Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 67.5% → 90.0%

Time: 30.3s

Alternatives: 22

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t z) (/ (- x y) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-270)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_2 2e+122) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - z) * ((x - y) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-270) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 2e+122) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - z) * ((x - y) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-270) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 2e+122) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - z) * ((x - y) / (a - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-270:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((x * (z - a)) / t)
	elif t_2 <= 2e+122:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - z) * Float64(Float64(x - y) / Float64(a - t))))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-270)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_2 <= 2e+122)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - z) * ((x - y) / (a - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-270)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((x * (z - a)) / t);
	elseif (t_2 <= 2e+122)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-270], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+122], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 2.00000000000000003e122 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 54.5%

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

      1. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-270 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.00000000000000003e122

   1. Initial program 95.8%

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

   if -2.0000000000000001e-270 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

      1. associate-*l/ 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. unsub-neg 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-270}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-270} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-270) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (* x (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-270) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-2d-270)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((x * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-270) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -2e-270) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((x * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-270) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-270) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((x * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-270], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-270 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 76.5%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   if -2.0000000000000001e-270 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

      1. associate-*l/ 3.7%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. unsub-neg 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-270} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-187}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7700000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.9e+24)
     y
     (if (<= t -1.8e-133)
       t_2
       (if (<= t -6e-187)
         (/ (* y z) (- a t))
         (if (<= t -1.75e-227)
           t_2
           (if (<= t -4.2e-307)
             t_1
             (if (<= t 2.8e-227) t_2 (if (<= t 7700000000.0) t_1 y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.9e+24) {
		tmp = y;
	} else if (t <= -1.8e-133) {
		tmp = t_2;
	} else if (t <= -6e-187) {
		tmp = (y * z) / (a - t);
	} else if (t <= -1.75e-227) {
		tmp = t_2;
	} else if (t <= -4.2e-307) {
		tmp = t_1;
	} else if (t <= 2.8e-227) {
		tmp = t_2;
	} else if (t <= 7700000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-2.9d+24)) then
        tmp = y
    else if (t <= (-1.8d-133)) then
        tmp = t_2
    else if (t <= (-6d-187)) then
        tmp = (y * z) / (a - t)
    else if (t <= (-1.75d-227)) then
        tmp = t_2
    else if (t <= (-4.2d-307)) then
        tmp = t_1
    else if (t <= 2.8d-227) then
        tmp = t_2
    else if (t <= 7700000000.0d0) then
        tmp = t_1
    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 t_1 = x + (y * (z / a));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.9e+24) {
		tmp = y;
	} else if (t <= -1.8e-133) {
		tmp = t_2;
	} else if (t <= -6e-187) {
		tmp = (y * z) / (a - t);
	} else if (t <= -1.75e-227) {
		tmp = t_2;
	} else if (t <= -4.2e-307) {
		tmp = t_1;
	} else if (t <= 2.8e-227) {
		tmp = t_2;
	} else if (t <= 7700000000.0) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -2.9e+24:
		tmp = y
	elif t <= -1.8e-133:
		tmp = t_2
	elif t <= -6e-187:
		tmp = (y * z) / (a - t)
	elif t <= -1.75e-227:
		tmp = t_2
	elif t <= -4.2e-307:
		tmp = t_1
	elif t <= 2.8e-227:
		tmp = t_2
	elif t <= 7700000000.0:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -2.9e+24)
		tmp = y;
	elseif (t <= -1.8e-133)
		tmp = t_2;
	elseif (t <= -6e-187)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= -1.75e-227)
		tmp = t_2;
	elseif (t <= -4.2e-307)
		tmp = t_1;
	elseif (t <= 2.8e-227)
		tmp = t_2;
	elseif (t <= 7700000000.0)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -2.9e+24)
		tmp = y;
	elseif (t <= -1.8e-133)
		tmp = t_2;
	elseif (t <= -6e-187)
		tmp = (y * z) / (a - t);
	elseif (t <= -1.75e-227)
		tmp = t_2;
	elseif (t <= -4.2e-307)
		tmp = t_1;
	elseif (t <= 2.8e-227)
		tmp = t_2;
	elseif (t <= 7700000000.0)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+24], y, If[LessEqual[t, -1.8e-133], t$95$2, If[LessEqual[t, -6e-187], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-227], t$95$2, If[LessEqual[t, -4.2e-307], t$95$1, If[LessEqual[t, 2.8e-227], t$95$2, If[LessEqual[t, 7700000000.0], t$95$1, y]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.89999999999999979e24 or 7.7e9 < t

   1. Initial program 44.3%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in t around inf 44.7%

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

   if -2.89999999999999979e24 < t < -1.8000000000000002e-133 or -6.00000000000000008e-187 < t < -1.75000000000000005e-227 or -4.2000000000000002e-307 < t < 2.7999999999999998e-227

   1. Initial program 92.4%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around 0 77.3%

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

   6. Taylor expanded in x around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. unsub-neg 70.4%

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

   8. Simplified 70.4%

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

   if -1.8000000000000002e-133 < t < -6.00000000000000008e-187

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l/ 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in z around -inf 71.1%

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

       1. *-commutative 71.1%

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

   11. Simplified 71.1%

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

   12. Taylor expanded in y around inf 70.7%

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

       1. *-commutative 70.7%

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

   14. Simplified 70.7%

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

   if -1.75000000000000005e-227 < t < -4.2000000000000002e-307 or 2.7999999999999998e-227 < t < 7.7e9

