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

Percentage Accurate: 76.1% → 90.1%

Time: 10.4s

Alternatives: 10

Speedup: 0.6×

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: 76.1% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+130} \lor \neg \left(t \leq 1.95 \cdot 10^{+117}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e+130) (not (<= t 1.95e+117)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (fma (- z t) (/ y (- t a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+130) || !(t <= 1.95e+117)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = fma((z - t), (y / (t - a)), (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e+130) || !(t <= 1.95e+117))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e+130], N[Not[LessEqual[t, 1.95e+117]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999999e130 or 1.94999999999999995e117 < t

   1. Initial program 46.3%

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

      1. +-commutative 46.3%

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

      2. associate--l+ 46.3%

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

      3. *-commutative 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in t around inf 72.5%

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

      1. sub-neg 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. associate-/l* 81.8%

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

      5. mul-1-neg 81.8%

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

      6. remove-double-neg 81.8%

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

      7. associate-/l* 91.8%

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

   7. Simplified 91.8%

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

   if -2.8999999999999999e130 < t < 1.94999999999999995e117

   1. Initial program 85.4%

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

      1. sub-neg 85.4%

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

      2. +-commutative 85.4%

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

      3. distribute-frac-neg 85.4%

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

      4. distribute-rgt-neg-out 85.4%

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

      5. associate-/l* 89.5%

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

      6. fma-define 89.6%

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

      7. distribute-frac-neg 89.6%

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

      8. distribute-neg-frac2 89.6%

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

      9. sub-neg 89.6%

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

      10. distribute-neg-in 89.6%

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

      11. remove-double-neg 89.6%

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

      12. +-commutative 89.6%

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

      13. sub-neg 89.6%

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

   3. Simplified 89.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+130} \lor \neg \left(t \leq 1.95 \cdot 10^{+117}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t} + \left(x + y\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 240000000:\\ \;\;\;\;y + \left(x - y \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* y (/ z t)) (+ x y))))
   (if (<= t -1.1e+129)
     x
     (if (<= t -1.1e-44)
       t_1
       (if (<= t 240000000.0)
         (+ y (- x (* y (/ z a))))
         (if (<= t 9.5e+117) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z / t)) + (x + y);
	double tmp;
	if (t <= -1.1e+129) {
		tmp = x;
	} else if (t <= -1.1e-44) {
		tmp = t_1;
	} else if (t <= 240000000.0) {
		tmp = y + (x - (y * (z / a)));
	} else if (t <= 9.5e+117) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z / t)) + (x + y)
    if (t <= (-1.1d+129)) then
        tmp = x
    else if (t <= (-1.1d-44)) then
        tmp = t_1
    else if (t <= 240000000.0d0) then
        tmp = y + (x - (y * (z / a)))
    else if (t <= 9.5d+117) then
        tmp = t_1
    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 t_1 = (y * (z / t)) + (x + y);
	double tmp;
	if (t <= -1.1e+129) {
		tmp = x;
	} else if (t <= -1.1e-44) {
		tmp = t_1;
	} else if (t <= 240000000.0) {
		tmp = y + (x - (y * (z / a)));
	} else if (t <= 9.5e+117) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z / t)) + (x + y)
	tmp = 0
	if t <= -1.1e+129:
		tmp = x
	elif t <= -1.1e-44:
		tmp = t_1
	elif t <= 240000000.0:
		tmp = y + (x - (y * (z / a)))
	elif t <= 9.5e+117:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z / t)) + Float64(x + y))
	tmp = 0.0
	if (t <= -1.1e+129)
		tmp = x;
	elseif (t <= -1.1e-44)
		tmp = t_1;
	elseif (t <= 240000000.0)
		tmp = Float64(y + Float64(x - Float64(y * Float64(z / a))));
	elseif (t <= 9.5e+117)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z / t)) + (x + y);
	tmp = 0.0;
	if (t <= -1.1e+129)
		tmp = x;
	elseif (t <= -1.1e-44)
		tmp = t_1;
	elseif (t <= 240000000.0)
		tmp = y + (x - (y * (z / a)));
	elseif (t <= 9.5e+117)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+129], x, If[LessEqual[t, -1.1e-44], t$95$1, If[LessEqual[t, 240000000.0], N[(y + N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+117], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e129 or 9.50000000000000041e117 < t

