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

Percentage Accurate: 68.5% → 90.8%

Time: 19.1s

Alternatives: 25

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: 68.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-300} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-300) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (+ (* (- y x) a) (* 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 <= -2e-300) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((((y - x) * a) + (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 <= -2e-300) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + 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, -2e-300], 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[(N[(y - x), $MachinePrecision] * a), $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))) < -2.00000000000000005e-300 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 90.8%

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

      3. fma-define 90.8%

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

   3. Simplified 90.8%

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

   if -2.00000000000000005e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-300} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ t_2 := y \cdot \left(\frac{t\_1}{y} + \frac{z - t}{a - t}\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+70}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- z t) (- t a)) 1.0)))
        (t_2 (* y (+ (/ t_1 y) (/ (- z t) (- a t))))))
   (if (<= t -1.85e-13)
     t_2
     (if (<= t 1.35e+50)
       (+ x (/ (* (- y x) (- z t)) (- a t)))
       (if (<= t 1.4e+70)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t 4.5e+70) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - t) / (t - a)) + 1.0);
	double t_2 = y * ((t_1 / y) + ((z - t) / (a - t)));
	double tmp;
	if (t <= -1.85e-13) {
		tmp = t_2;
	} else if (t <= 1.35e+50) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.4e+70) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 4.5e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((z - t) / (t - a)) + 1.0d0)
    t_2 = y * ((t_1 / y) + ((z - t) / (a - t)))
    if (t <= (-1.85d-13)) then
        tmp = t_2
    else if (t <= 1.35d+50) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else if (t <= 1.4d+70) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (t <= 4.5d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - t) / (t - a)) + 1.0);
	double t_2 = y * ((t_1 / y) + ((z - t) / (a - t)));
	double tmp;
	if (t <= -1.85e-13) {
		tmp = t_2;
	} else if (t <= 1.35e+50) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.4e+70) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 4.5e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((z - t) / (t - a)) + 1.0)
	t_2 = y * ((t_1 / y) + ((z - t) / (a - t)))
	tmp = 0
	if t <= -1.85e-13:
		tmp = t_2
	elif t <= 1.35e+50:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	elif t <= 1.4e+70:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t <= 4.5e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0))
	t_2 = Float64(y * Float64(Float64(t_1 / y) + Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.85e-13)
		tmp = t_2;
	elseif (t <= 1.35e+50)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	elseif (t <= 1.4e+70)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t <= 4.5e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((z - t) / (t - a)) + 1.0);
	t_2 = y * ((t_1 / y) + ((z - t) / (a - t)));
	tmp = 0.0;
	if (t <= -1.85e-13)
		tmp = t_2;
	elseif (t <= 1.35e+50)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	elseif (t <= 1.4e+70)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t <= 4.5e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t$95$1 / y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e-13], t$95$2, If[LessEqual[t, 1.35e+50], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+70], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+70], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.84999999999999994e-13 or 4.4999999999999999e70 < t