   1. Initial program 93.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around 0 77.1%

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

   6. Taylor expanded in y around inf 73.0%

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

      1. associate-*r/ 73.1%

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

   8. Simplified 73.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-187}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7700000000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-50}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t))))
        (t_2 (+ x (* (- z t) (/ y a))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= a -8.5e+26)
     t_2
     (if (<= a 9.5e-201)
       t_1
       (if (<= a 3.1e-50)
         t_3
         (if (<= a 4500000000.0) t_1 (if (<= a 2.8e+103) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x + ((z - t) * (y / a));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -8.5e+26) {
		tmp = t_2;
	} else if (a <= 9.5e-201) {
		tmp = t_1;
	} else if (a <= 3.1e-50) {
		tmp = t_3;
	} else if (a <= 4500000000.0) {
		tmp = t_1;
	} else if (a <= 2.8e+103) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    t_2 = x + ((z - t) * (y / a))
    t_3 = z * ((y - x) / (a - t))
    if (a <= (-8.5d+26)) then
        tmp = t_2
    else if (a <= 9.5d-201) then
        tmp = t_1
    else if (a <= 3.1d-50) then
        tmp = t_3
    else if (a <= 4500000000.0d0) then
        tmp = t_1
    else if (a <= 2.8d+103) then
        tmp = t_3
    else
        tmp = t_2
    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 * (1.0 - (z / t));
	double t_2 = x + ((z - t) * (y / a));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -8.5e+26) {
		tmp = t_2;
	} else if (a <= 9.5e-201) {
		tmp = t_1;
	} else if (a <= 3.1e-50) {
		tmp = t_3;
	} else if (a <= 4500000000.0) {
		tmp = t_1;
	} else if (a <= 2.8e+103) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x + ((z - t) * (y / a))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -8.5e+26:
		tmp = t_2
	elif a <= 9.5e-201:
		tmp = t_1
	elif a <= 3.1e-50:
		tmp = t_3
	elif a <= 4500000000.0:
		tmp = t_1
	elif a <= 2.8e+103:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / a)))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -8.5e+26)
		tmp = t_2;
	elseif (a <= 9.5e-201)
		tmp = t_1;
	elseif (a <= 3.1e-50)
		tmp = t_3;
	elseif (a <= 4500000000.0)
		tmp = t_1;
	elseif (a <= 2.8e+103)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x + ((z - t) * (y / a));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -8.5e+26)
		tmp = t_2;
	elseif (a <= 9.5e-201)
		tmp = t_1;
	elseif (a <= 3.1e-50)
		tmp = t_3;
	elseif (a <= 4500000000.0)
		tmp = t_1;
	elseif (a <= 2.8e+103)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+26], t$95$2, If[LessEqual[a, 9.5e-201], t$95$1, If[LessEqual[a, 3.1e-50], t$95$3, If[LessEqual[a, 4500000000.0], t$95$1, If[LessEqual[a, 2.8e+103], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5e26 or 2.80000000000000008e103 < a

   1. Initial program 70.9%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in y around inf 75.2%

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

   6. Taylor expanded in a around inf 69.8%

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

   if -8.5e26 < a < 9.5000000000000001e-201 or 3.1000000000000002e-50 < a < 4.5e9

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-*l/ 81.2%

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

      3. fma-define 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in a around 0 63.9%

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

      1. associate-*r/ 63.9%

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

      2. neg-mul-1 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in y around -inf 65.4%

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

      1. associate-*r* 65.4%

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

      2. neg-mul-1 65.4%

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

      3. sub-neg 65.4%

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

      4. metadata-eval 65.4%

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

   10. Simplified 65.4%

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

   if 9.5000000000000001e-201 < a < 3.1000000000000002e-50 or 4.5e9 < a < 2.80000000000000008e103

   1. Initial program 60.4%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in z around inf 58.2%

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

      1. div-sub 58.2%

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

   7. Simplified 58.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4500000000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= a -6e+24)
     (+ x (/ y (/ a (- z t))))
     (if (<= a 7.6e-206)
       t_1
       (if (<= a 7.8e-51)
         t_2
         (if (<= a 4500000000.0)
           t_1
           (if (<= a 1.45e+102) t_2 (+ x (* (- z t) (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -6e+24) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 7.6e-206) {
		tmp = t_1;
	} else if (a <= 7.8e-51) {
		tmp = t_2;
	} else if (a <= 4500000000.0) {
		tmp = t_1;
	} else if (a <= 1.45e+102) {
		tmp = t_2;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    t_2 = z * ((y - x) / (a - t))
    if (a <= (-6d+24)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= 7.6d-206) then
        tmp = t_1
    else if (a <= 7.8d-51) then
        tmp = t_2
    else if (a <= 4500000000.0d0) then
        tmp = t_1
    else if (a <= 1.45d+102) then
        tmp = t_2
    else
        tmp = x + ((z - t) * (y / a))
    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 * (1.0 - (z / t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -6e+24) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 7.6e-206) {
		tmp = t_1;
	} else if (a <= 7.8e-51) {
		tmp = t_2;
	} else if (a <= 4500000000.0) {
		tmp = t_1;
	} else if (a <= 1.45e+102) {
		tmp = t_2;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -6e+24:
		tmp = x + (y / (a / (z - t)))
	elif a <= 7.6e-206:
		tmp = t_1
	elif a <= 7.8e-51:
		tmp = t_2
	elif a <= 4500000000.0:
		tmp = t_1
	elif a <= 1.45e+102:
		tmp = t_2
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -6e+24)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 7.6e-206)
		tmp = t_1;
	elseif (a <= 7.8e-51)
		tmp = t_2;
	elseif (a <= 4500000000.0)
		tmp = t_1;
	elseif (a <= 1.45e+102)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -6e+24)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= 7.6e-206)
		tmp = t_1;
	elseif (a <= 7.8e-51)
		tmp = t_2;
	elseif (a <= 4500000000.0)
		tmp = t_1;
	elseif (a <= 1.45e+102)
		tmp = t_2;
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+24], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-206], t$95$1, If[LessEqual[a, 7.8e-51], t$95$2, If[LessEqual[a, 4500000000.0], t$95$1, If[LessEqual[a, 1.45e+102], t$95$2, N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.9999999999999999e24

   1. Initial program 69.4%

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

      1. associate-*l/ 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in y around inf 71.6%

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

   6. Taylor expanded in a around inf 65.9%

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

      1. associate-/l* 71.4%

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

   8. Simplified 71.4%

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

   if -5.9999999999999999e24 < a < 7.60000000000000005e-206 or 7.7999999999999995e-51 < a < 4.5e9

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-*l/ 81.2%

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

      3. fma-define 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in a around 0 63.9%

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

      1. associate-*r/ 63.9%

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

      2. neg-mul-1 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in y around -inf 65.4%

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

      1. associate-*r* 65.4%

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

      2. neg-mul-1 65.4%

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

      3. sub-neg 65.4%

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

      4. metadata-eval 65.4%

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

   10. Simplified 65.4%

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

   if 7.60000000000000005e-206 < a < 7.7999999999999995e-51 or 4.5e9 < a < 1.4500000000000001e102