   1. Initial program 46.5%

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

      1. sub-neg 46.5%

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

      2. +-commutative 46.5%

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

      3. distribute-frac-neg 46.5%

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

      4. distribute-rgt-neg-out 46.5%

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

      5. associate-/l* 59.9%

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

      6. fma-define 60.2%

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

      7. distribute-frac-neg 60.2%

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

      8. distribute-neg-frac2 60.2%

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

      9. sub-neg 60.2%

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

      10. distribute-neg-in 60.2%

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

      11. remove-double-neg 60.2%

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

      12. +-commutative 60.2%

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

      13. sub-neg 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in y around 0 71.7%

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

   if -1.1e129 < t < -1.10000000000000006e-44 or 2.4e8 < t < 9.50000000000000041e117

   1. Initial program 76.6%

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

      1. +-commutative 76.6%

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

      2. associate--l+ 76.6%

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

      3. *-commutative 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in z around inf 79.4%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in a around 0 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

      3. mul-1-neg 76.5%

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

      4. remove-double-neg 76.5%

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

      5. associate-/l* 79.2%

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

   10. Simplified 79.2%

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

   if -1.10000000000000006e-44 < t < 2.4e8

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate--l+ 90.9%

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

      3. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 83.5%

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

      1. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z}{t} + \left(x + y\right)\\ \mathbf{elif}\;t \leq 240000000:\\ \;\;\;\;y + \left(x - y \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{z}{t} + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+131} \lor \neg \left(t \leq 2.35 \cdot 10^{+117}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + y \cdot \frac{z}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+131) (not (<= t 2.35e+117)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (+ y (+ x (* y (/ z (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+131) || !(t <= 2.35e+117)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = y + (x + (y * (z / (t - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.3d+131)) .or. (.not. (t <= 2.35d+117))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = y + (x + (y * (z / (t - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+131) || !(t <= 2.35e+117)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = y + (x + (y * (z / (t - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+131) or not (t <= 2.35e+117):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = y + (x + (y * (z / (t - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+131) || !(t <= 2.35e+117))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + Float64(x + Float64(y * Float64(z / Float64(t - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e+131) || ~((t <= 2.35e+117)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = y + (x + (y * (z / (t - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+131], N[Not[LessEqual[t, 2.35e+117]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e131 or 2.35000000000000003e117 < t

   1. Initial program 46.3%

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

      1. +-commutative 46.3%

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

      2. associate--l+ 46.3%

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

      3. *-commutative 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in t around inf 72.5%

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

      1. sub-neg 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. associate-/l* 81.8%

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

      5. mul-1-neg 81.8%

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

      6. remove-double-neg 81.8%

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

      7. associate-/l* 91.8%

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

   7. Simplified 91.8%

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

   if -1.3e131 < t < 2.35000000000000003e117

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate--l+ 85.4%

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

      3. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+131} \lor \neg \left(t \leq 2.35 \cdot 10^{+117}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + y \cdot \frac{z}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{-49} \lor \neg \left(a \leq 720\right):\\ \;\;\;\;y + \left(x + y \cdot \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - a \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.28e-49) (not (<= a 720.0)))
   (+ y (+ x (* y (/ z (- t a)))))
   (+ x (/ (- (* y z) (* a y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.28e-49) || !(a <= 720.0)) {
		tmp = y + (x + (y * (z / (t - a))));
	} else {
		tmp = x + (((y * z) - (a * y)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.28d-49)) .or. (.not. (a <= 720.0d0))) then
        tmp = y + (x + (y * (z / (t - a))))
    else
        tmp = x + (((y * z) - (a * y)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.28e-49) || !(a <= 720.0)) {
		tmp = y + (x + (y * (z / (t - a))));
	} else {
		tmp = x + (((y * z) - (a * y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.28e-49) or not (a <= 720.0):
		tmp = y + (x + (y * (z / (t - a))))
	else:
		tmp = x + (((y * z) - (a * y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.28e-49) || !(a <= 720.0))
		tmp = Float64(y + Float64(x + Float64(y * Float64(z / Float64(t - a)))));
	else
		tmp = Float64(x + Float64(Float64(Float64(y * z) - Float64(a * y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.28e-49) || ~((a <= 720.0)))
		tmp = y + (x + (y * (z / (t - a))));
	else
		tmp = x + (((y * z) - (a * y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.28e-49], N[Not[LessEqual[a, 720.0]], $MachinePrecision]], N[(y + N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y * z), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.28e-49 or 720 < a

