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

Percentage Accurate: 67.3% → 88.8%

Time: 15.9s

Alternatives: 26

Speedup: 0.6×

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: 67.3% 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: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{a \cdot \left(x - y\right) - z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+268}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a))))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -4e+276)
     t_1
     (if (<= t_2 -1e-168)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (- (* a (- x y)) (* z (- x y))) t))
         (if (<= t_2 1e+268) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -4e+276) {
		tmp = t_1;
	} else if (t_2 <= -1e-168) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((a * (x - y)) - (z * (x - y))) / t);
	} else if (t_2 <= 1e+268) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) * ((-1.0d0) / (t - a))))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-4d+276)) then
        tmp = t_1
    else if (t_2 <= (-1d-168)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = y - (((a * (x - y)) - (z * (x - y))) / t)
    else if (t_2 <= 1d+268) then
        tmp = t_2
    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 + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -4e+276) {
		tmp = t_1;
	} else if (t_2 <= -1e-168) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((a * (x - y)) - (z * (x - y))) / t);
	} else if (t_2 <= 1e+268) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -4e+276:
		tmp = t_1
	elif t_2 <= -1e-168:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((a * (x - y)) - (z * (x - y))) / t)
	elif t_2 <= 1e+268:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -4e+276)
		tmp = t_1;
	elseif (t_2 <= -1e-168)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(a * Float64(x - y)) - Float64(z * Float64(x - y))) / t));
	elseif (t_2 <= 1e+268)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -4e+276)
		tmp = t_1;
	elseif (t_2 <= -1e-168)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((a * (x - y)) - (z * (x - y))) / t);
	elseif (t_2 <= 1e+268)
		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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+276], t$95$1, If[LessEqual[t$95$2, -1e-168], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+268], 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))) < -4.0000000000000002e276 or 9.9999999999999997e267 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 53.8%

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

      1. div-inv 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-*l* 85.8%

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

   4. Applied egg-rr 85.8%

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

   if -4.0000000000000002e276 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-168 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999997e267

   1. Initial program 98.0%

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

   if -1e-168 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 11.0%

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

   3. Taylor expanded in t around -inf 99.8%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{+276}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{a \cdot \left(x - y\right) - z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+268}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-168} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a \cdot \left(x - y\right) - z \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-168) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (- y (/ (- (* a (- x y)) (* z (- x y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-168) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y - (((a * (x - y)) - (z * (x - y))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-168) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y - Float64(Float64(Float64(a * Float64(x - y)) - Float64(z * Float64(x - y))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-168], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y - N[(N[(N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(x - y), $MachinePrecision]), $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))) < -1e-168 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   if -1e-168 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 11.0%

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

   3. Taylor expanded in t around -inf 99.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-168} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a \cdot \left(x - y\right) - z \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+268}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a))))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -4e+276)
     t_1
     (if (<= t_2 -1e-168)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_2 1e+268) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -4e+276) {
		tmp = t_1;
	} else if (t_2 <= -1e-168) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 1e+268) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) * ((-1.0d0) / (t - a))))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-4d+276)) then
        tmp = t_1
    else if (t_2 <= (-1d-168)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = y + (((z - a) * (x - y)) / t)
    else if (t_2 <= 1d+268) then
        tmp = t_2
    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 + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -4e+276) {
		tmp = t_1;
	} else if (t_2 <= -1e-168) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 1e+268) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -4e+276:
		tmp = t_1
	elif t_2 <= -1e-168:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_2 <= 1e+268:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -4e+276)
		tmp = t_1;
	elseif (t_2 <= -1e-168)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_2 <= 1e+268)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -4e+276)
		tmp = t_1;
	elseif (t_2 <= -1e-168)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_2 <= 1e+268)
		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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+276], t$95$1, If[LessEqual[t$95$2, -1e-168], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+268], 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))) < -4.0000000000000002e276 or 9.9999999999999997e267 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 53.8%

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

      1. div-inv 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-*l* 85.8%

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

   4. Applied egg-rr 85.8%

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

   if -4.0000000000000002e276 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-168 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999997e267

   1. Initial program 98.0%

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

   if -1e-168 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 11.0%

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

      1. +-commutative 11.0%

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

      2. associate-/l* 11.0%

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

      3. fma-define 11.0%

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

   3. Simplified 11.0%

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

      1. clear-num 11.0%

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

      2. associate-/r/ 10.9%

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

   6. Applied egg-rr 10.9%

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

   7. Taylor expanded in t around inf 99.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   8. 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. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{+276}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+268}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+80}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-175}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) (- t a)))))
   (if (<= t -4.2e+115)
     (* y (/ (- t z) t))
     (if (<= t -1.3e+80)
       (- x (/ (* x z) a))
       (if (<= t -7.2e+18)
         t_1
         (if (<= t -2.05e-175)
           (+ x (* y (/ z a)))
           (if (<= t 4.2e-306)
             t_1
             (if (<= t 1.25e-155)
               (- x (* x (/ z a)))
               (if (<= t 3e+52) t_1 (- y (/ z (/ t y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -4.2e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -1.3e+80) {
		tmp = x - ((x * z) / a);
	} else if (t <= -7.2e+18) {
		tmp = t_1;
	} else if (t <= -2.05e-175) {
		tmp = x + (y * (z / a));
	} else if (t <= 4.2e-306) {
		tmp = t_1;
	} else if (t <= 1.25e-155) {
		tmp = x - (x * (z / a));
	} else if (t <= 3e+52) {
		tmp = t_1;
	} else {
		tmp = y - (z / (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) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / (t - a))
    if (t <= (-4.2d+115)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-1.3d+80)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-7.2d+18)) then
        tmp = t_1
    else if (t <= (-2.05d-175)) then
        tmp = x + (y * (z / a))
    else if (t <= 4.2d-306) then
        tmp = t_1
    else if (t <= 1.25d-155) then
        tmp = x - (x * (z / a))
    else if (t <= 3d+52) then
        tmp = t_1
    else
        tmp = y - (z / (t / 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 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -4.2e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -1.3e+80) {
		tmp = x - ((x * z) / a);
	} else if (t <= -7.2e+18) {
		tmp = t_1;
	} else if (t <= -2.05e-175) {
		tmp = x + (y * (z / a));
	} else if (t <= 4.2e-306) {
		tmp = t_1;
	} else if (t <= 1.25e-155) {
		tmp = x - (x * (z / a));
	} else if (t <= 3e+52) {
		tmp = t_1;
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / (t - a))
	tmp = 0
	if t <= -4.2e+115:
		tmp = y * ((t - z) / t)
	elif t <= -1.3e+80:
		tmp = x - ((x * z) / a)
	elif t <= -7.2e+18:
		tmp = t_1
	elif t <= -2.05e-175:
		tmp = x + (y * (z / a))
	elif t <= 4.2e-306:
		tmp = t_1
	elif t <= 1.25e-155:
		tmp = x - (x * (z / a))
	elif t <= 3e+52:
		tmp = t_1
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (t <= -4.2e+115)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -1.3e+80)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -7.2e+18)
		tmp = t_1;
	elseif (t <= -2.05e-175)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 4.2e-306)
		tmp = t_1;
	elseif (t <= 1.25e-155)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 3e+52)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (t <= -4.2e+115)
		tmp = y * ((t - z) / t);
	elseif (t <= -1.3e+80)
		tmp = x - ((x * z) / a);
	elseif (t <= -7.2e+18)
		tmp = t_1;
	elseif (t <= -2.05e-175)
		tmp = x + (y * (z / a));
	elseif (t <= 4.2e-306)
		tmp = t_1;
	elseif (t <= 1.25e-155)
		tmp = x - (x * (z / a));
	elseif (t <= 3e+52)
		tmp = t_1;
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+115], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e+80], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e+18], t$95$1, If[LessEqual[t, -2.05e-175], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-306], t$95$1, If[LessEqual[t, 1.25e-155], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+52], t$95$1, N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.20000000000000007e115

   1. Initial program 26.8%

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

      1. +-commutative 26.8%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.4%

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

   3. Simplified 58.4%

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

      1. clear-num 58.3%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r/ 56.1%

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

   9. Simplified 56.1%

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

   10. Taylor expanded in a around 0 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   12. Simplified 62.3%

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

   if -4.20000000000000007e115 < t < -1.29999999999999991e80

   1. Initial program 35.8%

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

   3. Taylor expanded in t around 0 54.2%

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

   4. Taylor expanded in y around 0 54.2%

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

      1. associate-*r/ 54.2%

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

      2. mul-1-neg 54.2%

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

   6. Simplified 54.2%

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

   if -1.29999999999999991e80 < t < -7.2e18 or -2.04999999999999999e-175 < t < 4.2000000000000002e-306 or 1.25e-155 < t < 3e52

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. associate-/l* 89.0%

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

      3. fma-define 89.0%

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

   3. Simplified 89.0%

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

      1. clear-num 88.9%

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

      2. associate-/r/ 89.0%

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

   6. Applied egg-rr 89.0%

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

   7. Taylor expanded in z around inf 72.1%

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

      1. div-sub 72.1%

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

   9. Simplified 72.1%

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

   if -7.2e18 < t < -2.04999999999999999e-175

   1. Initial program 88.4%

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

   3. Taylor expanded in t around 0 67.8%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

   if 4.2000000000000002e-306 < t < 1.25e-155

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 94.4%

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

   4. Taylor expanded in y around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. associate-/l* 78.0%

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

   6. Simplified 78.0%

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

   if 3e52 < t

   1. Initial program 43.3%

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

      1. +-commutative 43.3%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. associate-*r/ 47.2%