   1. Initial program 60.4%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in z around inf 58.2%

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

      1. div-sub 58.2%

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

   7. Simplified 58.2%

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

   if 1.4500000000000001e102 < a

   1. Initial program 73.2%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around inf 81.0%

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

   6. Taylor expanded in a around inf 72.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4500000000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.8e+24)
     y
     (if (<= t -8.2e-132)
       t_2
       (if (<= t -3.9e-307)
         t_1
         (if (<= t 3.5e-225) t_2 (if (<= t 8000000000.0) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.8e+24) {
		tmp = y;
	} else if (t <= -8.2e-132) {
		tmp = t_2;
	} else if (t <= -3.9e-307) {
		tmp = t_1;
	} else if (t <= 3.5e-225) {
		tmp = t_2;
	} else if (t <= 8000000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-3.8d+24)) then
        tmp = y
    else if (t <= (-8.2d-132)) then
        tmp = t_2
    else if (t <= (-3.9d-307)) then
        tmp = t_1
    else if (t <= 3.5d-225) then
        tmp = t_2
    else if (t <= 8000000000.0d0) then
        tmp = t_1
    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 t_1 = x + (y * (z / a));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.8e+24) {
		tmp = y;
	} else if (t <= -8.2e-132) {
		tmp = t_2;
	} else if (t <= -3.9e-307) {
		tmp = t_1;
	} else if (t <= 3.5e-225) {
		tmp = t_2;
	} else if (t <= 8000000000.0) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.8e+24:
		tmp = y
	elif t <= -8.2e-132:
		tmp = t_2
	elif t <= -3.9e-307:
		tmp = t_1
	elif t <= 3.5e-225:
		tmp = t_2
	elif t <= 8000000000.0:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.8e+24)
		tmp = y;
	elseif (t <= -8.2e-132)
		tmp = t_2;
	elseif (t <= -3.9e-307)
		tmp = t_1;
	elseif (t <= 3.5e-225)
		tmp = t_2;
	elseif (t <= 8000000000.0)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.8e+24)
		tmp = y;
	elseif (t <= -8.2e-132)
		tmp = t_2;
	elseif (t <= -3.9e-307)
		tmp = t_1;
	elseif (t <= 3.5e-225)
		tmp = t_2;
	elseif (t <= 8000000000.0)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+24], y, If[LessEqual[t, -8.2e-132], t$95$2, If[LessEqual[t, -3.9e-307], t$95$1, If[LessEqual[t, 3.5e-225], t$95$2, If[LessEqual[t, 8000000000.0], t$95$1, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000015e24 or 8e9 < t

   1. Initial program 44.3%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in t around inf 44.7%

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

   if -3.80000000000000015e24 < t < -8.20000000000000013e-132 or -3.9e-307 < t < 3.4999999999999997e-225

   1. Initial program 92.9%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 78.7%

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

   6. Taylor expanded in x around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

   8. Simplified 70.9%

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

   if -8.20000000000000013e-132 < t < -3.9e-307 or 3.4999999999999997e-225 < t < 8e9

   1. Initial program 94.1%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 74.4%

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

   6. Taylor expanded in y around inf 66.5%

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

      1. associate-*r/ 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-307}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8000000000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-275}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-232}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+48}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t z))))
   (if (<= a -4.8e+30)
     x
     (if (<= a -2.2e-275)
       y
       (if (<= a 1.2e-306)
         t_1
         (if (<= a 4.5e-232)
           y
           (if (<= a 1.65e-72) t_1 (if (<= a 1.02e+48) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / z);
	double tmp;
	if (a <= -4.8e+30) {
		tmp = x;
	} else if (a <= -2.2e-275) {
		tmp = y;
	} else if (a <= 1.2e-306) {
		tmp = t_1;
	} else if (a <= 4.5e-232) {
		tmp = y;
	} else if (a <= 1.65e-72) {
		tmp = t_1;
	} else if (a <= 1.02e+48) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x / (t / z)
    if (a <= (-4.8d+30)) then
        tmp = x
    else if (a <= (-2.2d-275)) then
        tmp = y
    else if (a <= 1.2d-306) then
        tmp = t_1
    else if (a <= 4.5d-232) then
        tmp = y
    else if (a <= 1.65d-72) then
        tmp = t_1
    else if (a <= 1.02d+48) 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 t_1 = x / (t / z);
	double tmp;
	if (a <= -4.8e+30) {
		tmp = x;
	} else if (a <= -2.2e-275) {
		tmp = y;
	} else if (a <= 1.2e-306) {
		tmp = t_1;
	} else if (a <= 4.5e-232) {
		tmp = y;
	} else if (a <= 1.65e-72) {
		tmp = t_1;
	} else if (a <= 1.02e+48) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / z)
	tmp = 0
	if a <= -4.8e+30:
		tmp = x
	elif a <= -2.2e-275:
		tmp = y
	elif a <= 1.2e-306:
		tmp = t_1
	elif a <= 4.5e-232:
		tmp = y
	elif a <= 1.65e-72:
		tmp = t_1
	elif a <= 1.02e+48:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / z))
	tmp = 0.0
	if (a <= -4.8e+30)
		tmp = x;
	elseif (a <= -2.2e-275)
		tmp = y;
	elseif (a <= 1.2e-306)
		tmp = t_1;
	elseif (a <= 4.5e-232)
		tmp = y;
	elseif (a <= 1.65e-72)
		tmp = t_1;
	elseif (a <= 1.02e+48)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / z);
	tmp = 0.0;
	if (a <= -4.8e+30)
		tmp = x;
	elseif (a <= -2.2e-275)
		tmp = y;
	elseif (a <= 1.2e-306)
		tmp = t_1;
	elseif (a <= 4.5e-232)
		tmp = y;
	elseif (a <= 1.65e-72)
		tmp = t_1;
	elseif (a <= 1.02e+48)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+30], x, If[LessEqual[a, -2.2e-275], y, If[LessEqual[a, 1.2e-306], t$95$1, If[LessEqual[a, 4.5e-232], y, If[LessEqual[a, 1.65e-72], t$95$1, If[LessEqual[a, 1.02e+48], y, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.7999999999999999e30 or 1.02e48 < a

   1. Initial program 67.8%

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

      1. associate-*l/ 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in a around inf 49.5%

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

   if -4.7999999999999999e30 < a < -2.19999999999999989e-275 or 1.2e-306 < a < 4.49999999999999967e-232 or 1.65e-72 < a < 1.02e48

   1. Initial program 74.3%

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

      1. associate-*l/ 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in t around inf 45.4%

