distribute-lft-neg-in 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-100} \lor \neg \left(a \leq 5.5 \cdot 10^{-101}\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+142}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+113}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+142)
   (+ x (* y (/ z t)))
   (if (<= t 9e+113)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (+ x (* (/ y t) (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+142) {
		tmp = x + (y * (z / t));
	} else if (t <= 9e+113) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+142)) then
        tmp = x + (y * (z / t))
    else if (t <= 9d+113) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x + ((y / t) * (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+142) {
		tmp = x + (y * (z / t));
	} else if (t <= 9e+113) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+142:
		tmp = x + (y * (z / t))
	elif t <= 9e+113:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x + ((y / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+142)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 9e+113)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+142)
		tmp = x + (y * (z / t));
	elseif (t <= 9e+113)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x + ((y / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+142], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+113], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e142

   1. Initial program 56.2%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in a around 0 53.8%

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

      1. associate--l+ 53.8%

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

      2. sub-neg 53.8%

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

      3. mul-1-neg 53.8%

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

      4. remove-double-neg 53.8%

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

      5. *-commutative 53.8%

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

      6. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 80.9%

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

      1. associate-/l* 96.2%

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

   9. Simplified 96.2%

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

   10. Taylor expanded in y around 0 80.9%

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

       1. associate-*r/ 96.3%

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

   12. Simplified 96.3%

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

   if -2.8e142 < t < 9.0000000000000001e113

   1. Initial program 90.6%

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

      1. associate--l+ 92.4%

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

      2. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   if 9.0000000000000001e113 < t

   1. Initial program 59.0%

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

      1. associate-*l/ 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in t around -inf 82.5%

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

      1. +-commutative 82.5%

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

      2. mul-1-neg 82.5%

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

      3. unsub-neg 82.5%

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

      4. distribute-lft-out-- 82.6%

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

   6. Simplified 82.6%

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

      1. expm1-log1p-u 76.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 67.6%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

      3. associate-/l* 72.6%

         \[\leadsto x - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{t}{a - z}}}\right)} - 1\right) \]

   8. Applied egg-rr 72.6%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 79.0%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)\right)} \]

      2. expm1-log1p 90.7%

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

      3. associate-/r/ 91.4%

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

   10. Simplified 91.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+142}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+113}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \]

Alternative 3: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+143}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+114}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+143)
   (+ (- x (/ y (/ t a))) (/ y (/ t z)))
   (if (<= t 6e+114)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (+ x (* (/ y t) (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+143) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else if (t <= 6e+114) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.8d+143)) then
        tmp = (x - (y / (t / a))) + (y / (t / z))
    else if (t <= 6d+114) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x + ((y / t) * (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+143) {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	} else if (t <= 6e+114) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+143:
		tmp = (x - (y / (t / a))) + (y / (t / z))
	elif t <= 6e+114:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x + ((y / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+143)
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	elseif (t <= 6e+114)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+143)
		tmp = (x - (y / (t / a))) + (y / (t / z));
	elseif (t <= 6e+114)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x + ((y / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+143], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+114], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8e143

   1. Initial program 56.2%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in t around inf 78.4%

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

      1. sub-neg 78.4%

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

      2. +-commutative 78.4%

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

      3. mul-1-neg 78.4%

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

      4. unsub-neg 78.4%

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

      5. associate-/l* 80.9%

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

      6. mul-1-neg 80.9%

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

      7. remove-double-neg 80.9%

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

      8. associate-/l* 97.4%

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

   6. Simplified 97.4%

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

   if -3.8e143 < t < 6.0000000000000001e114

   1. Initial program 90.6%

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

      1. associate--l+ 92.4%

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

      2. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   if 6.0000000000000001e114 < t

   1. Initial program 59.0%

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

      1. associate-*l/ 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in t around -inf 82.5%

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

      1. +-commutative 82.5%

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

      2. mul-1-neg 82.5%

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

      3. unsub-neg 82.5%

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

      4. distribute-lft-out-- 82.6%

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

   6. Simplified 82.6%

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

      1. expm1-log1p-u 76.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 67.6%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

      3. associate-/l* 72.6%

         \[\leadsto x - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{t}{a - z}}}\right)} - 1\right) \]

   8. Applied egg-rr 72.6%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 79.0%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)\right)} \]