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

      3. *-commutative 47.2%

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

      4. associate-*r/ 60.0%

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

   9. Simplified 60.0%

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

   10. Taylor expanded in a around 0 58.2%

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

       1. associate-*r/ 58.2%

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

       2. neg-mul-1 58.2%

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

   12. Simplified 58.2%

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

   13. Taylor expanded in z around 0 62.6%

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

       1. mul-1-neg 62.6%

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

       2. associate-*l/ 70.5%

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

       3. unsub-neg 70.5%

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

       4. associate-*l/ 62.6%

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

       5. associate-/l* 70.4%

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

       6. *-commutative 70.4%

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

       7. associate-/r/ 70.4%

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

   15. Simplified 70.4%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+80}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-175}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+23}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) (- t a)))))
   (if (<= t -4.2e+115)
     (* y (/ (- t z) t))
     (if (<= t -6.8e+75)
       (- x (/ (* x z) a))
       (if (<= t -2.4e+23)
         (* (- z t) (/ y (- a t)))
         (if (<= t -3.8e-173)
           (+ x (* y (/ z a)))
           (if (<= t 2.55e-306)
             t_1
             (if (<= t 1.5e-155)
               (- x (* x (/ z a)))
               (if (<= t 5.4e+51) t_1 (- y (/ z (/ t y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -4.2e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.8e+75) {
		tmp = x - ((x * z) / a);
	} else if (t <= -2.4e+23) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= -3.8e-173) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.55e-306) {
		tmp = t_1;
	} else if (t <= 1.5e-155) {
		tmp = x - (x * (z / a));
	} else if (t <= 5.4e+51) {
		tmp = t_1;
	} else {
		tmp = y - (z / (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) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / (t - a))
    if (t <= (-4.2d+115)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-6.8d+75)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-2.4d+23)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= (-3.8d-173)) then
        tmp = x + (y * (z / a))
    else if (t <= 2.55d-306) then
        tmp = t_1
    else if (t <= 1.5d-155) then
        tmp = x - (x * (z / a))
    else if (t <= 5.4d+51) then
        tmp = t_1
    else
        tmp = y - (z / (t / 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 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -4.2e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.8e+75) {
		tmp = x - ((x * z) / a);
	} else if (t <= -2.4e+23) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= -3.8e-173) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.55e-306) {
		tmp = t_1;
	} else if (t <= 1.5e-155) {
		tmp = x - (x * (z / a));
	} else if (t <= 5.4e+51) {
		tmp = t_1;
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / (t - a))
	tmp = 0
	if t <= -4.2e+115:
		tmp = y * ((t - z) / t)
	elif t <= -6.8e+75:
		tmp = x - ((x * z) / a)
	elif t <= -2.4e+23:
		tmp = (z - t) * (y / (a - t))
	elif t <= -3.8e-173:
		tmp = x + (y * (z / a))
	elif t <= 2.55e-306:
		tmp = t_1
	elif t <= 1.5e-155:
		tmp = x - (x * (z / a))
	elif t <= 5.4e+51:
		tmp = t_1
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (t <= -4.2e+115)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -6.8e+75)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -2.4e+23)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= -3.8e-173)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.55e-306)
		tmp = t_1;
	elseif (t <= 1.5e-155)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 5.4e+51)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (t <= -4.2e+115)
		tmp = y * ((t - z) / t);
	elseif (t <= -6.8e+75)
		tmp = x - ((x * z) / a);
	elseif (t <= -2.4e+23)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= -3.8e-173)
		tmp = x + (y * (z / a));
	elseif (t <= 2.55e-306)
		tmp = t_1;
	elseif (t <= 1.5e-155)
		tmp = x - (x * (z / a));
	elseif (t <= 5.4e+51)
		tmp = t_1;
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+115], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e+75], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e+23], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-173], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-306], t$95$1, If[LessEqual[t, 1.5e-155], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+51], t$95$1, N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -4.20000000000000007e115

   1. Initial program 26.8%

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

      1. +-commutative 26.8%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.4%

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

   3. Simplified 58.4%

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

      1. clear-num 58.3%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r/ 56.1%

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

   9. Simplified 56.1%

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

   10. Taylor expanded in a around 0 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   12. Simplified 62.3%

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

   if -4.20000000000000007e115 < t < -6.80000000000000022e75

   1. Initial program 42.2%

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

   3. Taylor expanded in t around 0 58.7%

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

   4. Taylor expanded in y around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. mul-1-neg 58.7%

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

   6. Simplified 58.7%

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

   if -6.80000000000000022e75 < t < -2.4e23

   1. Initial program 52.7%

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

      1. +-commutative 52.7%

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

      2. associate-/l* 61.9%

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

      3. fma-define 61.9%

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

   3. Simplified 61.9%

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

      1. clear-num 61.9%

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

      2. associate-/r/ 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in y around inf 52.9%

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

      1. div-sub 52.9%

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

      2. associate-*r/ 52.9%

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

      3. *-commutative 52.9%

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

      4. associate-*r/ 52.5%

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

   9. Simplified 52.5%

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

   if -2.4e23 < t < -3.8000000000000003e-173

   1. Initial program 88.4%

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

   3. Taylor expanded in t around 0 67.8%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

   if -3.8000000000000003e-173 < t < 2.54999999999999986e-306 or 1.49999999999999992e-155 < t < 5.39999999999999983e51

   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* 92.4%

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

      3. fma-define 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 92.3%

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

      2. associate-/r/ 92.4%

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

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in z around inf 74.4%

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

      1. div-sub 74.4%

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

   9. Simplified 74.4%

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

   if 2.54999999999999986e-306 < t < 1.49999999999999992e-155

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 94.4%

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

   4. Taylor expanded in y around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. associate-/l* 78.0%

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

   6. Simplified 78.0%

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

   if 5.39999999999999983e51 < t

   1. Initial program 43.3%

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

      1. +-commutative 43.3%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. associate-*r/ 47.2%

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

      3. *-commutative 47.2%

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

      4. associate-*r/ 60.0%

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

   9. Simplified 60.0%

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

   10. Taylor expanded in a around 0 58.2%

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

       1. associate-*r/ 58.2%

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

       2. neg-mul-1 58.2%

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

   12. Simplified 58.2%

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

   13. Taylor expanded in z around 0 62.6%

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

       1. mul-1-neg 62.6%

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

       2. associate-*l/ 70.5%

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

       3. unsub-neg 70.5%

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

       4. associate-*l/ 62.6%

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

       5. associate-/l* 70.4%

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

       6. *-commutative 70.4%

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

       7. associate-/r/ 70.4%

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

   15. Simplified 70.4%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+23}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x - y \cdot \frac{t - z}{a}\\ t_3 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-162}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t)))
        (t_2 (- x (* y (/ (- t z) a))))
        (t_3 (* z (/ (- x y) (- t a)))))
   (if (<= a -2.1e+70)
     t_2
     (if (<= a -7.6e-162)
       (* (- z t) (/ y (- a t)))
       (if (<= a 3.5e-291)
         t_3
         (if (<= a 1.3e-201)
           t_1
           (if (<= a 3.6e-101) t_3 (if (<= a 3.3e-36) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x - (y * ((t - z) / a));
	double t_3 = z * ((x - y) / (t - a));
	double tmp;
	if (a <= -2.1e+70) {
		tmp = t_2;
	} else if (a <= -7.6e-162) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= 3.5e-291) {
		tmp = t_3;
	} else if (a <= 1.3e-201) {
		tmp = t_1;
	} else if (a <= 3.6e-101) {
		tmp = t_3;
	} else if (a <= 3.3e-36) {
		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) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x - (y * ((t - z) / a))
    t_3 = z * ((x - y) / (t - a))
    if (a <= (-2.1d+70)) then
        tmp = t_2
    else if (a <= (-7.6d-162)) then
        tmp = (z - t) * (y / (a - t))
    else if (a <= 3.5d-291) then
        tmp = t_3
    else if (a <= 1.3d-201) then
        tmp = t_1
    else if (a <= 3.6d-101) then
        tmp = t_3
    else if (a <= 3.3d-36) 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 = y * ((t - z) / t);
	double t_2 = x - (y * ((t - z) / a));
	double t_3 = z * ((x - y) / (t - a));
	double tmp;
	if (a <= -2.1e+70) {
		tmp = t_2;
	} else if (a <= -7.6e-162) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= 3.5e-291) {
		tmp = t_3;
	} else if (a <= 1.3e-201) {
		tmp = t_1;
	} else if (a <= 3.6e-101) {
		tmp = t_3;
	} else if (a <= 3.3e-36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x - (y * ((t - z) / a))
	t_3 = z * ((x - y) / (t - a))
	tmp = 0
	if a <= -2.1e+70:
		tmp = t_2
	elif a <= -7.6e-162:
		tmp = (z - t) * (y / (a - t))
	elif a <= 3.5e-291:
		tmp = t_3
	elif a <= 1.3e-201:
		tmp = t_1
	elif a <= 3.6e-101:
		tmp = t_3
	elif a <= 3.3e-36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x - Float64(y * Float64(Float64(t - z) / a)))
	t_3 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (a <= -2.1e+70)
		tmp = t_2;
	elseif (a <= -7.6e-162)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (a <= 3.5e-291)
		tmp = t_3;
	elseif (a <= 1.3e-201)
		tmp = t_1;
	elseif (a <= 3.6e-101)
		tmp = t_3;
	elseif (a <= 3.3e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x - (y * ((t - z) / a));
	t_3 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (a <= -2.1e+70)
		tmp = t_2;
	elseif (a <= -7.6e-162)
		tmp = (z - t) * (y / (a - t));
	elseif (a <= 3.5e-291)
		tmp = t_3;
	elseif (a <= 1.3e-201)
		tmp = t_1;
	elseif (a <= 3.6e-101)
		tmp = t_3;
	elseif (a <= 3.3e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+70], t$95$2, If[LessEqual[a, -7.6e-162], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-291], t$95$3, If[LessEqual[a, 1.3e-201], t$95$1, If[LessEqual[a, 3.6e-101], t$95$3, If[LessEqual[a, 3.3e-36], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.10000000000000008e70 or 3.29999999999999991e-36 < a