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

   if -2.19999999999999989e-275 < a < 1.2e-306 or 4.49999999999999967e-232 < a < 1.65e-72

   1. Initial program 72.1%

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

      1. +-commutative 72.1%

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

      2. associate-*l/ 67.2%

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

      3. fma-define 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in a around 0 57.3%

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

      1. associate-*r/ 57.3%

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

      2. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in x around inf 39.9%

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

      1. associate-/l* 45.7%

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

   10. Simplified 45.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-275}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-232}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+48}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;z \leq 14500000000000:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= z -2.4e+63)
     t_1
     (if (<= z -6.8e-60)
       (+ x (* z (/ y a)))
       (if (<= z -3.1e-120)
         (* y (- 1.0 (/ z t)))
         (if (<= z 14500000000000.0) (- x (/ t (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -2.4e+63) {
		tmp = t_1;
	} else if (z <= -6.8e-60) {
		tmp = x + (z * (y / a));
	} else if (z <= -3.1e-120) {
		tmp = y * (1.0 - (z / t));
	} else if (z <= 14500000000000.0) {
		tmp = x - (t / (a / y));
	} 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) :: tmp
    t_1 = z * ((y - x) / (a - t))
    if (z <= (-2.4d+63)) then
        tmp = t_1
    else if (z <= (-6.8d-60)) then
        tmp = x + (z * (y / a))
    else if (z <= (-3.1d-120)) then
        tmp = y * (1.0d0 - (z / t))
    else if (z <= 14500000000000.0d0) then
        tmp = x - (t / (a / y))
    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 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -2.4e+63) {
		tmp = t_1;
	} else if (z <= -6.8e-60) {
		tmp = x + (z * (y / a));
	} else if (z <= -3.1e-120) {
		tmp = y * (1.0 - (z / t));
	} else if (z <= 14500000000000.0) {
		tmp = x - (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -2.4e+63:
		tmp = t_1
	elif z <= -6.8e-60:
		tmp = x + (z * (y / a))
	elif z <= -3.1e-120:
		tmp = y * (1.0 - (z / t))
	elif z <= 14500000000000.0:
		tmp = x - (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.4e+63)
		tmp = t_1;
	elseif (z <= -6.8e-60)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (z <= -3.1e-120)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (z <= 14500000000000.0)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -2.4e+63)
		tmp = t_1;
	elseif (z <= -6.8e-60)
		tmp = x + (z * (y / a));
	elseif (z <= -3.1e-120)
		tmp = y * (1.0 - (z / t));
	elseif (z <= 14500000000000.0)
		tmp = x - (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+63], t$95$1, If[LessEqual[z, -6.8e-60], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-120], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 14500000000000.0], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e63 or 1.45e13 < z

   1. Initial program 67.2%

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

      1. associate-*l/ 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in z around inf 72.4%

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

      1. div-sub 72.4%

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

   7. Simplified 72.4%

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

   if -2.4e63 < z < -6.80000000000000013e-60

   1. Initial program 86.7%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around 0 68.7%

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

   6. Taylor expanded in y around inf 70.3%

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

      1. associate-*r/ 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in y around 0 70.3%

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

       1. associate-/l* 68.7%

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

       2. associate-/r/ 70.3%

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

   11. Simplified 70.3%

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

   if -6.80000000000000013e-60 < z < -3.10000000000000019e-120

   1. Initial program 67.8%

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

      1. +-commutative 67.8%

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

      2. associate-*l/ 60.0%

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

      3. fma-define 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in a around 0 37.6%

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

      1. associate-*r/ 37.6%

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

      2. neg-mul-1 37.6%

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

   7. Simplified 37.6%

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

   8. Taylor expanded in y around -inf 53.1%

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

      1. associate-*r* 53.1%

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

      2. neg-mul-1 53.1%

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

      3. sub-neg 53.1%

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

      4. metadata-eval 53.1%

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

   10. Simplified 53.1%

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

   if -3.10000000000000019e-120 < z < 1.45e13

   1. Initial program 72.4%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in y around inf 72.4%

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

   6. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

   9. Taylor expanded in z around 0 46.4%

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

       1. mul-1-neg 46.4%

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

       2. unsub-neg 46.4%

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

       3. associate-/l* 49.9%

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

   11. Simplified 49.9%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;z \leq 14500000000000:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 88000000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -1.65e+17)
     t_1
     (if (<= t 2.7e-137)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 4.5e-107)
         (* z (/ (- y x) (- a t)))
         (if (<= t 88000000000000.0) (+ x (/ y (/ a (- z t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -1.65e+17) {
		tmp = t_1;
	} else if (t <= 2.7e-137) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 4.5e-107) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 88000000000000.0) {
		tmp = x + (y / (a / (z - 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) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    if (t <= (-1.65d+17)) then
        tmp = t_1
    else if (t <= 2.7d-137) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 4.5d-107) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 88000000000000.0d0) then
        tmp = x + (y / (a / (z - 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 * (1.0 - (z / t));
	double tmp;
	if (t <= -1.65e+17) {
		tmp = t_1;
	} else if (t <= 2.7e-137) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 4.5e-107) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 88000000000000.0) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -1.65e+17:
		tmp = t_1
	elif t <= 2.7e-137:
		tmp = x + (z / (a / (y - x)))
	elif t <= 4.5e-107:
		tmp = z * ((y - x) / (a - t))
	elif t <= 88000000000000.0:
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -1.65e+17)
		tmp = t_1;
	elseif (t <= 2.7e-137)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 4.5e-107)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 88000000000000.0)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -1.65e+17)
		tmp = t_1;
	elseif (t <= 2.7e-137)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 4.5e-107)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 88000000000000.0)
		tmp = x + (y / (a / (z - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+17], t$95$1, If[LessEqual[t, 2.7e-137], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-107], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 88000000000000.0], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65e17 or 8.8e13 < t

   1. Initial program 45.5%

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

      1. +-commutative 45.5%

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

      2. associate-*l/ 63.9%

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

      3. fma-define 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. associate-*r/ 42.1%