   1. Initial program 52.4%

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

   3. Taylor expanded in y around -inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. *-commutative 64.8%

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

      3. distribute-rgt-neg-in 64.8%

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

   5. Simplified 82.5%

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

   if -1.84999999999999994e-13 < t < 1.35e50

   1. Initial program 92.5%

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

   if 1.35e50 < t < 1.39999999999999995e70

   1. Initial program 19.7%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

   5. Simplified 100.0%

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

   if 1.39999999999999995e70 < t < 4.4999999999999999e70

   1. Initial program 55.5%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z - t}{a - t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(\frac{x \cdot \left(\frac{z - t}{t - a} + 1\right)}{y} + \frac{z - t}{a - t}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+70}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x \cdot \left(\frac{z - t}{t - a} + 1\right)}{y} + \frac{z - t}{a - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 35.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+56)
   y
   (if (<= t -7.8e-157)
     x
     (if (<= t -2.2e-241)
       (* y (/ z (- t)))
       (if (<= t 1.25e-247)
         x
         (if (<= t 1.02e-9)
           (* y (/ z a))
           (if (<= t 1.95e+70) (* x (/ (- z a) t)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+56) {
		tmp = y;
	} else if (t <= -7.8e-157) {
		tmp = x;
	} else if (t <= -2.2e-241) {
		tmp = y * (z / -t);
	} else if (t <= 1.25e-247) {
		tmp = x;
	} else if (t <= 1.02e-9) {
		tmp = y * (z / a);
	} else if (t <= 1.95e+70) {
		tmp = x * ((z - a) / t);
	} 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 <= (-3d+56)) then
        tmp = y
    else if (t <= (-7.8d-157)) then
        tmp = x
    else if (t <= (-2.2d-241)) then
        tmp = y * (z / -t)
    else if (t <= 1.25d-247) then
        tmp = x
    else if (t <= 1.02d-9) then
        tmp = y * (z / a)
    else if (t <= 1.95d+70) then
        tmp = x * ((z - a) / t)
    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 <= -3e+56) {
		tmp = y;
	} else if (t <= -7.8e-157) {
		tmp = x;
	} else if (t <= -2.2e-241) {
		tmp = y * (z / -t);
	} else if (t <= 1.25e-247) {
		tmp = x;
	} else if (t <= 1.02e-9) {
		tmp = y * (z / a);
	} else if (t <= 1.95e+70) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+56:
		tmp = y
	elif t <= -7.8e-157:
		tmp = x
	elif t <= -2.2e-241:
		tmp = y * (z / -t)
	elif t <= 1.25e-247:
		tmp = x
	elif t <= 1.02e-9:
		tmp = y * (z / a)
	elif t <= 1.95e+70:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+56)
		tmp = y;
	elseif (t <= -7.8e-157)
		tmp = x;
	elseif (t <= -2.2e-241)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (t <= 1.25e-247)
		tmp = x;
	elseif (t <= 1.02e-9)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.95e+70)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+56)
		tmp = y;
	elseif (t <= -7.8e-157)
		tmp = x;
	elseif (t <= -2.2e-241)
		tmp = y * (z / -t);
	elseif (t <= 1.25e-247)
		tmp = x;
	elseif (t <= 1.02e-9)
		tmp = y * (z / a);
	elseif (t <= 1.95e+70)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+56], y, If[LessEqual[t, -7.8e-157], x, If[LessEqual[t, -2.2e-241], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-247], x, If[LessEqual[t, 1.02e-9], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+70], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.00000000000000006e56 or 1.94999999999999987e70 < t

   1. Initial program 51.2%

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

   3. Taylor expanded in t around inf 54.0%

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

   if -3.00000000000000006e56 < t < -7.79999999999999998e-157 or -2.1999999999999999e-241 < t < 1.24999999999999994e-247

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf 46.1%

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

   if -7.79999999999999998e-157 < t < -2.1999999999999999e-241

   1. Initial program 95.1%

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

   3. Taylor expanded in a around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

      3. associate-/l* 52.1%

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

      4. div-sub 52.1%

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

      5. sub-neg 52.1%

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

      6. *-inverses 52.1%

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

      7. metadata-eval 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in y around inf 42.4%