   1. Initial program 71.7%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in a around inf 63.0%

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

      1. associate-/l* 66.1%

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

   8. Simplified 66.1%

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

   if -2.10000000000000008e70 < a < -7.6000000000000001e-162

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 85.5%

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

      3. fma-define 85.5%

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

   3. Simplified 85.5%

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

      1. clear-num 85.6%

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

      2. associate-/r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

      2. associate-*r/ 57.6%

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

      3. *-commutative 57.6%

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

      4. associate-*r/ 66.3%

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

   9. Simplified 66.3%

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

   if -7.6000000000000001e-162 < a < 3.49999999999999996e-291 or 1.29999999999999991e-201 < a < 3.6e-101

   1. Initial program 70.2%

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

      1. +-commutative 70.2%

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

      2. associate-/l* 71.8%

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

      3. fma-define 71.8%

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

   3. Simplified 71.8%

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

      1. clear-num 71.7%

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

      2. associate-/r/ 71.8%

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

   6. Applied egg-rr 71.8%

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

   7. Taylor expanded in z around inf 69.3%

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

      1. div-sub 69.3%

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

   9. Simplified 69.3%

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

   if 3.49999999999999996e-291 < a < 1.29999999999999991e-201 or 3.6e-101 < a < 3.29999999999999991e-36

   1. Initial program 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-/l* 72.2%

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

      3. fma-define 72.2%

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

   3. Simplified 72.2%

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

      1. clear-num 72.1%

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

      2. associate-/r/ 72.0%

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

   6. Applied egg-rr 72.0%

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

   7. Taylor expanded in y around inf 77.2%

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

      1. div-sub 77.2%

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

      2. associate-*r/ 66.5%

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

      3. *-commutative 66.5%

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

      4. associate-*r/ 63.0%

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

   9. Simplified 63.0%

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

   10. Taylor expanded in a around 0 70.8%

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

       1. mul-1-neg 70.8%

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

       2. associate-/l* 84.9%

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

       3. distribute-rgt-neg-in 84.9%

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

   12. Simplified 84.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+70}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-162}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-101}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-153}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+115)
   (* y (/ (- t z) t))
   (if (<= t -6.9e+75)
     (- x (/ (* x z) a))
     (if (<= t -9.5e+28)
       (* (- z t) (/ y (- a t)))
       (if (<= t -1.85e-22)
         (+ x y)
         (if (<= t 8.6e-153)
           (+ x (* z (/ (- y x) a)))
           (if (<= t 2.3e+54)
             (* z (/ (- x y) (- t a)))
             (- y (/ z (/ t y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.9e+75) {
		tmp = x - ((x * z) / a);
	} else if (t <= -9.5e+28) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= -1.85e-22) {
		tmp = x + y;
	} else if (t <= 8.6e-153) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 2.3e+54) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = y - (z / (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 (t <= (-4.2d+115)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-6.9d+75)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-9.5d+28)) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= (-1.85d-22)) then
        tmp = x + y
    else if (t <= 8.6d-153) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 2.3d+54) then
        tmp = z * ((x - y) / (t - a))
    else
        tmp = y - (z / (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 (t <= -4.2e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.9e+75) {
		tmp = x - ((x * z) / a);
	} else if (t <= -9.5e+28) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= -1.85e-22) {
		tmp = x + y;
	} else if (t <= 8.6e-153) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 2.3e+54) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+115:
		tmp = y * ((t - z) / t)
	elif t <= -6.9e+75:
		tmp = x - ((x * z) / a)
	elif t <= -9.5e+28:
		tmp = (z - t) * (y / (a - t))
	elif t <= -1.85e-22:
		tmp = x + y
	elif t <= 8.6e-153:
		tmp = x + (z * ((y - x) / a))
	elif t <= 2.3e+54:
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+115)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -6.9e+75)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -9.5e+28)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= -1.85e-22)
		tmp = Float64(x + y);
	elseif (t <= 8.6e-153)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 2.3e+54)
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+115)
		tmp = y * ((t - z) / t);
	elseif (t <= -6.9e+75)
		tmp = x - ((x * z) / a);
	elseif (t <= -9.5e+28)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= -1.85e-22)
		tmp = x + y;
	elseif (t <= 8.6e-153)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 2.3e+54)
		tmp = z * ((x - y) / (t - a));
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+115], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.9e+75], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e+28], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.85e-22], N[(x + y), $MachinePrecision], If[LessEqual[t, 8.6e-153], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+54], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -4.20000000000000007e115

   1. Initial program 26.8%

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

      1. +-commutative 26.8%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.4%

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

   3. Simplified 58.4%

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

      1. clear-num 58.3%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r/ 56.1%

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

   9. Simplified 56.1%

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

   10. Taylor expanded in a around 0 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   12. Simplified 62.3%

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

   if -4.20000000000000007e115 < t < -6.9000000000000004e75

   1. Initial program 42.2%

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

   3. Taylor expanded in t around 0 58.7%

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

   4. Taylor expanded in y around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. mul-1-neg 58.7%

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

   6. Simplified 58.7%

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

   if -6.9000000000000004e75 < t < -9.49999999999999927e28

   1. Initial program 52.7%

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

      1. +-commutative 52.7%

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

      2. associate-/l* 61.9%

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

      3. fma-define 61.9%

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

   3. Simplified 61.9%

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

      1. clear-num 61.9%

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

      2. associate-/r/ 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in y around inf 52.9%

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

      1. div-sub 52.9%

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

      2. associate-*r/ 52.9%

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

      3. *-commutative 52.9%

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

      4. associate-*r/ 52.5%

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

   9. Simplified 52.5%

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

   if -9.49999999999999927e28 < t < -1.85e-22

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 75.2%

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

      1. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in t around inf 54.1%

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

   if -1.85e-22 < t < 8.6000000000000001e-153

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 82.0%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   if 8.6000000000000001e-153 < t < 2.29999999999999994e54

   1. Initial program 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-/l* 93.9%

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

      3. fma-define 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 93.8%

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

      2. associate-/r/ 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around inf 65.6%

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

      1. div-sub 65.6%

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

   9. Simplified 65.6%

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

   if 2.29999999999999994e54 < t

   1. Initial program 43.3%

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

      1. +-commutative 43.3%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. associate-*r/ 47.2%

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

      3. *-commutative 47.2%

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

      4. associate-*r/ 60.0%

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

   9. Simplified 60.0%

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

   10. Taylor expanded in a around 0 58.2%

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

       1. associate-*r/ 58.2%

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

       2. neg-mul-1 58.2%

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

   12. Simplified 58.2%

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

   13. Taylor expanded in z around 0 62.6%

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

       1. mul-1-neg 62.6%

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

       2. associate-*l/ 70.5%

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

       3. unsub-neg 70.5%

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

       4. associate-*l/ 62.6%

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

       5. associate-/l* 70.4%

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

       6. *-commutative 70.4%

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

       7. associate-/r/ 70.4%

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

   15. Simplified 70.4%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-153}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y}}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+52}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t y)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -1.35e+116)
     t_1
     (if (<= t -9.5e+52)
       (- x (* x (/ z a)))
       (if (<= t -2.3e+27)
         t_1
         (if (<= t -2.6e-195)
           t_2
           (if (<= t 1.4e-303)
             (* z (/ (- y x) a))
             (if (<= t 1.75e+14) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / y));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -1.35e+116) {
		tmp = t_1;
	} else if (t <= -9.5e+52) {
		tmp = x - (x * (z / a));
	} else if (t <= -2.3e+27) {
		tmp = t_1;
	} else if (t <= -2.6e-195) {
		tmp = t_2;
	} else if (t <= 1.4e-303) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.75e+14) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (z / (t / y))
    t_2 = x + (y * (z / a))
    if (t <= (-1.35d+116)) then
        tmp = t_1
    else if (t <= (-9.5d+52)) then
        tmp = x - (x * (z / a))
    else if (t <= (-2.3d+27)) then
        tmp = t_1
    else if (t <= (-2.6d-195)) then
        tmp = t_2
    else if (t <= 1.4d-303) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.75d+14) then
        tmp = t_2
    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 - (z / (t / y));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -1.35e+116) {
		tmp = t_1;
	} else if (t <= -9.5e+52) {
		tmp = x - (x * (z / a));
	} else if (t <= -2.3e+27) {
		tmp = t_1;
	} else if (t <= -2.6e-195) {
		tmp = t_2;
	} else if (t <= 1.4e-303) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.75e+14) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z / (t / y))
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -1.35e+116:
		tmp = t_1
	elif t <= -9.5e+52:
		tmp = x - (x * (z / a))
	elif t <= -2.3e+27:
		tmp = t_1
	elif t <= -2.6e-195:
		tmp = t_2
	elif t <= 1.4e-303:
		tmp = z * ((y - x) / a)
	elif t <= 1.75e+14:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z / Float64(t / y)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.35e+116)
		tmp = t_1;
	elseif (t <= -9.5e+52)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= -2.3e+27)
		tmp = t_1;
	elseif (t <= -2.6e-195)
		tmp = t_2;
	elseif (t <= 1.4e-303)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.75e+14)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z / (t / y));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.35e+116)
		tmp = t_1;
	elseif (t <= -9.5e+52)
		tmp = x - (x * (z / a));
	elseif (t <= -2.3e+27)
		tmp = t_1;
	elseif (t <= -2.6e-195)
		tmp = t_2;
	elseif (t <= 1.4e-303)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.75e+14)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+116], t$95$1, If[LessEqual[t, -9.5e+52], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e+27], t$95$1, If[LessEqual[t, -2.6e-195], t$95$2, If[LessEqual[t, 1.4e-303], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+14], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e116 or -9.49999999999999994e52 < t < -2.3000000000000001e27 or 1.75e14 < t

   1. Initial program 44.8%

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

      1. +-commutative 44.8%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.4%

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

   6. Applied egg-rr 70.4%

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

   7. Taylor expanded in y around inf 69.9%

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

      1. div-sub 69.9%

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

      2. associate-*r/ 48.5%

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

      3. *-commutative 48.5%

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

      4. associate-*r/ 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in a around 0 54.8%