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

      2. neg-mul-1 42.1%

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

   7. Simplified 42.1%

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

   8. Taylor expanded in y around -inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. neg-mul-1 51.7%

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

      3. sub-neg 51.7%

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

      4. metadata-eval 51.7%

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

   10. Simplified 51.7%

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

   if -1.65e17 < t < 2.69999999999999993e-137

   1. Initial program 94.3%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. associate-/l* 80.5%

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

   7. Simplified 80.5%

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

   if 2.69999999999999993e-137 < t < 4.50000000000000016e-107

   1. Initial program 89.2%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. div-sub 78.7%

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

   7. Simplified 78.7%

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

   if 4.50000000000000016e-107 < t < 8.8e13

   1. Initial program 88.3%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around inf 75.7%

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

   6. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 67.4%

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

   8. Simplified 67.4%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 88000000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z}}\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 170000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a z)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -9e+20)
     t_2
     (if (<= t 8.5e-137)
       t_1
       (if (<= t 1.05e-107)
         (* z (/ (- y x) (- a t)))
         (if (<= t 170000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -9e+20) {
		tmp = t_2;
	} else if (t <= 8.5e-137) {
		tmp = t_1;
	} else if (t <= 1.05e-107) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 170000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + ((y - x) / (a / z))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-9d+20)) then
        tmp = t_2
    else if (t <= 8.5d-137) then
        tmp = t_1
    else if (t <= 1.05d-107) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 170000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -9e+20) {
		tmp = t_2;
	} else if (t <= 8.5e-137) {
		tmp = t_1;
	} else if (t <= 1.05e-107) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 170000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / z))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -9e+20:
		tmp = t_2
	elif t <= 8.5e-137:
		tmp = t_1
	elif t <= 1.05e-107:
		tmp = z * ((y - x) / (a - t))
	elif t <= 170000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -9e+20)
		tmp = t_2;
	elseif (t <= 8.5e-137)
		tmp = t_1;
	elseif (t <= 1.05e-107)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 170000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / z));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -9e+20)
		tmp = t_2;
	elseif (t <= 8.5e-137)
		tmp = t_1;
	elseif (t <= 1.05e-107)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 170000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+20], t$95$2, If[LessEqual[t, 8.5e-137], t$95$1, If[LessEqual[t, 1.05e-107], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9e20 or 1.7e11 < t

   1. Initial program 45.5%

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

      1. +-commutative 45.5%

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

      2. associate-*l/ 63.9%

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

      3. fma-define 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. associate-*r/ 42.1%

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

      2. neg-mul-1 42.1%

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

   7. Simplified 42.1%

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

   8. Taylor expanded in y around -inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. neg-mul-1 51.7%

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

      3. sub-neg 51.7%

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

      4. metadata-eval 51.7%

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

   10. Simplified 51.7%

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

   if -9e20 < t < 8.5000000000000001e-137 or 1.05e-107 < t < 1.7e11

   1. Initial program 93.2%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 80.3%

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

   if 8.5000000000000001e-137 < t < 1.05e-107

   1. Initial program 89.2%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. div-sub 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 170000000000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.8e+24)
     y
     (if (<= t 8.5e-137)
       t_1
       (if (<= t 1.5e-106) (/ x (/ t z)) (if (<= t 1.26e+14) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.8e+24) {
		tmp = y;
	} else if (t <= 8.5e-137) {
		tmp = t_1;
	} else if (t <= 1.5e-106) {
		tmp = x / (t / z);
	} else if (t <= 1.26e+14) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-3.8d+24)) then
        tmp = y
    else if (t <= 8.5d-137) then
        tmp = t_1
    else if (t <= 1.5d-106) then
        tmp = x / (t / z)
    else if (t <= 1.26d+14) then
        tmp = t_1
    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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.8e+24) {
		tmp = y;
	} else if (t <= 8.5e-137) {
		tmp = t_1;
	} else if (t <= 1.5e-106) {
		tmp = x / (t / z);
	} else if (t <= 1.26e+14) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.8e+24:
		tmp = y
	elif t <= 8.5e-137:
		tmp = t_1
	elif t <= 1.5e-106:
		tmp = x / (t / z)
	elif t <= 1.26e+14:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.8e+24)
		tmp = y;
	elseif (t <= 8.5e-137)
		tmp = t_1;
	elseif (t <= 1.5e-106)
		tmp = Float64(x / Float64(t / z));
	elseif (t <= 1.26e+14)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.8e+24)
		tmp = y;
	elseif (t <= 8.5e-137)
		tmp = t_1;
	elseif (t <= 1.5e-106)
		tmp = x / (t / z);
	elseif (t <= 1.26e+14)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+24], y, If[LessEqual[t, 8.5e-137], t$95$1, If[LessEqual[t, 1.5e-106], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.26e+14], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000015e24 or 1.26e14 < t

   1. Initial program 44.6%

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

      1. associate-*l/ 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in t around inf 45.1%

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

   if -3.80000000000000015e24 < t < 8.5000000000000001e-137 or 1.50000000000000009e-106 < t < 1.26e14

   1. Initial program 93.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 79.8%

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

   6. Taylor expanded in x around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. unsub-neg 62.5%

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

   8. Simplified 62.5%

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

   if 8.5000000000000001e-137 < t < 1.50000000000000009e-106

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. associate-*l/ 90.3%

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

      3. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in a around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. neg-mul-1 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around inf 42.5%

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

      1. associate-/l* 52.1%

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

   10. Simplified 52.1%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.35e+24)
     y
     (if (<= t 8e-139)
       t_1
       (if (<= t 4e-107) (* z (/ (- x y) t)) (if (<= t 3.35e+15) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.35e+24) {
		tmp = y;
	} else if (t <= 8e-139) {
		tmp = t_1;
	} else if (t <= 4e-107) {
		tmp = z * ((x - y) / t);
	} else if (t <= 3.35e+15) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.35d+24)) then
        tmp = y
    else if (t <= 8d-139) then
        tmp = t_1
    else if (t <= 4d-107) then
        tmp = z * ((x - y) / t)
    else if (t <= 3.35d+15) then
        tmp = t_1
    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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.35e+24) {
		tmp = y;
	} else if (t <= 8e-139) {
		tmp = t_1;
	} else if (t <= 4e-107) {
		tmp = z * ((x - y) / t);
	} else if (t <= 3.35e+15) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.35e+24:
		tmp = y
	elif t <= 8e-139:
		tmp = t_1
	elif t <= 4e-107:
		tmp = z * ((x - y) / t)
	elif t <= 3.35e+15:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.35e+24)
		tmp = y;
	elseif (t <= 8e-139)
		tmp = t_1;
	elseif (t <= 4e-107)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 3.35e+15)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.35e+24)
		tmp = y;
	elseif (t <= 8e-139)
		tmp = t_1;
	elseif (t <= 4e-107)
		tmp = z * ((x - y) / t);
	elseif (t <= 3.35e+15)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+24], y, If[LessEqual[t, 8e-139], t$95$1, If[LessEqual[t, 4e-107], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.35e+15], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e24 or 3.35e15 < t