      2. expm1-log1p 90.7%

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

      3. associate-/r/ 91.4%

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

   10. Simplified 91.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+143}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+114}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \]

Alternative 4: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-71} \lor \neg \left(a \leq 2 \cdot 10^{-39}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e-71) (not (<= a 2e-39)))
   (+ y (- x (/ y (/ a z))))
   (+ x (* (/ y t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e-71) || !(a <= 2e-39)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.15d-71)) .or. (.not. (a <= 2d-39))) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + ((y / t) * (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e-71) || !(a <= 2e-39)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.15e-71) or not (a <= 2e-39):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + ((y / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e-71) || !(a <= 2e-39))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.15e-71) || ~((a <= 2e-39)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + ((y / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e-71], N[Not[LessEqual[a, 2e-39]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1499999999999999e-71 or 1.99999999999999986e-39 < a

   1. Initial program 88.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around 0 83.8%

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

      1. associate--l+ 83.8%

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

      2. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

   if -1.1499999999999999e-71 < a < 1.99999999999999986e-39

   1. Initial program 70.2%

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

      1. associate-*l/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. distribute-lft-out-- 83.1%

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

   6. Simplified 83.1%

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

      1. expm1-log1p-u 61.3%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 56.1%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

      3. associate-/l* 53.8%

         \[\leadsto x - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{t}{a - z}}}\right)} - 1\right) \]

   8. Applied egg-rr 53.8%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 57.4%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)\right)} \]

      2. expm1-log1p 81.1%

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

      3. associate-/r/ 85.7%

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

   10. Simplified 85.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-71} \lor \neg \left(a \leq 2 \cdot 10^{-39}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \]

Alternative 5: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+51} \lor \neg \left(a \leq 1.45 \cdot 10^{-37}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e+51) (not (<= a 1.45e-37)))
   (- (+ x y) (* y (/ z a)))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e+51) || !(a <= 1.45e-37)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d+51)) .or. (.not. (a <= 1.45d-37))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x - (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e+51) || !(a <= 1.45e-37)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e+51) or not (a <= 1.45e-37):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e+51) || !(a <= 1.45e-37))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e+51) || ~((a <= 1.45e-37)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e+51], N[Not[LessEqual[a, 1.45e-37]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.4999999999999999e51 or 1.45000000000000002e-37 < a

   1. Initial program 90.3%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around 0 89.2%

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

   if -8.4999999999999999e51 < a < 1.45000000000000002e-37

   1. Initial program 70.8%

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

      1. associate--l+ 77.9%

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

      2. sub-neg 77.9%

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

      3. +-commutative 77.9%

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

      4. associate-/l* 80.9%

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

      5. distribute-neg-frac 80.9%

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

      6. associate-/r/ 82.9%

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

      7. fma-def 82.9%

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

      8. sub-neg 82.9%

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

      9. +-commutative 82.9%

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

      10. distribute-neg-in 82.9%

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

      11. unsub-neg 82.9%

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

      12. remove-double-neg 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-*r/ 87.3%

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

      4. distribute-lft-neg-in 87.3%

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

   6. Simplified 87.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+51} \lor \neg \left(a \leq 1.45 \cdot 10^{-37}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 6: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+110}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e-36)
   (+ x (* y (/ z t)))
   (if (<= t 2.95e+110) (+ y (- x (/ y (/ a z)))) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e-36) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.95e+110) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (z * (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 (t <= (-1.8d-36)) then
        tmp = x + (y * (z / t))
    else if (t <= 2.95d+110) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + (z * (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 (t <= -1.8e-36) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.95e+110) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e-36:
		tmp = x + (y * (z / t))
	elif t <= 2.95e+110:
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e-36)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 2.95e+110)
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e-36)
		tmp = x + (y * (z / t));
	elseif (t <= 2.95e+110)
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e-36], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+110], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000016e-36

   1. Initial program 66.3%

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

      1. associate-*l/ 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in a around 0 58.5%

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

      1. associate--l+ 58.5%

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

      2. sub-neg 58.5%

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

      3. mul-1-neg 58.5%

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

      4. remove-double-neg 58.5%

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

      5. *-commutative 58.5%

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

      6. associate-/l* 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. associate-/l* 88.8%