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

       1. associate-*r/ 54.8%

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

       2. neg-mul-1 54.8%

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

   12. Simplified 54.8%

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

   13. Taylor expanded in z around 0 58.3%

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

       1. mul-1-neg 58.3%

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

       2. associate-*l/ 64.4%

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

       3. unsub-neg 64.4%

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

       4. associate-*l/ 58.3%

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

       5. associate-/l* 65.0%

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

       6. *-commutative 65.0%

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

       7. associate-/r/ 64.4%

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

   15. Simplified 64.4%

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

   if -1.35e116 < t < -9.49999999999999994e52

   1. Initial program 38.1%

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

   3. Taylor expanded in t around 0 52.6%

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

   4. Taylor expanded in y around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

      3. associate-/l* 46.9%

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

   6. Simplified 46.9%

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

   if -2.3000000000000001e27 < t < -2.6000000000000002e-195 or 1.4e-303 < t < 1.75e14

   1. Initial program 93.1%

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

   3. Taylor expanded in t around 0 71.3%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

   if -2.6000000000000002e-195 < t < 1.4e-303

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 79.8%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. div-sub 75.9%

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

   6. Simplified 75.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+52}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6800000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -4.6e+115)
     t_1
     (if (<= t -1.9e+52)
       (- x (* x (/ z a)))
       (if (<= t -1.1e+28)
         t_1
         (if (<= t -1.15e-197)
           t_2
           (if (<= t 5e-300)
             (* z (/ (- y x) a))
             (if (<= t 6800000.0) t_2 (- y (/ z (/ t y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -4.6e+115) {
		tmp = t_1;
	} else if (t <= -1.9e+52) {
		tmp = x - (x * (z / a));
	} else if (t <= -1.1e+28) {
		tmp = t_1;
	} else if (t <= -1.15e-197) {
		tmp = t_2;
	} else if (t <= 5e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6800000.0) {
		tmp = t_2;
	} else {
		tmp = y - (z / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x + (y * (z / a))
    if (t <= (-4.6d+115)) then
        tmp = t_1
    else if (t <= (-1.9d+52)) then
        tmp = x - (x * (z / a))
    else if (t <= (-1.1d+28)) then
        tmp = t_1
    else if (t <= (-1.15d-197)) then
        tmp = t_2
    else if (t <= 5d-300) then
        tmp = z * ((y - x) / a)
    else if (t <= 6800000.0d0) then
        tmp = t_2
    else
        tmp = y - (z / (t / 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 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -4.6e+115) {
		tmp = t_1;
	} else if (t <= -1.9e+52) {
		tmp = x - (x * (z / a));
	} else if (t <= -1.1e+28) {
		tmp = t_1;
	} else if (t <= -1.15e-197) {
		tmp = t_2;
	} else if (t <= 5e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6800000.0) {
		tmp = t_2;
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -4.6e+115:
		tmp = t_1
	elif t <= -1.9e+52:
		tmp = x - (x * (z / a))
	elif t <= -1.1e+28:
		tmp = t_1
	elif t <= -1.15e-197:
		tmp = t_2
	elif t <= 5e-300:
		tmp = z * ((y - x) / a)
	elif t <= 6800000.0:
		tmp = t_2
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -4.6e+115)
		tmp = t_1;
	elseif (t <= -1.9e+52)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= -1.1e+28)
		tmp = t_1;
	elseif (t <= -1.15e-197)
		tmp = t_2;
	elseif (t <= 5e-300)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 6800000.0)
		tmp = t_2;
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -4.6e+115)
		tmp = t_1;
	elseif (t <= -1.9e+52)
		tmp = x - (x * (z / a));
	elseif (t <= -1.1e+28)
		tmp = t_1;
	elseif (t <= -1.15e-197)
		tmp = t_2;
	elseif (t <= 5e-300)
		tmp = z * ((y - x) / a);
	elseif (t <= 6800000.0)
		tmp = t_2;
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+115], t$95$1, If[LessEqual[t, -1.9e+52], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e+28], t$95$1, If[LessEqual[t, -1.15e-197], t$95$2, If[LessEqual[t, 5e-300], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6800000.0], t$95$2, N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.60000000000000007e115 or -1.9e52 < t < -1.09999999999999993e28

   1. Initial program 32.9%

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

      1. +-commutative 32.9%

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

      2. associate-/l* 61.8%

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

      3. fma-define 61.8%

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

   3. Simplified 61.8%

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

      1. clear-num 61.8%

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

      2. associate-/r/ 61.8%

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

   6. Applied egg-rr 61.8%

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

   7. Taylor expanded in y around inf 71.1%

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

      1. div-sub 71.0%

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

      2. associate-*r/ 51.0%

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

      3. *-commutative 51.0%

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

      4. associate-*r/ 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in a around 0 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-/l* 65.5%

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

       3. distribute-rgt-neg-in 65.5%

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

   12. Simplified 65.5%

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

   if -4.60000000000000007e115 < t < -1.9e52

   1. Initial program 38.1%

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

   3. Taylor expanded in t around 0 52.6%

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

   4. Taylor expanded in y around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

      3. associate-/l* 46.9%

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

   6. Simplified 46.9%

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

   if -1.09999999999999993e28 < t < -1.15e-197 or 4.99999999999999996e-300 < t < 6.8e6

   1. Initial program 93.1%

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

   3. Taylor expanded in t around 0 71.3%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

   if -1.15e-197 < t < 4.99999999999999996e-300

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 79.8%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. div-sub 75.9%

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

   6. Simplified 75.9%

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

   if 6.8e6 < t

   1. Initial program 51.6%

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

      1. +-commutative 51.6%

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

      2. associate-/l* 75.5%

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

      3. fma-define 75.5%

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

   3. Simplified 75.5%

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

      1. clear-num 75.4%

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

      2. associate-/r/ 75.3%

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

   6. Applied egg-rr 75.3%

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

   7. Taylor expanded in y around inf 69.3%

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

      1. div-sub 69.3%

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

      2. associate-*r/ 47.1%

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

      3. *-commutative 47.1%

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

      4. associate-*r/ 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in a around 0 55.2%

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

       1. associate-*r/ 55.2%

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

       2. neg-mul-1 55.2%

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

   12. Simplified 55.2%

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

   13. Taylor expanded in z around 0 57.3%

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

       1. mul-1-neg 57.3%

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

       2. associate-*l/ 64.7%

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

       3. unsub-neg 64.7%

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

       4. associate-*l/ 57.3%

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

       5. associate-/l* 64.7%

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

       6. *-commutative 64.7%

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

       7. associate-/r/ 64.7%

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

   15. Simplified 64.7%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-197}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6800000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4100:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -4.2e+115)
     t_1
     (if (<= t -1.1e+52)
       (- x (/ (* x z) a))
       (if (<= t -4.8e+27)
         t_1
         (if (<= t -4.5e-197)
           t_2
           (if (<= t 6.6e-303)
             (* z (/ (- y x) a))
             (if (<= t 4100.0) t_2 (- y (/ z (/ t y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -4.2e+115) {
		tmp = t_1;
	} else if (t <= -1.1e+52) {
		tmp = x - ((x * z) / a);
	} else if (t <= -4.8e+27) {
		tmp = t_1;
	} else if (t <= -4.5e-197) {
		tmp = t_2;
	} else if (t <= 6.6e-303) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4100.0) {
		tmp = t_2;
	} else {
		tmp = y - (z / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x + (y * (z / a))
    if (t <= (-4.2d+115)) then
        tmp = t_1
    else if (t <= (-1.1d+52)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-4.8d+27)) then
        tmp = t_1
    else if (t <= (-4.5d-197)) then
        tmp = t_2
    else if (t <= 6.6d-303) then
        tmp = z * ((y - x) / a)
    else if (t <= 4100.0d0) then
        tmp = t_2
    else
        tmp = y - (z / (t / 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 = y * ((t - z) / t);
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -4.2e+115) {
		tmp = t_1;
	} else if (t <= -1.1e+52) {
		tmp = x - ((x * z) / a);
	} else if (t <= -4.8e+27) {
		tmp = t_1;
	} else if (t <= -4.5e-197) {
		tmp = t_2;
	} else if (t <= 6.6e-303) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4100.0) {
		tmp = t_2;
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -4.2e+115:
		tmp = t_1
	elif t <= -1.1e+52:
		tmp = x - ((x * z) / a)
	elif t <= -4.8e+27:
		tmp = t_1
	elif t <= -4.5e-197:
		tmp = t_2
	elif t <= 6.6e-303:
		tmp = z * ((y - x) / a)
	elif t <= 4100.0:
		tmp = t_2
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -4.2e+115)
		tmp = t_1;
	elseif (t <= -1.1e+52)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -4.8e+27)
		tmp = t_1;
	elseif (t <= -4.5e-197)
		tmp = t_2;
	elseif (t <= 6.6e-303)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 4100.0)
		tmp = t_2;
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -4.2e+115)
		tmp = t_1;
	elseif (t <= -1.1e+52)
		tmp = x - ((x * z) / a);
	elseif (t <= -4.8e+27)
		tmp = t_1;
	elseif (t <= -4.5e-197)
		tmp = t_2;
	elseif (t <= 6.6e-303)
		tmp = z * ((y - x) / a);
	elseif (t <= 4100.0)
		tmp = t_2;
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+115], t$95$1, If[LessEqual[t, -1.1e+52], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.8e+27], t$95$1, If[LessEqual[t, -4.5e-197], t$95$2, If[LessEqual[t, 6.6e-303], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4100.0], t$95$2, N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.20000000000000007e115 or -1.1e52 < t < -4.79999999999999995e27

   1. Initial program 32.9%

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

      1. +-commutative 32.9%

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

      2. associate-/l* 61.8%

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

      3. fma-define 61.8%

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

   3. Simplified 61.8%

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

      1. clear-num 61.8%

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

      2. associate-/r/ 61.8%

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

   6. Applied egg-rr 61.8%

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

   7. Taylor expanded in y around inf 71.1%

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

      1. div-sub 71.0%

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

      2. associate-*r/ 51.0%

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

      3. *-commutative 51.0%

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

      4. associate-*r/ 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in a around 0 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-/l* 65.5%