   1. Initial program 44.6%

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

      1. associate-*l/ 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in t around inf 45.1%

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

   if -1.35e24 < t < 8.00000000000000024e-139 or 4e-107 < t < 3.35e15

   1. Initial program 93.2%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 79.6%

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

   6. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   8. Simplified 62.2%

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

   if 8.00000000000000024e-139 < t < 4e-107

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-*l/ 91.2%

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

      3. fma-define 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in a around 0 68.2%

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

      1. associate-*r/ 68.2%

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

      2. neg-mul-1 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in z around inf 59.7%

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

      1. div-sub 59.7%

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

   10. Simplified 59.7%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= a -3.2e+23)
     (+ x (* y (/ z a)))
     (if (<= a 3.1e-182)
       t_1
       (if (<= a 2.2e-74)
         (/ x (/ t (- z a)))
         (if (<= a 1.25e+41) t_1 (+ x (* z (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -3.2e+23) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.1e-182) {
		tmp = t_1;
	} else if (a <= 2.2e-74) {
		tmp = x / (t / (z - a));
	} else if (a <= 1.25e+41) {
		tmp = t_1;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    if (a <= (-3.2d+23)) then
        tmp = x + (y * (z / a))
    else if (a <= 3.1d-182) then
        tmp = t_1
    else if (a <= 2.2d-74) then
        tmp = x / (t / (z - a))
    else if (a <= 1.25d+41) then
        tmp = t_1
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -3.2e+23) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.1e-182) {
		tmp = t_1;
	} else if (a <= 2.2e-74) {
		tmp = x / (t / (z - a));
	} else if (a <= 1.25e+41) {
		tmp = t_1;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	tmp = 0
	if a <= -3.2e+23:
		tmp = x + (y * (z / a))
	elif a <= 3.1e-182:
		tmp = t_1
	elif a <= 2.2e-74:
		tmp = x / (t / (z - a))
	elif a <= 1.25e+41:
		tmp = t_1
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (a <= -3.2e+23)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 3.1e-182)
		tmp = t_1;
	elseif (a <= 2.2e-74)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (a <= 1.25e+41)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (a <= -3.2e+23)
		tmp = x + (y * (z / a));
	elseif (a <= 3.1e-182)
		tmp = t_1;
	elseif (a <= 2.2e-74)
		tmp = x / (t / (z - a));
	elseif (a <= 1.25e+41)
		tmp = t_1;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+23], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-182], t$95$1, If[LessEqual[a, 2.2e-74], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+41], t$95$1, N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2e23

   1. Initial program 69.4%

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

      1. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around 0 73.2%

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

   6. Taylor expanded in y around inf 63.4%

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

      1. associate-*r/ 63.4%

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

   8. Simplified 63.4%

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

   if -3.2e23 < a < 3.10000000000000008e-182 or 2.2000000000000001e-74 < a < 1.25000000000000006e41

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*l/ 81.1%

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

      3. fma-define 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in a around 0 61.9%

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

      1. associate-*r/ 61.9%

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

      2. neg-mul-1 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in y around -inf 63.2%

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

      1. associate-*r* 63.2%

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

      2. neg-mul-1 63.2%

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

      3. sub-neg 63.2%

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

      4. metadata-eval 63.2%

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

   10. Simplified 63.2%

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

   if 3.10000000000000008e-182 < a < 2.2000000000000001e-74

   1. Initial program 63.6%

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

      1. associate-*l/ 59.0%

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

   3. Simplified 59.0%

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

   5. Taylor expanded in t around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 76.7%

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

      5. distribute-lft-out-- 76.7%

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

      6. associate-*r/ 76.7%

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

      7. mul-1-neg 76.7%

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

      8. unsub-neg 76.7%

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

      9. distribute-rgt-out-- 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in y around 0 43.8%

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

      1. associate-/l* 55.8%

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

   10. Simplified 55.8%

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

   if 1.25000000000000006e41 < a

   1. Initial program 66.9%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around 0 67.3%

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

   6. Taylor expanded in y around inf 51.7%

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

      1. associate-*r/ 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in y around 0 51.7%

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

       1. associate-/l* 56.8%

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

       2. associate-/r/ 56.9%

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

   11. Simplified 56.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= y -2.8e-78)
     t_1
     (if (<= y 1.45e-245)
       (* x (+ (/ (- t z) (- a t)) 1.0))
       (if (<= y 3.4e-86) (+ y (/ (* x (- z a)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (y <= -2.8e-78) {
		tmp = t_1;
	} else if (y <= 1.45e-245) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (y <= 3.4e-86) {
		tmp = y + ((x * (z - 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) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (y <= (-2.8d-78)) then
        tmp = t_1
    else if (y <= 1.45d-245) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if (y <= 3.4d-86) then
        tmp = y + ((x * (z - 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 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (y <= -2.8e-78) {
		tmp = t_1;
	} else if (y <= 1.45e-245) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (y <= 3.4e-86) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if y <= -2.8e-78:
		tmp = t_1
	elif y <= 1.45e-245:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif y <= 3.4e-86:
		tmp = y + ((x * (z - a)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (y <= -2.8e-78)
		tmp = t_1;
	elseif (y <= 1.45e-245)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif (y <= 3.4e-86)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (y <= -2.8e-78)
		tmp = t_1;
	elseif (y <= 1.45e-245)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif (y <= 3.4e-86)
		tmp = y + ((x * (z - a)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-78], t$95$1, If[LessEqual[y, 1.45e-245], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-86], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000024e-78 or 3.4e-86 < y

   1. Initial program 77.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around inf 82.9%

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

   if -2.80000000000000024e-78 < y < 1.45e-245

   1. Initial program 64.3%

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

      1. associate-*l/ 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in x around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   7. Simplified 64.3%

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

   if 1.45e-245 < y < 3.4e-86

   1. Initial program 54.7%

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

      1. associate-*l/ 51.4%

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

   3. Simplified 51.4%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.0%

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

      5. distribute-lft-out-- 70.0%

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

      6. associate-*r/ 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

      9. distribute-rgt-out-- 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in y around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. *-commutative 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