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. associate--l+ 78.0%

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

      3. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in z around inf 79.2%

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

      1. associate-/l* 89.0%

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

   7. Simplified 89.0%

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

   if -1.28e-49 < a < 720

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. associate--l+ 70.0%

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

      3. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in t around -inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-commutative 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{-49} \lor \neg \left(a \leq 720\right):\\ \;\;\;\;y + \left(x + y \cdot \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - a \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+198}:\\ \;\;\;\;y + \left(x + y \cdot \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.4e+134)
   x
   (if (<= t 1.2e+198) (+ y (+ x (* y (/ z (- t a))))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+134) {
		tmp = x;
	} else if (t <= 1.2e+198) {
		tmp = y + (x + (y * (z / (t - a))));
	} 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 (t <= (-1.4d+134)) then
        tmp = x
    else if (t <= 1.2d+198) then
        tmp = y + (x + (y * (z / (t - a))))
    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 (t <= -1.4e+134) {
		tmp = x;
	} else if (t <= 1.2e+198) {
		tmp = y + (x + (y * (z / (t - a))));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.4e+134:
		tmp = x
	elif t <= 1.2e+198:
		tmp = y + (x + (y * (z / (t - a))))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.4e+134)
		tmp = x;
	elseif (t <= 1.2e+198)
		tmp = Float64(y + Float64(x + Float64(y * Float64(z / Float64(t - a)))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.4e+134)
		tmp = x;
	elseif (t <= 1.2e+198)
		tmp = y + (x + (y * (z / (t - a))));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.4e+134], x, If[LessEqual[t, 1.2e+198], N[(y + N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e134 or 1.2000000000000001e198 < t

   1. Initial program 46.4%

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

      1. sub-neg 46.4%

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

      2. +-commutative 46.4%

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

      3. distribute-frac-neg 46.4%

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

      4. distribute-rgt-neg-out 46.4%

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

      5. associate-/l* 55.9%

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

      6. fma-define 56.0%

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

      7. distribute-frac-neg 56.0%

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

      8. distribute-neg-frac2 56.0%

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

      9. sub-neg 56.0%

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

      10. distribute-neg-in 56.0%

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

      11. remove-double-neg 56.0%

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

      12. +-commutative 56.0%

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

      13. sub-neg 56.0%

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

   3. Simplified 56.0%

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

   5. Taylor expanded in y around 0 76.5%

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

   if -1.3999999999999999e134 < t < 1.2000000000000001e198

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. associate--l+ 81.9%

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

      3. *-commutative 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+198}:\\ \;\;\;\;y + \left(x + y \cdot \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+116}:\\ \;\;\;\;y + \left(x - y \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+132) x (if (<= t 2.05e+116) (+ y (- x (* y (/ z a)))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+132) {
		tmp = x;
	} else if (t <= 2.05e+116) {
		tmp = y + (x - (y * (z / a)));
	} 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 (t <= (-7.2d+132)) then
        tmp = x
    else if (t <= 2.05d+116) then
        tmp = y + (x - (y * (z / a)))
    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 (t <= -7.2e+132) {
		tmp = x;
	} else if (t <= 2.05e+116) {
		tmp = y + (x - (y * (z / a)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+132:
		tmp = x
	elif t <= 2.05e+116:
		tmp = y + (x - (y * (z / a)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+132)
		tmp = x;
	elseif (t <= 2.05e+116)
		tmp = Float64(y + Float64(x - Float64(y * Float64(z / a))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+132)
		tmp = x;
	elseif (t <= 2.05e+116)
		tmp = y + (x - (y * (z / a)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+132], x, If[LessEqual[t, 2.05e+116], N[(y + N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000031e132 or 2.0499999999999999e116 < t

   1. Initial program 46.3%

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

      1. sub-neg 46.3%

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

      2. +-commutative 46.3%

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

      3. distribute-frac-neg 46.3%

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

      4. distribute-rgt-neg-out 46.3%

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

      5. associate-/l* 58.8%

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

      6. fma-define 59.1%

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

      7. distribute-frac-neg 59.1%

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

      8. distribute-neg-frac2 59.1%

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

      9. sub-neg 59.1%

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

      10. distribute-neg-in 59.1%

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

      11. remove-double-neg 59.1%

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

      12. +-commutative 59.1%

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

      13. sub-neg 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in y around 0 72.2%

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

   if -7.20000000000000031e132 < t < 2.0499999999999999e116

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate--l+ 85.4%

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

      3. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 75.8%

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

      1. associate-/l* 77.9%

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

   7. Simplified 77.9%

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

Alternative 7: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-19} \lor \neg \left(a \leq 24000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.1e-19) (not (<= a 24000000000.0))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e-19) || !(a <= 24000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.1d-19)) .or. (.not. (a <= 24000000000.0d0))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e-19) || !(a <= 24000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.1e-19) or not (a <= 24000000000.0):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.1e-19) || !(a <= 24000000000.0))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.1e-19) || ~((a <= 24000000000.0)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.1e-19], N[Not[LessEqual[a, 24000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.0999999999999999e-19 or 2.4e10 < a