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

   9. Simplified 88.8%

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

   10. Taylor expanded in y around 0 79.8%

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

       1. associate-*r/ 88.8%

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

   12. Simplified 88.8%

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

   if -1.80000000000000016e-36 < t < 2.9499999999999999e110

   1. Initial program 94.2%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 82.2%

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

      1. associate--l+ 82.2%

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

      2. associate-/l* 83.6%

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

   6. Simplified 83.6%

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

   if 2.9499999999999999e110 < t

   1. Initial program 60.1%

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

      1. associate-*l/ 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in a around 0 54.5%

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

      1. associate--l+ 54.5%

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

      2. sub-neg 54.5%

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

      3. mul-1-neg 54.5%

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

      4. remove-double-neg 54.5%

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

      5. *-commutative 54.5%

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

      6. associate-/l* 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in y around 0 76.3%

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

      1. associate-/l* 81.6%

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

   9. Simplified 81.6%

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

       1. associate-/r/ 81.7%

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

   11. Applied egg-rr 81.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+110}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-71}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e-71)
   (+ y (- x (/ y (/ a z))))
   (if (<= a 2.15e-41) (+ x (* (/ y t) (- z a))) (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e-71) {
		tmp = y + (x - (y / (a / z)));
	} else if (a <= 2.15e-41) {
		tmp = x + ((y / t) * (z - a));
	} 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 (a <= (-5d-71)) then
        tmp = y + (x - (y / (a / z)))
    else if (a <= 2.15d-41) then
        tmp = x + ((y / t) * (z - a))
    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 (a <= -5e-71) {
		tmp = y + (x - (y / (a / z)));
	} else if (a <= 2.15e-41) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e-71:
		tmp = y + (x - (y / (a / z)))
	elif a <= 2.15e-41:
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e-71)
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	elseif (a <= 2.15e-41)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e-71)
		tmp = y + (x - (y / (a / z)));
	elseif (a <= 2.15e-41)
		tmp = x + ((y / t) * (z - a));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e-71], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e-41], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.99999999999999998e-71

   1. Initial program 87.3%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around 0 79.6%

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

      1. associate--l+ 79.6%

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

      2. associate-/l* 83.3%

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

   6. Simplified 83.3%

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

   if -4.99999999999999998e-71 < a < 2.1499999999999999e-41

   1. Initial program 70.2%

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

      1. associate-*l/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in t around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. distribute-lft-out-- 83.1%

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

   6. Simplified 83.1%

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

      1. expm1-log1p-u 61.3%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 56.1%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

      3. associate-/l* 53.8%

         \[\leadsto x - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{t}{a - z}}}\right)} - 1\right) \]

   8. Applied egg-rr 53.8%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 57.4%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{t}{a - z}}\right)\right)} \]

      2. expm1-log1p 81.1%

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

      3. associate-/r/ 85.7%

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

   10. Simplified 85.7%

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

   if 2.1499999999999999e-41 < a

   1. Initial program 89.9%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around 0 89.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-71}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-70} \lor \neg \left(a \leq 9.2 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.75e-70) (not (<= a 9.2e-42))) (+ x y) (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e-70) || !(a <= 9.2e-42)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (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 <= (-1.75d-70)) .or. (.not. (a <= 9.2d-42))) then
        tmp = x + y
    else
        tmp = x + (z * (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 <= -1.75e-70) || !(a <= 9.2e-42)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.75e-70) or not (a <= 9.2e-42):
		tmp = x + y
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.75e-70) || !(a <= 9.2e-42))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.75e-70) || ~((a <= 9.2e-42)))
		tmp = x + y;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.75e-70], N[Not[LessEqual[a, 9.2e-42]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.74999999999999987e-70 or 9.20000000000000015e-42 < a

   1. Initial program 88.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in a around inf 79.3%

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

   if -1.74999999999999987e-70 < a < 9.20000000000000015e-42

   1. Initial program 70.2%

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

      1. associate-*l/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in a around 0 58.0%

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

      1. associate--l+ 58.0%

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

      2. sub-neg 58.0%

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

      3. mul-1-neg 58.0%

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

      4. remove-double-neg 58.0%

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

      5. *-commutative 58.0%

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

      6. associate-/l* 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in y around 0 79.2%