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

       3. distribute-rgt-neg-in 65.5%

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

   12. Simplified 65.5%

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

   if -4.20000000000000007e115 < t < -1.1e52

   1. Initial program 38.1%

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

   3. Taylor expanded in t around 0 52.6%

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

   4. Taylor expanded in y around 0 47.0%

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

      1. associate-*r/ 47.0%

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

      2. mul-1-neg 47.0%

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

   6. Simplified 47.0%

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

   if -4.79999999999999995e27 < t < -4.5000000000000001e-197 or 6.5999999999999994e-303 < t < 4100

   1. Initial program 93.1%

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

   3. Taylor expanded in t around 0 71.3%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

   if -4.5000000000000001e-197 < t < 6.5999999999999994e-303

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 79.8%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. div-sub 75.9%

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

   6. Simplified 75.9%

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

   if 4100 < t

   1. Initial program 51.6%

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

      1. +-commutative 51.6%

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

      2. associate-/l* 75.5%

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

      3. fma-define 75.5%

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

   3. Simplified 75.5%

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

      1. clear-num 75.4%

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

      2. associate-/r/ 75.3%

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

   6. Applied egg-rr 75.3%

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

   7. Taylor expanded in y around inf 69.3%

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

      1. div-sub 69.3%

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

      2. associate-*r/ 47.1%

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

      3. *-commutative 47.1%

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

      4. associate-*r/ 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in a around 0 55.2%

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

       1. associate-*r/ 55.2%

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

       2. neg-mul-1 55.2%

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

   12. Simplified 55.2%

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

   13. Taylor expanded in z around 0 57.3%

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

       1. mul-1-neg 57.3%

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

       2. associate-*l/ 64.7%

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

       3. unsub-neg 64.7%

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

       4. associate-*l/ 57.3%

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

       5. associate-/l* 64.7%

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

       6. *-commutative 64.7%

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

       7. associate-/r/ 64.7%

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

   15. Simplified 64.7%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-197}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4100:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_2 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))) (t_2 (* z (/ (- x y) (- t a)))))
   (if (<= t -1.35e+116)
     (* y (/ (- t z) t))
     (if (<= t -4.7e-176)
       t_1
       (if (<= t -3.5e-276)
         t_2
         (if (<= t 1.7e-152)
           t_1
           (if (<= t 3.8e+52) t_2 (- y (/ z (/ t y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double t_2 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -1.35e+116) {
		tmp = y * ((t - z) / t);
	} else if (t <= -4.7e-176) {
		tmp = t_1;
	} else if (t <= -3.5e-276) {
		tmp = t_2;
	} else if (t <= 1.7e-152) {
		tmp = t_1;
	} else if (t <= 3.8e+52) {
		tmp = t_2;
	} else {
		tmp = y - (z / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    t_2 = z * ((x - y) / (t - a))
    if (t <= (-1.35d+116)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-4.7d-176)) then
        tmp = t_1
    else if (t <= (-3.5d-276)) then
        tmp = t_2
    else if (t <= 1.7d-152) then
        tmp = t_1
    else if (t <= 3.8d+52) then
        tmp = t_2
    else
        tmp = y - (z / (t / 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 - x) * (z / a));
	double t_2 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -1.35e+116) {
		tmp = y * ((t - z) / t);
	} else if (t <= -4.7e-176) {
		tmp = t_1;
	} else if (t <= -3.5e-276) {
		tmp = t_2;
	} else if (t <= 1.7e-152) {
		tmp = t_1;
	} else if (t <= 3.8e+52) {
		tmp = t_2;
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	t_2 = z * ((x - y) / (t - a))
	tmp = 0
	if t <= -1.35e+116:
		tmp = y * ((t - z) / t)
	elif t <= -4.7e-176:
		tmp = t_1
	elif t <= -3.5e-276:
		tmp = t_2
	elif t <= 1.7e-152:
		tmp = t_1
	elif t <= 3.8e+52:
		tmp = t_2
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	t_2 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (t <= -1.35e+116)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -4.7e-176)
		tmp = t_1;
	elseif (t <= -3.5e-276)
		tmp = t_2;
	elseif (t <= 1.7e-152)
		tmp = t_1;
	elseif (t <= 3.8e+52)
		tmp = t_2;
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	t_2 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (t <= -1.35e+116)
		tmp = y * ((t - z) / t);
	elseif (t <= -4.7e-176)
		tmp = t_1;
	elseif (t <= -3.5e-276)
		tmp = t_2;
	elseif (t <= 1.7e-152)
		tmp = t_1;
	elseif (t <= 3.8e+52)
		tmp = t_2;
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+116], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-176], t$95$1, If[LessEqual[t, -3.5e-276], t$95$2, If[LessEqual[t, 1.7e-152], t$95$1, If[LessEqual[t, 3.8e+52], t$95$2, N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e116

   1. Initial program 26.8%

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

      1. +-commutative 26.8%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.4%

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

   3. Simplified 58.4%

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

      1. clear-num 58.3%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r/ 56.1%

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

   9. Simplified 56.1%

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

   10. Taylor expanded in a around 0 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   12. Simplified 62.3%

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

   if -1.35e116 < t < -4.69999999999999984e-176 or -3.49999999999999993e-276 < t < 1.69999999999999992e-152

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 72.2%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in z around inf 75.1%

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

   if -4.69999999999999984e-176 < t < -3.49999999999999993e-276 or 1.69999999999999992e-152 < t < 3.8e52

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-/l* 91.8%

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

      3. fma-define 91.8%

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

   3. Simplified 91.8%

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

      1. clear-num 91.7%

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

      2. associate-/r/ 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in z around inf 73.9%

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

      1. div-sub 73.9%

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

   9. Simplified 73.9%

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

   if 3.8e52 < t

   1. Initial program 43.3%

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

      1. +-commutative 43.3%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. associate-*r/ 47.2%

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

      3. *-commutative 47.2%

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

      4. associate-*r/ 60.0%

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

   9. Simplified 60.0%

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

   10. Taylor expanded in a around 0 58.2%

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

       1. associate-*r/ 58.2%

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

       2. neg-mul-1 58.2%

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

   12. Simplified 58.2%

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

   13. Taylor expanded in z around 0 62.6%

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

       1. mul-1-neg 62.6%

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

       2. associate-*l/ 70.5%

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

       3. unsub-neg 70.5%

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

       4. associate-*l/ 62.6%

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

       5. associate-/l* 70.4%

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

       6. *-commutative 70.4%

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

       7. associate-/r/ 70.4%

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

   15. Simplified 70.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-176}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-152}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-176}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-152}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) (- t a)))))
   (if (<= t -4.5e+115)
     (* y (/ (- t z) t))
     (if (<= t -4.9e-176)
       (+ x (* (- y x) (/ z a)))
       (if (<= t -6.8e-263)
         t_1
         (if (<= t 1.25e-152)
           (- x (/ (* z (- x y)) a))
           (if (<= t 2.1e+54) t_1 (- y (/ z (/ t y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -4.5e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -4.9e-176) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= -6.8e-263) {
		tmp = t_1;
	} else if (t <= 1.25e-152) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= 2.1e+54) {
		tmp = t_1;
	} else {
		tmp = y - (z / (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) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / (t - a))
    if (t <= (-4.5d+115)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-4.9d-176)) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= (-6.8d-263)) then
        tmp = t_1
    else if (t <= 1.25d-152) then
        tmp = x - ((z * (x - y)) / a)
    else if (t <= 2.1d+54) then
        tmp = t_1
    else
        tmp = y - (z / (t / 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 = z * ((x - y) / (t - a));
	double tmp;
	if (t <= -4.5e+115) {
		tmp = y * ((t - z) / t);
	} else if (t <= -4.9e-176) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= -6.8e-263) {
		tmp = t_1;
	} else if (t <= 1.25e-152) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= 2.1e+54) {
		tmp = t_1;
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / (t - a))
	tmp = 0
	if t <= -4.5e+115:
		tmp = y * ((t - z) / t)
	elif t <= -4.9e-176:
		tmp = x + ((y - x) * (z / a))
	elif t <= -6.8e-263:
		tmp = t_1
	elif t <= 1.25e-152:
		tmp = x - ((z * (x - y)) / a)
	elif t <= 2.1e+54:
		tmp = t_1
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (t <= -4.5e+115)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -4.9e-176)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= -6.8e-263)
		tmp = t_1;
	elseif (t <= 1.25e-152)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	elseif (t <= 2.1e+54)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (t <= -4.5e+115)
		tmp = y * ((t - z) / t);
	elseif (t <= -4.9e-176)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= -6.8e-263)
		tmp = t_1;
	elseif (t <= 1.25e-152)
		tmp = x - ((z * (x - y)) / a);
	elseif (t <= 2.1e+54)
		tmp = t_1;
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+115], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.9e-176], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-263], t$95$1, If[LessEqual[t, 1.25e-152], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+54], t$95$1, N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.49999999999999963e115

   1. Initial program 26.8%

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

      1. +-commutative 26.8%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.4%

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

   3. Simplified 58.4%

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

      1. clear-num 58.3%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r/ 56.1%

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

   9. Simplified 56.1%

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

   10. Taylor expanded in a around 0 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   12. Simplified 62.3%

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

   if -4.49999999999999963e115 < t < -4.8999999999999997e-176

   1. Initial program 75.2%

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

   3. Taylor expanded in a around inf 57.5%

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

      1. associate-/l* 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in z around inf 63.6%

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

   if -4.8999999999999997e-176 < t < -6.80000000000000008e-263 or 1.2499999999999999e-152 < t < 2.09999999999999986e54

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-/l* 91.7%

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

      3. fma-define 91.7%

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

   3. Simplified 91.7%

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

      1. clear-num 91.6%

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

      2. associate-/r/ 91.7%

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

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. div-sub 73.6%

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

   9. Simplified 73.6%

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

   if -6.80000000000000008e-263 < t < 1.2499999999999999e-152

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 95.1%

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

   if 2.09999999999999986e54 < t

   1. Initial program 43.3%

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

      1. +-commutative 43.3%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. associate-*r/ 47.2%