   1. Initial program 78.3%

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

      1. sub-neg 78.3%

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

      2. +-commutative 78.3%

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

      3. distribute-frac-neg 78.3%

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

      4. distribute-rgt-neg-out 78.3%

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

      5. associate-/l* 90.0%

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

      6. fma-define 90.1%

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

      7. distribute-frac-neg 90.1%

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

      8. distribute-neg-frac2 90.1%

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

      9. sub-neg 90.1%

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

      10. distribute-neg-in 90.1%

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

      11. remove-double-neg 90.1%

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

      12. +-commutative 90.1%

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

      13. sub-neg 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in a around inf 78.4%

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

      1. +-commutative 78.4%

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

   7. Simplified 78.4%

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

   if -2.0999999999999999e-19 < a < 2.4e10

   1. Initial program 70.1%

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

      1. sub-neg 70.1%

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

      2. +-commutative 70.1%

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

      3. distribute-frac-neg 70.1%

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

      4. distribute-rgt-neg-out 70.1%

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

      5. associate-/l* 71.4%

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

      6. fma-define 71.6%

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

      7. distribute-frac-neg 71.6%

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

      8. distribute-neg-frac2 71.6%

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

      9. sub-neg 71.6%

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

      10. distribute-neg-in 71.6%

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

      11. remove-double-neg 71.6%

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

      12. +-commutative 71.6%

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

      13. sub-neg 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in y around 0 57.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-19} \lor \neg \left(a \leq 24000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+87}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9e+87) y (if (<= y 7.5e+127) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+87) {
		tmp = y;
	} else if (y <= 7.5e+127) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-9d+87)) then
        tmp = y
    else if (y <= 7.5d+127) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+87) {
		tmp = y;
	} else if (y <= 7.5e+127) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9e+87:
		tmp = y
	elif y <= 7.5e+127:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9e+87)
		tmp = y;
	elseif (y <= 7.5e+127)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9e+87)
		tmp = y;
	elseif (y <= 7.5e+127)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9e+87], y, If[LessEqual[y, 7.5e+127], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000005e87 or 7.4999999999999996e127 < y

   1. Initial program 55.4%

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

      1. +-commutative 55.4%

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

      2. associate--l+ 55.4%

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

      3. *-commutative 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in y around -inf 65.9%

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

      1. neg-mul-1 65.9%

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

      2. unsub-neg 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in a around inf 35.9%

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

   if -9.0000000000000005e87 < y < 7.4999999999999996e127

   1. Initial program 85.0%

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

      1. sub-neg 85.0%

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

      2. +-commutative 85.0%

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

      3. distribute-frac-neg 85.0%

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

      4. distribute-rgt-neg-out 85.0%

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

      5. associate-/l* 86.3%

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

      6. fma-define 86.4%

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

      7. distribute-frac-neg 86.4%

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

      8. distribute-neg-frac2 86.4%

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

      9. sub-neg 86.4%

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

      10. distribute-neg-in 86.4%

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

      11. remove-double-neg 86.4%

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

      12. +-commutative 86.4%

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

      13. sub-neg 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around 0 71.1%

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

Alternative 9: 50.3% 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 74.2%

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

   1. sub-neg 74.2%

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

   2. +-commutative 74.2%

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

   3. distribute-frac-neg 74.2%

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

   4. distribute-rgt-neg-out 74.2%

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

   5. associate-/l* 80.8%

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

   6. fma-define 80.9%

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

   7. distribute-frac-neg 80.9%

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

   8. distribute-neg-frac2 80.9%

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

   9. sub-neg 80.9%

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

   10. distribute-neg-in 80.9%

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

   11. remove-double-neg 80.9%

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

   12. +-commutative 80.9%

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

   13. sub-neg 80.9%

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

3. Simplified 80.9%

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

5. Taylor expanded in y around 0 51.9%

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

Alternative 10: 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 74.2%

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

   1. +-commutative 74.2%

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

   2. associate--l+ 74.2%

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

   3. *-commutative 74.2%

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

3. Simplified 74.2%

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

5. Taylor expanded in t around inf 42.9%

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

6. Taylor expanded in x around 0 2.6%

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

   1. neg-mul-1 2.6%

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

8. Simplified 2.6%

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

9. Taylor expanded in y around 0 2.6%

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

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

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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