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

      1. associate-/l* 77.2%

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

   9. Simplified 77.2%

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

       1. associate-/r/ 81.8%

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

   11. Applied egg-rr 81.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-70} \lor \neg \left(a \leq 9.2 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 9: 76.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-41}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-69) (+ x y) (if (<= a 2.1e-41) (+ x (* y (/ z t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-69) {
		tmp = x + y;
	} else if (a <= 2.1e-41) {
		tmp = x + (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 (a <= (-2.4d-69)) then
        tmp = x + y
    else if (a <= 2.1d-41) then
        tmp = x + (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 (a <= -2.4e-69) {
		tmp = x + y;
	} else if (a <= 2.1e-41) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-69:
		tmp = x + y
	elif a <= 2.1e-41:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-69)
		tmp = Float64(x + y);
	elseif (a <= 2.1e-41)
		tmp = Float64(x + 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 (a <= -2.4e-69)
		tmp = x + y;
	elseif (a <= 2.1e-41)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-69], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.1e-41], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4000000000000001e-69 or 2.10000000000000013e-41 < a

   1. Initial program 88.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in a around inf 79.3%

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

   if -2.4000000000000001e-69 < a < 2.10000000000000013e-41

   1. Initial program 70.2%

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

      1. associate-*l/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in a around 0 58.0%

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

      1. associate--l+ 58.0%

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

      2. sub-neg 58.0%

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

      3. mul-1-neg 58.0%

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

      4. remove-double-neg 58.0%

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

      5. *-commutative 58.0%

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

      6. associate-/l* 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in y around 0 79.2%

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

      1. associate-/l* 77.2%

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

   9. Simplified 77.2%

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

   10. Taylor expanded in y around 0 79.2%

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

       1. associate-*r/ 76.8%

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

   12. Simplified 76.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-41}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 63.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e-100) (+ x y) (if (<= a 4.6e-98) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e-100) {
		tmp = x + y;
	} else if (a <= 4.6e-98) {
		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 <= (-3.4d-100)) then
        tmp = x + y
    else if (a <= 4.6d-98) 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 <= -3.4e-100) {
		tmp = x + y;
	} else if (a <= 4.6e-98) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e-100:
		tmp = x + y
	elif a <= 4.6e-98:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e-100)
		tmp = Float64(x + y);
	elseif (a <= 4.6e-98)
		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 <= -3.4e-100)
		tmp = x + y;
	elseif (a <= 4.6e-98)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e-100], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.6e-98], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.39999999999999976e-100 or 4.60000000000000001e-98 < a

   1. Initial program 87.3%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around inf 76.3%

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

   if -3.39999999999999976e-100 < a < 4.60000000000000001e-98

   1. Initial program 69.3%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around inf 47.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 51.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.5e-111) x (if (<= x 2.3e-15) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.5e-111) {
		tmp = x;
	} else if (x <= 2.3e-15) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4.5d-111)) then
        tmp = x
    else if (x <= 2.3d-15) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.5e-111) {
		tmp = x;
	} else if (x <= 2.3e-15) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.5e-111:
		tmp = x
	elif x <= 2.3e-15:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.5e-111)
		tmp = x;
	elseif (x <= 2.3e-15)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.5e-111)
		tmp = x;
	elseif (x <= 2.3e-15)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.5e-111], x, If[LessEqual[x, 2.3e-15], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999994e-111 or 2.2999999999999999e-15 < x

   1. Initial program 85.6%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around inf 69.5%

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

   if -4.49999999999999994e-111 < x < 2.2999999999999999e-15

   1. Initial program 73.2%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

      1. associate-*l/ 73.2%

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

      2. flip-+ 53.4%

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

      3. frac-sub 42.8%

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

      4. difference-of-squares 42.8%

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

      5. +-commutative 42.8%

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

      6. *-commutative 42.8%

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

   5. Applied egg-rr 42.8%

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

   6. Taylor expanded in a around inf 31.7%

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

   7. Taylor expanded in y around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-/l* 36.0%

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

   9. Simplified 36.0%

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

   10. Taylor expanded in a around inf 37.1%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.0% 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 80.6%

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

   1. associate-*l/ 83.5%

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

3. Simplified 83.5%

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

4. Taylor expanded in x around inf 49.4%

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

5. Final simplification 49.4%

   \[\leadsto x \]

Developer target: 88.2% 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 2023181 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (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))))