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

      3. *-commutative 47.2%

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

      4. associate-*r/ 60.0%

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

   9. Simplified 60.0%

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

   10. Taylor expanded in a around 0 58.2%

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

       1. associate-*r/ 58.2%

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

       2. neg-mul-1 58.2%

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

   12. Simplified 58.2%

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

   13. Taylor expanded in z around 0 62.6%

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

       1. mul-1-neg 62.6%

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

       2. associate-*l/ 70.5%

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

       3. unsub-neg 70.5%

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

       4. associate-*l/ 62.6%

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

       5. associate-/l* 70.4%

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

       6. *-commutative 70.4%

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

       7. associate-/r/ 70.4%

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

   15. Simplified 70.4%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-176}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-152}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+56}:\\ \;\;\;\;\frac{x \cdot z}{t - a}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+61}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+105)
   (* y (/ (- t z) t))
   (if (<= t -2.35e+56)
     (/ (* x z) (- t a))
     (if (<= t -5e-49)
       (+ x (* y (/ (- z t) (- a t))))
       (if (<= t 9e+61)
         (+ x (* z (/ (- x y) (- t a))))
         (- y (/ z (/ t y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+105) {
		tmp = y * ((t - z) / t);
	} else if (t <= -2.35e+56) {
		tmp = (x * z) / (t - a);
	} else if (t <= -5e-49) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (t <= 9e+61) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = y - (z / (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 (t <= (-3.6d+105)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-2.35d+56)) then
        tmp = (x * z) / (t - a)
    else if (t <= (-5d-49)) then
        tmp = x + (y * ((z - t) / (a - t)))
    else if (t <= 9d+61) then
        tmp = x + (z * ((x - y) / (t - a)))
    else
        tmp = y - (z / (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 (t <= -3.6e+105) {
		tmp = y * ((t - z) / t);
	} else if (t <= -2.35e+56) {
		tmp = (x * z) / (t - a);
	} else if (t <= -5e-49) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (t <= 9e+61) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+105:
		tmp = y * ((t - z) / t)
	elif t <= -2.35e+56:
		tmp = (x * z) / (t - a)
	elif t <= -5e-49:
		tmp = x + (y * ((z - t) / (a - t)))
	elif t <= 9e+61:
		tmp = x + (z * ((x - y) / (t - a)))
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+105)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -2.35e+56)
		tmp = Float64(Float64(x * z) / Float64(t - a));
	elseif (t <= -5e-49)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	elseif (t <= 9e+61)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+105)
		tmp = y * ((t - z) / t);
	elseif (t <= -2.35e+56)
		tmp = (x * z) / (t - a);
	elseif (t <= -5e-49)
		tmp = x + (y * ((z - t) / (a - t)));
	elseif (t <= 9e+61)
		tmp = x + (z * ((x - y) / (t - a)));
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+105], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.35e+56], N[(N[(x * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-49], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+61], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.5999999999999999e105

   1. Initial program 24.9%

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

      1. +-commutative 24.9%

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

      2. associate-/l* 56.4%

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

      3. fma-define 56.4%

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

   3. Simplified 56.4%

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

      1. clear-num 56.4%

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

      2. associate-/r/ 56.3%

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

   6. Applied egg-rr 56.3%

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

   7. Taylor expanded in y around inf 63.2%

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

      1. div-sub 63.1%

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

      2. associate-*r/ 43.1%

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

      3. *-commutative 43.1%

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

      4. associate-*r/ 51.8%

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

   9. Simplified 51.8%

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

   10. Taylor expanded in a around 0 40.4%

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

       1. mul-1-neg 40.4%

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

       2. associate-/l* 57.6%

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

       3. distribute-rgt-neg-in 57.6%

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

   12. Simplified 57.6%

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

   if -3.5999999999999999e105 < t < -2.35e56

   1. Initial program 44.1%

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

   3. Taylor expanded in y around 0 34.2%

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

      1. associate-*r/ 34.2%

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

      2. mul-1-neg 34.2%

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

      3. distribute-lft-neg-out 34.2%

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

      4. *-commutative 34.2%

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

   5. Simplified 34.2%

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

   6. Taylor expanded in z around inf 58.6%

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

      1. associate-*r/ 58.6%

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

      2. mul-1-neg 58.6%

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

   8. Simplified 58.6%

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

   if -2.35e56 < t < -4.9999999999999999e-49

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

   if -4.9999999999999999e-49 < t < 9e61

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if 9e61 < t

   1. Initial program 42.8%

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

      1. +-commutative 42.8%

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

      2. associate-/l* 69.3%

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

      3. fma-define 69.3%

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

   3. Simplified 69.3%

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

      1. clear-num 69.3%

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

      2. associate-/r/ 69.0%

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

   6. Applied egg-rr 69.0%

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

   7. Taylor expanded in y around inf 73.2%

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

      1. div-sub 73.2%

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

      2. associate-*r/ 49.0%

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

      3. *-commutative 49.0%

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

      4. associate-*r/ 60.3%

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

   9. Simplified 60.3%

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

   10. Taylor expanded in a around 0 58.5%

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

       1. associate-*r/ 58.5%

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

       2. neg-mul-1 58.5%

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

   12. Simplified 58.5%

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

   13. Taylor expanded in z around 0 65.1%

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

       1. mul-1-neg 65.1%

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

       2. associate-*l/ 71.3%

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

       3. unsub-neg 71.3%

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

       4. associate-*l/ 65.1%

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

       5. associate-/l* 71.3%

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

       6. *-commutative 71.3%

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

       7. associate-/r/ 71.3%

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

   15. Simplified 71.3%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+56}:\\ \;\;\;\;\frac{x \cdot z}{t - a}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+61}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+75}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+60}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+117)
   (* y (/ (- t z) t))
   (if (<= t -6.9e+75)
     (+ x (* (- y x) (/ (- z t) a)))
     (if (<= t -1.26e-49)
       (+ x (* y (/ (- z t) (- a t))))
       (if (<= t 6.5e+60)
         (+ x (* z (/ (- x y) (- t a))))
         (- y (/ z (/ t y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+117) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.9e+75) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else if (t <= -1.26e-49) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (t <= 6.5e+60) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = y - (z / (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 (t <= (-2.4d+117)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-6.9d+75)) then
        tmp = x + ((y - x) * ((z - t) / a))
    else if (t <= (-1.26d-49)) then
        tmp = x + (y * ((z - t) / (a - t)))
    else if (t <= 6.5d+60) then
        tmp = x + (z * ((x - y) / (t - a)))
    else
        tmp = y - (z / (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 (t <= -2.4e+117) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.9e+75) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else if (t <= -1.26e-49) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (t <= 6.5e+60) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = y - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+117:
		tmp = y * ((t - z) / t)
	elif t <= -6.9e+75:
		tmp = x + ((y - x) * ((z - t) / a))
	elif t <= -1.26e-49:
		tmp = x + (y * ((z - t) / (a - t)))
	elif t <= 6.5e+60:
		tmp = x + (z * ((x - y) / (t - a)))
	else:
		tmp = y - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+117)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -6.9e+75)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	elseif (t <= -1.26e-49)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	elseif (t <= 6.5e+60)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	else
		tmp = Float64(y - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+117)
		tmp = y * ((t - z) / t);
	elseif (t <= -6.9e+75)
		tmp = x + ((y - x) * ((z - t) / a));
	elseif (t <= -1.26e-49)
		tmp = x + (y * ((z - t) / (a - t)));
	elseif (t <= 6.5e+60)
		tmp = x + (z * ((x - y) / (t - a)));
	else
		tmp = y - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+117], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.9e+75], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.26e-49], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+60], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.3999999999999999e117

   1. Initial program 26.8%

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

      1. +-commutative 26.8%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.4%

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

   3. Simplified 58.4%

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

      1. clear-num 58.3%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.4%

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

      2. associate-*r/ 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r/ 56.1%

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

   9. Simplified 56.1%

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

   10. Taylor expanded in a around 0 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

   12. Simplified 62.3%

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

   if -2.3999999999999999e117 < t < -6.9000000000000004e75

   1. Initial program 42.2%

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

   3. Taylor expanded in a around inf 41.4%

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

      1. associate-/l* 60.4%

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

   5. Simplified 60.4%

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

   if -6.9000000000000004e75 < t < -1.26000000000000005e-49

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   if -1.26000000000000005e-49 < t < 6.49999999999999931e60

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   if 6.49999999999999931e60 < t