   10. Simplified 66.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-78}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-98}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= y -2.15e-78)
     t_1
     (if (<= y 2.8e-244)
       (- x (/ x (/ (- a t) (- z t))))
       (if (<= y 6.2e-98) (+ y (/ (* x (- z a)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (y <= -2.15e-78) {
		tmp = t_1;
	} else if (y <= 2.8e-244) {
		tmp = x - (x / ((a - t) / (z - t)));
	} else if (y <= 6.2e-98) {
		tmp = y + ((x * (z - 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) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (y <= (-2.15d-78)) then
        tmp = t_1
    else if (y <= 2.8d-244) then
        tmp = x - (x / ((a - t) / (z - t)))
    else if (y <= 6.2d-98) then
        tmp = y + ((x * (z - 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 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (y <= -2.15e-78) {
		tmp = t_1;
	} else if (y <= 2.8e-244) {
		tmp = x - (x / ((a - t) / (z - t)));
	} else if (y <= 6.2e-98) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if y <= -2.15e-78:
		tmp = t_1
	elif y <= 2.8e-244:
		tmp = x - (x / ((a - t) / (z - t)))
	elif y <= 6.2e-98:
		tmp = y + ((x * (z - a)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (y <= -2.15e-78)
		tmp = t_1;
	elseif (y <= 2.8e-244)
		tmp = Float64(x - Float64(x / Float64(Float64(a - t) / Float64(z - t))));
	elseif (y <= 6.2e-98)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (y <= -2.15e-78)
		tmp = t_1;
	elseif (y <= 2.8e-244)
		tmp = x - (x / ((a - t) / (z - t)));
	elseif (y <= 6.2e-98)
		tmp = y + ((x * (z - a)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e-78], t$95$1, If[LessEqual[y, 2.8e-244], N[(x - N[(x / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-98], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.14999999999999997e-78 or 6.2e-98 < y

   1. Initial program 77.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around inf 82.9%

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

   if -2.14999999999999997e-78 < y < 2.80000000000000013e-244

   1. Initial program 64.3%

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

      1. +-commutative 64.3%

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

      2. associate-*l/ 65.2%

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

      3. fma-define 65.7%

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

   3. Simplified 65.7%

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

      1. clear-num 64.7%

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

      2. inv-pow 64.7%

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

   6. Applied egg-rr 64.7%

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

      1. unpow-1 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in y around 0 53.8%

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

       1. mul-1-neg 53.8%

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

       2. unsub-neg 53.8%

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

       3. associate-/l* 64.5%

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

   11. Simplified 64.5%

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

   if 2.80000000000000013e-244 < y < 6.2e-98

   1. Initial program 54.7%

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

      1. associate-*l/ 51.4%

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

   3. Simplified 51.4%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.0%

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

      5. distribute-lft-out-- 70.0%

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

      6. associate-*r/ 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

      9. distribute-rgt-out-- 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in y around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. *-commutative 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

   10. Simplified 66.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-78}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-98}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-91}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= y -2.2e-78)
     t_1
     (if (<= y 2.8e-244)
       (- x (/ x (/ (- a t) (- z t))))
       (if (<= y 9e-91) (+ y (/ (* (- y x) (- a z)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (y <= -2.2e-78) {
		tmp = t_1;
	} else if (y <= 2.8e-244) {
		tmp = x - (x / ((a - t) / (z - t)));
	} else if (y <= 9e-91) {
		tmp = y + (((y - x) * (a - z)) / 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) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (y <= (-2.2d-78)) then
        tmp = t_1
    else if (y <= 2.8d-244) then
        tmp = x - (x / ((a - t) / (z - t)))
    else if (y <= 9d-91) then
        tmp = y + (((y - x) * (a - z)) / 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 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (y <= -2.2e-78) {
		tmp = t_1;
	} else if (y <= 2.8e-244) {
		tmp = x - (x / ((a - t) / (z - t)));
	} else if (y <= 9e-91) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if y <= -2.2e-78:
		tmp = t_1
	elif y <= 2.8e-244:
		tmp = x - (x / ((a - t) / (z - t)))
	elif y <= 9e-91:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (y <= -2.2e-78)
		tmp = t_1;
	elseif (y <= 2.8e-244)
		tmp = Float64(x - Float64(x / Float64(Float64(a - t) / Float64(z - t))));
	elseif (y <= 9e-91)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (y <= -2.2e-78)
		tmp = t_1;
	elseif (y <= 2.8e-244)
		tmp = x - (x / ((a - t) / (z - t)));
	elseif (y <= 9e-91)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-78], t$95$1, If[LessEqual[y, 2.8e-244], N[(x - N[(x / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-91], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e-78 or 8.99999999999999952e-91 < y

   1. Initial program 77.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around inf 82.9%

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

   if -2.1999999999999999e-78 < y < 2.80000000000000013e-244

   1. Initial program 64.3%

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

      1. +-commutative 64.3%

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

      2. associate-*l/ 65.2%

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

      3. fma-define 65.7%

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

   3. Simplified 65.7%

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

      1. clear-num 64.7%

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

      2. inv-pow 64.7%

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

   6. Applied egg-rr 64.7%

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

      1. unpow-1 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in y around 0 53.8%

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

       1. mul-1-neg 53.8%

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

       2. unsub-neg 53.8%

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

       3. associate-/l* 64.5%

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

   11. Simplified 64.5%

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

   if 2.80000000000000013e-244 < y < 8.99999999999999952e-91

   1. Initial program 54.7%

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

      1. associate-*l/ 51.4%

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

   3. Simplified 51.4%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.0%

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

      5. distribute-lft-out-- 70.0%

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

      6. associate-*r/ 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

      9. distribute-rgt-out-- 70.3%

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

   7. Simplified 70.3%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-91}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-226}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-34}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e-15)
   (+ x (/ (- y x) (/ a z)))
   (if (<= a -4.7e-226)
     (/ y (/ (- a t) (- z t)))
     (if (<= a 7.4e-34) (+ y (/ (* x (- z a)) t)) (+ x (/ z (/ a (- y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e-15) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -4.7e-226) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 7.4e-34) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = x + (z / (a / (y - 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 <= (-5d-15)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= (-4.7d-226)) then
        tmp = y / ((a - t) / (z - t))
    else if (a <= 7.4d-34) then
        tmp = y + ((x * (z - a)) / t)
    else
        tmp = x + (z / (a / (y - 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 <= -5e-15) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= -4.7e-226) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 7.4e-34) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e-15:
		tmp = x + ((y - x) / (a / z))
	elif a <= -4.7e-226:
		tmp = y / ((a - t) / (z - t))
	elif a <= 7.4e-34:
		tmp = y + ((x * (z - a)) / t)
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e-15)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= -4.7e-226)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (a <= 7.4e-34)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e-15)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= -4.7e-226)
		tmp = y / ((a - t) / (z - t));
	elseif (a <= 7.4e-34)
		tmp = y + ((x * (z - a)) / t);
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e-15], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.7e-226], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e-34], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.99999999999999999e-15

   1. Initial program 70.2%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 71.2%

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

   if -4.99999999999999999e-15 < a < -4.69999999999999999e-226

   1. Initial program 73.7%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around 0 68.5%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if -4.69999999999999999e-226 < a < 7.39999999999999976e-34

   1. Initial program 72.4%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in t around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. associate-*r/ 81.6%

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

      3. associate-*r/ 81.6%

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

      4. div-sub 82.9%

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

      5. distribute-lft-out-- 82.9%

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

      6. associate-*r/ 82.9%

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

      7. mul-1-neg 82.9%

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

      8. unsub-neg 82.9%

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

      9. distribute-rgt-out-- 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

   10. Simplified 71.8%

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

   if 7.39999999999999976e-34 < a

   1. Initial program 68.5%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around 0 52.1%

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

      1. associate-/l* 62.9%

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

   7. Simplified 62.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-226}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-34}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+65} \lor \neg \left(z \leq 1.8 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+65) (not (<= z 1.8e+24)))
   (* z (/ (- y x) (- a t)))
   (- x (/ t (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+65) || !(z <= 1.8e+24)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+65)) .or. (.not. (z <= 1.8d+24))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x - (t / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+65) || !(z <= 1.8e+24)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+65) or not (z <= 1.8e+24):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x - (t / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+65) || !(z <= 1.8e+24))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+65) || ~((z <= 1.8e+24)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x - (t / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+65], N[Not[LessEqual[z, 1.8e+24]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999999e65 or 1.79999999999999992e24 < z

   1. Initial program 66.7%

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

      1. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in z around inf 73.5%

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

      1. div-sub 73.5%

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

   7. Simplified 73.5%

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

   if -7.9999999999999999e65 < z < 1.79999999999999992e24

   1. Initial program 74.3%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in y around inf 74.2%

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

   6. Taylor expanded in z around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. unsub-neg 61.8%

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

      3. associate-/l* 66.9%

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

   8. Simplified 66.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+65} \lor \neg \left(z \leq 1.8 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 105000000000:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-15)
   (+ x (/ (- y x) (/ a z)))
   (if (<= a 105000000000.0)
     (/ y (/ (- a t) (- z t)))
     (+ x (/ z (/ a (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-15) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 105000000000.0) {
		tmp = y / ((a - t) / (z - t));
	} else {
		tmp = x + (z / (a / (y - 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 <= (-4.8d-15)) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 105000000000.0d0) then
        tmp = y / ((a - t) / (z - t))
    else
        tmp = x + (z / (a / (y - 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 <= -4.8e-15) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 105000000000.0) {
		tmp = y / ((a - t) / (z - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-15:
		tmp = x + ((y - x) / (a / z))
	elif a <= 105000000000.0:
		tmp = y / ((a - t) / (z - t))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-15)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 105000000000.0)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e-15)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 105000000000.0)
		tmp = y / ((a - t) / (z - t));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-15], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 105000000000.0], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.7999999999999999e-15

   1. Initial program 70.2%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 71.2%

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

   if -4.7999999999999999e-15 < a < 1.05e11

   1. Initial program 73.2%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around 0 59.0%

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

      1. associate-/l* 66.4%

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

   7. Simplified 66.4%

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

   if 1.05e11 < a

   1. Initial program 67.0%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in t around 0 53.0%

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

      1. associate-/l* 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 105000000000:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+180}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.55e+180)
   (+ y (/ (* x (- z a)) t))
   (+ x (* (- t z) (/ (- x y) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+180) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = x + ((t - z) * ((x - 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 (t <= (-2.55d+180)) then
        tmp = y + ((x * (z - a)) / t)
    else
        tmp = x + ((t - z) * ((x - 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 (t <= -2.55e+180) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.55e+180:
		tmp = y + ((x * (z - a)) / t)
	else:
		tmp = x + ((t - z) * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.55e+180)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	else
		tmp = Float64(x + Float64(Float64(t - z) * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.55e+180)
		tmp = y + ((x * (z - a)) / t);
	else
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.55e+180], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.54999999999999977e180

   1. Initial program 26.7%

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

      1. associate-*l/ 37.0%

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

   3. Simplified 37.0%

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

   5. Taylor expanded in t around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. associate-*r/ 81.6%

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

      3. associate-*r/ 81.6%

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

      4. div-sub 81.6%

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

      5. distribute-lft-out-- 81.6%

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

      6. associate-*r/ 81.6%

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

      7. mul-1-neg 81.6%

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

      8. unsub-neg 81.6%

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

      9. distribute-rgt-out-- 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. *-commutative 88.3%

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

      3. distribute-rgt-neg-in 88.3%

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

   10. Simplified 88.3%

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

   if -2.54999999999999977e180 < t

   1. Initial program 75.9%

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

      1. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+180}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+48}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.4e+30) x (if (<= a 1.02e+48) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e+30) {
		tmp = x;
	} else if (a <= 1.02e+48) {
		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 (a <= (-4.4d+30)) then
        tmp = x
    else if (a <= 1.02d+48) 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 (a <= -4.4e+30) {
		tmp = x;
	} else if (a <= 1.02e+48) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e+30:
		tmp = x
	elif a <= 1.02e+48:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e+30)
		tmp = x;
	elseif (a <= 1.02e+48)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e+30)
		tmp = x;
	elseif (a <= 1.02e+48)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e+30], x, If[LessEqual[a, 1.02e+48], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.4e30 or 1.02e48 < a

   1. Initial program 67.8%

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

      1. associate-*l/ 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in a around inf 49.5%

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

   if -4.4e30 < a < 1.02e48

   1. Initial program 73.6%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in t around inf 38.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+48}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.9%

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

   1. associate-*l/ 79.8%

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

3. Simplified 79.8%

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

5. Taylor expanded in a around inf 26.6%

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

6. Final simplification 26.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} 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) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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