   1. Initial program 42.8%

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

      1. +-commutative 42.8%

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

      2. associate-/l* 69.3%

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

      3. fma-define 69.3%

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

   3. Simplified 69.3%

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

      1. clear-num 69.3%

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

      2. associate-/r/ 69.0%

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

   6. Applied egg-rr 69.0%

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

   7. Taylor expanded in y around inf 73.2%

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

      1. div-sub 73.2%

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

      2. associate-*r/ 49.0%

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

      3. *-commutative 49.0%

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

      4. associate-*r/ 60.3%

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

   9. Simplified 60.3%

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

   10. Taylor expanded in a around 0 58.5%

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

       1. associate-*r/ 58.5%

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

       2. neg-mul-1 58.5%

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

   12. Simplified 58.5%

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

   13. Taylor expanded in z around 0 65.1%

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

       1. mul-1-neg 65.1%

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

       2. associate-*l/ 71.3%

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

       3. unsub-neg 71.3%

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

       4. associate-*l/ 65.1%

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

       5. associate-/l* 71.3%

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

       6. *-commutative 71.3%

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

       7. associate-/r/ 71.3%

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

   15. Simplified 71.3%

       \[\leadsto \color{blue}{y - \frac{z}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+75}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+60}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -4.8e+116)
     y
     (if (<= t -1.18e-197)
       t_1
       (if (<= t 1.4e-303) (* z (/ (- y x) a)) (if (<= t 4.5e+96) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -4.8e+116) {
		tmp = y;
	} else if (t <= -1.18e-197) {
		tmp = t_1;
	} else if (t <= 1.4e-303) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.5e+96) {
		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 + (y * (z / a))
    if (t <= (-4.8d+116)) then
        tmp = y
    else if (t <= (-1.18d-197)) then
        tmp = t_1
    else if (t <= 1.4d-303) then
        tmp = z * ((y - x) / a)
    else if (t <= 4.5d+96) 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 tmp;
	if (t <= -4.8e+116) {
		tmp = y;
	} else if (t <= -1.18e-197) {
		tmp = t_1;
	} else if (t <= 1.4e-303) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.5e+96) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -4.8e+116:
		tmp = y
	elif t <= -1.18e-197:
		tmp = t_1
	elif t <= 1.4e-303:
		tmp = z * ((y - x) / a)
	elif t <= 4.5e+96:
		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)))
	tmp = 0.0
	if (t <= -4.8e+116)
		tmp = y;
	elseif (t <= -1.18e-197)
		tmp = t_1;
	elseif (t <= 1.4e-303)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 4.5e+96)
		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));
	tmp = 0.0;
	if (t <= -4.8e+116)
		tmp = y;
	elseif (t <= -1.18e-197)
		tmp = t_1;
	elseif (t <= 1.4e-303)
		tmp = z * ((y - x) / a);
	elseif (t <= 4.5e+96)
		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]}, If[LessEqual[t, -4.8e+116], y, If[LessEqual[t, -1.18e-197], t$95$1, If[LessEqual[t, 1.4e-303], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+96], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000001e116 or 4.49999999999999957e96 < t

   1. Initial program 34.0%

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

   3. Taylor expanded in t around inf 61.2%

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

   if -4.8000000000000001e116 < t < -1.17999999999999995e-197 or 1.4e-303 < t < 4.49999999999999957e96

   1. Initial program 84.3%

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

   3. Taylor expanded in t around 0 64.2%

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

   4. Taylor expanded in y around inf 53.1%

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

      1. associate-/l* 54.9%

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

   6. Simplified 54.9%

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

   if -1.17999999999999995e-197 < t < 1.4e-303

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 79.8%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. div-sub 75.9%

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

   6. Simplified 75.9%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-197}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 410000000:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -9e+55)
     t_1
     (if (<= t -1.16e-48)
       (+ x (* y (/ (- z t) (- a t))))
       (if (<= t 410000000.0) (+ x (* z (/ (- x y) (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -9e+55) {
		tmp = t_1;
	} else if (t <= -1.16e-48) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (t <= 410000000.0) {
		tmp = x + (z * ((x - y) / (t - a)));
	} 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 + ((z - a) * ((x - y) / t))
    if (t <= (-9d+55)) then
        tmp = t_1
    else if (t <= (-1.16d-48)) then
        tmp = x + (y * ((z - t) / (a - t)))
    else if (t <= 410000000.0d0) then
        tmp = x + (z * ((x - y) / (t - a)))
    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 + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -9e+55) {
		tmp = t_1;
	} else if (t <= -1.16e-48) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (t <= 410000000.0) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -9e+55:
		tmp = t_1
	elif t <= -1.16e-48:
		tmp = x + (y * ((z - t) / (a - t)))
	elif t <= 410000000.0:
		tmp = x + (z * ((x - y) / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -9e+55)
		tmp = t_1;
	elseif (t <= -1.16e-48)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	elseif (t <= 410000000.0)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -9e+55)
		tmp = t_1;
	elseif (t <= -1.16e-48)
		tmp = x + (y * ((z - t) / (a - t)));
	elseif (t <= 410000000.0)
		tmp = x + (z * ((x - y) / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+55], t$95$1, If[LessEqual[t, -1.16e-48], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 410000000.0], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999996e55 or 4.1e8 < t

   1. Initial program 42.1%

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

   3. Taylor expanded in t around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. div-sub 66.6%

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

      7. associate-/l* 71.3%

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

      8. associate-/l* 79.1%

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

      9. distribute-rgt-out-- 80.1%

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

   5. Simplified 80.1%

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

   if -8.99999999999999996e55 < t < -1.16e-48

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

   if -1.16e-48 < t < 4.1e8

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+55}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 410000000:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+55} \lor \neg \left(t \leq 1.6 \cdot 10^{+60}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+55) (not (<= t 1.6e+60)))
   (+ y (* (- z a) (/ (- x y) t)))
   (+ x (/ (* (- y x) (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+55) || !(t <= 1.6e+60)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + (((y - x) * (z - t)) / (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 <= (-3.2d+55)) .or. (.not. (t <= 1.6d+60))) then
        tmp = y + ((z - a) * ((x - y) / t))
    else
        tmp = x + (((y - x) * (z - t)) / (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 <= -3.2e+55) || !(t <= 1.6e+60)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+55) or not (t <= 1.6e+60):
		tmp = y + ((z - a) * ((x - y) / t))
	else:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+55) || !(t <= 1.6e+60))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e+55) || ~((t <= 1.6e+60)))
		tmp = y + ((z - a) * ((x - y) / t));
	else
		tmp = x + (((y - x) * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e+55], N[Not[LessEqual[t, 1.6e+60]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000003e55 or 1.59999999999999995e60 < t

   1. Initial program 36.2%

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

   3. Taylor expanded in t around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. div-sub 67.9%

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

      7. associate-/l* 71.6%

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

      8. associate-/l* 79.7%

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

      9. distribute-rgt-out-- 80.8%

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

   5. Simplified 80.8%

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

   if -3.2000000000000003e55 < t < 1.59999999999999995e60

   1. Initial program 91.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+55} \lor \neg \left(t \leq 1.6 \cdot 10^{+60}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+57} \lor \neg \left(z \leq 3.2 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+57) (not (<= z 3.2e+153)))
   (* z (/ (- x y) (- t a)))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+57) || !(z <= 3.2e+153)) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = x + (y * ((z - t) / (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 ((z <= (-2d+57)) .or. (.not. (z <= 3.2d+153))) then
        tmp = z * ((x - y) / (t - a))
    else
        tmp = x + (y * ((z - t) / (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 ((z <= -2e+57) || !(z <= 3.2e+153)) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+57) or not (z <= 3.2e+153):
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+57) || !(z <= 3.2e+153))
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+57) || ~((z <= 3.2e+153)))
		tmp = z * ((x - y) / (t - a));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+57], N[Not[LessEqual[z, 3.2e+153]], $MachinePrecision]], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e57 or 3.2000000000000001e153 < z

   1. Initial program 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 90.5%

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

      3. fma-define 90.5%

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

   3. Simplified 90.5%

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

      1. clear-num 90.5%

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

      2. associate-/r/ 90.4%

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

   6. Applied egg-rr 90.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   7. Taylor expanded in z around inf 79.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 79.8%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   9. Simplified 79.8%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -2.0000000000000001e57 < z < 3.2000000000000001e153

   1. Initial program 66.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 69.1%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 69.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+57} \lor \neg \left(z \leq 3.2 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+28} \lor \neg \left(z \leq 3.5 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+28) (not (<= z 3.5e+55))) (* y (/ z (- a t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+28) || !(z <= 3.5e+55)) {
		tmp = y * (z / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+28)) .or. (.not. (z <= 3.5d+55))) then
        tmp = y * (z / (a - t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+28) || !(z <= 3.5e+55)) {
		tmp = y * (z / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+28) or not (z <= 3.5e+55):
		tmp = y * (z / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+28) || !(z <= 3.5e+55))
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+28) || ~((z <= 3.5e+55)))
		tmp = y * (z / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+28], N[Not[LessEqual[z, 3.5e+55]], $MachinePrecision]], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e28 or 3.5000000000000001e55 < z

   1. Initial program 76.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 90.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 90.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 90.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. associate-/r/ 90.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   6. Applied egg-rr 90.5%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   7. Taylor expanded in y around inf 55.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 55.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. associate-*r/ 44.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

      3. *-commutative 44.9%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

      4. associate-*r/ 52.6%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   9. Simplified 52.6%

      \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   10. Taylor expanded in z around inf 40.1%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   11. Step-by-step derivation

       1. associate-/l* 43.5%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   12. Simplified 43.5%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   if -1.9499999999999999e28 < z < 3.5000000000000001e55

   1. Initial program 66.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. *-commutative 60.3%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   5. Simplified 60.3%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   6. Taylor expanded in t around inf 44.1%

      \[\leadsto \color{blue}{x + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+28} \lor \neg \left(z \leq 3.5 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+25} \lor \neg \left(z \leq 2.5 \cdot 10^{+80}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+25) (not (<= z 2.5e+80))) (* z (/ (- y x) a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+25) || !(z <= 2.5e+80)) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+25)) .or. (.not. (z <= 2.5d+80))) then
        tmp = z * ((y - x) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+25) || !(z <= 2.5e+80)) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+25) or not (z <= 2.5e+80):
		tmp = z * ((y - x) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+25) || !(z <= 2.5e+80))
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+25) || ~((z <= 2.5e+80)))
		tmp = z * ((y - x) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+25], N[Not[LessEqual[z, 2.5e+80]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e25 or 2.4999999999999998e80 < z

   1. Initial program 75.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 58.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in z around inf 51.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a} - \frac{x}{a}\right)} \]
   5. Step-by-step derivation

      1. div-sub 51.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -1.6e25 < z < 2.4999999999999998e80

   1. Initial program 67.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   5. Simplified 60.4%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   6. Taylor expanded in t around inf 43.3%

      \[\leadsto \color{blue}{x + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+25} \lor \neg \left(z \leq 2.5 \cdot 10^{+80}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-37}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.75e+70)
   x
   (if (<= a -1.25e-15) (* z (/ y a)) (if (<= a 7.8e-37) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.75e+70) {
		tmp = x;
	} else if (a <= -1.25e-15) {
		tmp = z * (y / a);
	} else if (a <= 7.8e-37) {
		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 <= (-1.75d+70)) then
        tmp = x
    else if (a <= (-1.25d-15)) then
        tmp = z * (y / a)
    else if (a <= 7.8d-37) 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 <= -1.75e+70) {
		tmp = x;
	} else if (a <= -1.25e-15) {
		tmp = z * (y / a);
	} else if (a <= 7.8e-37) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.75e+70:
		tmp = x
	elif a <= -1.25e-15:
		tmp = z * (y / a)
	elif a <= 7.8e-37:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.75e+70)
		tmp = x;
	elseif (a <= -1.25e-15)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 7.8e-37)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.75e+70)
		tmp = x;
	elseif (a <= -1.25e-15)
		tmp = z * (y / a);
	elseif (a <= 7.8e-37)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.75e+70], x, If[LessEqual[a, -1.25e-15], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e-37], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75000000000000001e70 or 7.79999999999999981e-37 < a

   1. Initial program 71.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{x} \]

   if -1.75000000000000001e70 < a < -1.25e-15

   1. Initial program 78.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 78.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 84.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 84.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 84.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. associate-/r/ 84.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   6. Applied egg-rr 84.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   7. Taylor expanded in y around inf 70.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 70.6%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. associate-*r/ 67.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

      3. *-commutative 67.2%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

      4. associate-*r/ 67.1%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   9. Simplified 67.1%

      \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   10. Taylor expanded in a around inf 51.0%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a}} \]

   11. Taylor expanded in z around inf 48.1%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   12. Step-by-step derivation

       1. associate-*l/ 48.1%

          \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

       2. *-commutative 48.1%

          \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   13. Simplified 48.1%

       \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   if -1.25e-15 < a < 7.79999999999999981e-37

   1. Initial program 68.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-37}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+58)
   (* x (/ z (- a)))
   (if (<= z 3.2e+83) (+ x y) (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+58) {
		tmp = x * (z / -a);
	} else if (z <= 3.2e+83) {
		tmp = x + y;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+58)) then
        tmp = x * (z / -a)
    else if (z <= 3.2d+83) then
        tmp = x + y
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+58) {
		tmp = x * (z / -a);
	} else if (z <= 3.2e+83) {
		tmp = x + y;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+58:
		tmp = x * (z / -a)
	elif z <= 3.2e+83:
		tmp = x + y
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+58)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (z <= 3.2e+83)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+58)
		tmp = x * (z / -a);
	elseif (z <= 3.2e+83)
		tmp = x + y;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+58], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+83], N[(x + y), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999976e58

   1. Initial program 74.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 46.7%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 46.7%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(x \cdot \left(z - t\right)\right)}{a - t}} \]

      2. mul-1-neg 46.7%

         \[\leadsto x + \frac{\color{blue}{-x \cdot \left(z - t\right)}}{a - t} \]

      3. distribute-lft-neg-out 46.7%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot \left(z - t\right)}}{a - t} \]

      4. *-commutative 46.7%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(-x\right)}}{a - t} \]

   5. Simplified 46.7%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(-x\right)}{a - t}} \]

   6. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot \left(z - t\right)}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 36.8%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a}\right)} \]

      2. unsub-neg 36.8%

         \[\leadsto \color{blue}{x - \frac{x \cdot \left(z - t\right)}{a}} \]

      3. associate-/l* 37.0%

         \[\leadsto x - \color{blue}{x \cdot \frac{z - t}{a}} \]

   8. Simplified 37.0%

      \[\leadsto \color{blue}{x - x \cdot \frac{z - t}{a}} \]

   9. Taylor expanded in z around inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.9%

          \[\leadsto \color{blue}{-\frac{x \cdot z}{a}} \]

       2. associate-/l* 33.1%

          \[\leadsto -\color{blue}{x \cdot \frac{z}{a}} \]

   11. Simplified 33.1%

       \[\leadsto \color{blue}{-x \cdot \frac{z}{a}} \]

   if -5.19999999999999976e58 < z < 3.1999999999999999e83

   1. Initial program 66.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   5. Simplified 60.8%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   6. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{x + y} \]

   if 3.1999999999999999e83 < z

   1. Initial program 84.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 93.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 93.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 93.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. associate-/r/ 93.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   6. Applied egg-rr 93.5%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   7. Taylor expanded in y around inf 60.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 60.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. associate-*r/ 52.8%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

      3. *-commutative 52.8%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

      4. associate-*r/ 55.6%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   9. Simplified 55.6%

      \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   10. Taylor expanded in a around inf 41.9%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a}} \]

   11. Taylor expanded in z around inf 40.7%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   12. Step-by-step derivation

       1. associate-*l/ 42.0%

          \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

       2. *-commutative 42.0%

          \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   13. Simplified 42.0%

       \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+169)
   (* z (/ y (- t)))
   (if (<= z 2.9e+83) (+ x y) (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+169) {
		tmp = z * (y / -t);
	} else if (z <= 2.9e+83) {
		tmp = x + y;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+169)) then
        tmp = z * (y / -t)
    else if (z <= 2.9d+83) then
        tmp = x + y
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+169) {
		tmp = z * (y / -t);
	} else if (z <= 2.9e+83) {
		tmp = x + y;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+169:
		tmp = z * (y / -t)
	elif z <= 2.9e+83:
		tmp = x + y
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+169)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= 2.9e+83)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+169)
		tmp = z * (y / -t);
	elseif (z <= 2.9e+83)
		tmp = x + y;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+169], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+83], N[(x + y), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e169

   1. Initial program 77.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 77.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. associate-/r/ 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   6. Applied egg-rr 99.6%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   7. Taylor expanded in y around inf 52.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 52.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. associate-*r/ 38.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

      3. *-commutative 38.4%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

      4. associate-*r/ 48.3%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   10. Taylor expanded in a around 0 53.1%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\left(-1 \cdot \frac{y}{t}\right)} \]
   11. Step-by-step derivation

       1. associate-*r/ 53.1%

          \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{-1 \cdot y}{t}} \]

       2. neg-mul-1 53.1%

          \[\leadsto \left(z - t\right) \cdot \frac{\color{blue}{-y}}{t} \]

   12. Simplified 53.1%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{-y}{t}} \]

   13. Taylor expanded in z around inf 41.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   14. Step-by-step derivation

       1. associate-*l/ 48.5%

          \[\leadsto -1 \cdot \color{blue}{\left(\frac{y}{t} \cdot z\right)} \]

       2. associate-*r* 48.5%

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{t}\right) \cdot z} \]

       3. *-commutative 48.5%

          \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \frac{y}{t}\right)} \]

       4. mul-1-neg 48.5%

          \[\leadsto z \cdot \color{blue}{\left(-\frac{y}{t}\right)} \]

       5. distribute-frac-neg2 48.5%

          \[\leadsto z \cdot \color{blue}{\frac{y}{-t}} \]

   15. Simplified 48.5%

       \[\leadsto \color{blue}{z \cdot \frac{y}{-t}} \]

   if -1.3e169 < z < 2.89999999999999999e83

   1. Initial program 67.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 57.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   5. Simplified 57.6%

      \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   6. Taylor expanded in t around inf 39.7%

      \[\leadsto \color{blue}{x + y} \]

   if 2.89999999999999999e83 < z

   1. Initial program 84.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 93.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 93.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 93.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{\frac{a - t}{z - t}}}, x\right) \]

      2. associate-/r/ 93.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   6. Applied egg-rr 93.5%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, x\right) \]

   7. Taylor expanded in y around inf 60.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 60.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. associate-*r/ 52.8%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

      3. *-commutative 52.8%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

      4. associate-*r/ 55.6%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   9. Simplified 55.6%

      \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   10. Taylor expanded in a around inf 41.9%

       \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a}} \]

   11. Taylor expanded in z around inf 40.7%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   12. Step-by-step derivation

       1. associate-*l/ 42.0%

          \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

       2. *-commutative 42.0%

          \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]

   13. Simplified 42.0%

       \[\leadsto \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e+116) y (if (<= t 1.75e+18) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+116) {
		tmp = y;
	} else if (t <= 1.75e+18) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.35d+116)) then
        tmp = y
    else if (t <= 1.75d+18) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+116) {
		tmp = y;
	} else if (t <= 1.75e+18) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e+116:
		tmp = y
	elif t <= 1.75e+18:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e+116)
		tmp = y;
	elseif (t <= 1.75e+18)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.35e+116)
		tmp = y;
	elseif (t <= 1.75e+18)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e+116], y, If[LessEqual[t, 1.75e+18], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e116 or 1.75e18 < t

   1. Initial program 43.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 53.1%

      \[\leadsto \color{blue}{y} \]

   if -1.35e116 < t < 1.75e18

   1. Initial program 87.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 32.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 71.0%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 40.3%

   \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} \]
4. Step-by-step derivation

   1. associate-*r/ 40.3%

      \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(x \cdot \left(z - t\right)\right)}{a - t}} \]

   2. mul-1-neg 40.3%

      \[\leadsto x + \frac{\color{blue}{-x \cdot \left(z - t\right)}}{a - t} \]

   3. distribute-lft-neg-out 40.3%

      \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot \left(z - t\right)}}{a - t} \]

   4. *-commutative 40.3%

      \[\leadsto x + \frac{\color{blue}{\left(z - t\right) \cdot \left(-x\right)}}{a - t} \]

5. Simplified 40.3%

   \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(-x\right)}{a - t}} \]

6. Taylor expanded in t around inf 2.8%

   \[\leadsto \color{blue}{x + -1 \cdot x} \]
7. Step-by-step derivation

   1. distribute-rgt1-in 2.8%

      \[\leadsto \color{blue}{\left(-1 + 1\right) \cdot x} \]

   2. metadata-eval 2.8%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.8%

      \[\leadsto \color{blue}{0} \]

8. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]

9. Final simplification 2.8%

   \[\leadsto 0 \]
10. Add Preprocessing

Alternative 26: 25.4% 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 71.0%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 24.3%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 24.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.7% 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 2024130 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (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))))