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

   7. Taylor expanded in z around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. associate-/l* 42.3%

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

      3. distribute-lft-neg-in 42.3%

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

   9. Simplified 42.3%

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

   if 1.24999999999999994e-247 < t < 1.01999999999999999e-9

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 66.7%

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

   4. Taylor expanded in y around inf 54.2%

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

   5. Taylor expanded in x around 0 37.1%

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

      1. associate-*r/ 42.0%

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

   7. Simplified 42.0%

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

   if 1.01999999999999999e-9 < t < 1.94999999999999987e70

   1. Initial program 58.6%

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

   3. Taylor expanded in x around -inf 69.5%

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

      1. associate-*r* 69.5%

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

      2. neg-mul-1 69.5%

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

      3. +-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in t around -inf 53.1%

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

      1. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -60:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- z t) (/ y (- a t))))))
   (if (<= a -60.0)
     t_2
     (if (<= a -8.5e-163)
       t_1
       (if (<= a -1e-225)
         (/ (* z (- x y)) t)
         (if (<= a -1.6e-275)
           t_1
           (if (<= a 2.8e-109) (+ x (* (- y x) (- 1.0 (/ z t)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -60.0) {
		tmp = t_2;
	} else if (a <= -8.5e-163) {
		tmp = t_1;
	} else if (a <= -1e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= -1.6e-275) {
		tmp = t_1;
	} else if (a <= 2.8e-109) {
		tmp = x + ((y - x) * (1.0 - (z / t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((z - t) * (y / (a - t)))
    if (a <= (-60.0d0)) then
        tmp = t_2
    else if (a <= (-8.5d-163)) then
        tmp = t_1
    else if (a <= (-1d-225)) then
        tmp = (z * (x - y)) / t
    else if (a <= (-1.6d-275)) then
        tmp = t_1
    else if (a <= 2.8d-109) then
        tmp = x + ((y - x) * (1.0d0 - (z / t)))
    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 * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -60.0) {
		tmp = t_2;
	} else if (a <= -8.5e-163) {
		tmp = t_1;
	} else if (a <= -1e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= -1.6e-275) {
		tmp = t_1;
	} else if (a <= 2.8e-109) {
		tmp = x + ((y - x) * (1.0 - (z / t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((z - t) * (y / (a - t)))
	tmp = 0
	if a <= -60.0:
		tmp = t_2
	elif a <= -8.5e-163:
		tmp = t_1
	elif a <= -1e-225:
		tmp = (z * (x - y)) / t
	elif a <= -1.6e-275:
		tmp = t_1
	elif a <= 2.8e-109:
		tmp = x + ((y - x) * (1.0 - (z / t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (a <= -60.0)
		tmp = t_2;
	elseif (a <= -8.5e-163)
		tmp = t_1;
	elseif (a <= -1e-225)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= -1.6e-275)
		tmp = t_1;
	elseif (a <= 2.8e-109)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(1.0 - Float64(z / t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((z - t) * (y / (a - t)));
	tmp = 0.0;
	if (a <= -60.0)
		tmp = t_2;
	elseif (a <= -8.5e-163)
		tmp = t_1;
	elseif (a <= -1e-225)
		tmp = (z * (x - y)) / t;
	elseif (a <= -1.6e-275)
		tmp = t_1;
	elseif (a <= 2.8e-109)
		tmp = x + ((y - x) * (1.0 - (z / t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -60.0], t$95$2, If[LessEqual[a, -8.5e-163], t$95$1, If[LessEqual[a, -1e-225], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, -1.6e-275], t$95$1, If[LessEqual[a, 2.8e-109], N[(x + N[(N[(y - x), $MachinePrecision] * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -60 or 2.79999999999999979e-109 < a

   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 inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-lft-identity 73.0%

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

      3. times-frac 82.0%

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

      4. /-rgt-identity 82.0%

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

   5. Simplified 82.0%

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

   if -60 < a < -8.5e-163 or -9.9999999999999996e-226 < a < -1.6e-275

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 82.0%

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

      1. distribute-rgt-in 82.0%

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

      2. *-lft-identity 82.0%

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

      3. mul-1-neg 82.0%

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

      4. distribute-lft-neg-out 82.0%

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

      5. /-rgt-identity 82.0%

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

      6. times-frac 77.2%

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

      7. *-commutative 77.2%

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

      8. *-rgt-identity 77.2%

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

      9. mul-1-neg 77.2%

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

      10. associate-/l* 77.1%

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

      11. div-sub 77.1%

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

      12. associate-+r+ 63.2%

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

      13. +-commutative 63.2%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in y around inf 83.5%

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

      1. div-sub 83.5%

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

   8. Simplified 83.5%

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

   if -8.5e-163 < a < -9.9999999999999996e-226

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 66.3%

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

      4. div-sub 66.4%

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

      5. sub-neg 66.4%

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

      6. *-inverses 66.4%

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

      7. metadata-eval 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around -inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*r* 83.5%

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

      3. neg-mul-1 83.5%

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

   8. Simplified 83.5%

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

   if -1.6e-275 < a < 2.79999999999999979e-109

   1. Initial program 72.2%

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

   3. Taylor expanded in a around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

      3. associate-/l* 77.5%

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

      4. div-sub 77.4%

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

      5. sub-neg 77.4%

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

      6. *-inverses 77.4%

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

      7. metadata-eval 77.4%

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

   5. Simplified 77.4%

      \[\leadsto \color{blue}{x - \left(y - x\right) \cdot \left(\frac{z}{t} + -1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -60:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+57}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+57)
   y
   (if (<= t -7.5e-157)
     x
     (if (<= t -4.6e-240)
       (* y (/ z (- t)))
       (if (<= t 2.5e-244)
         x
         (if (<= t 4.3e-5)
           (* y (/ z a))
           (if (<= t 3.2e+71) (/ x (/ t z)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+57) {
		tmp = y;
	} else if (t <= -7.5e-157) {
		tmp = x;
	} else if (t <= -4.6e-240) {
		tmp = y * (z / -t);
	} else if (t <= 2.5e-244) {
		tmp = x;
	} else if (t <= 4.3e-5) {
		tmp = y * (z / a);
	} else if (t <= 3.2e+71) {
		tmp = x / (t / z);
	} 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 <= (-1.25d+57)) then
        tmp = y
    else if (t <= (-7.5d-157)) then
        tmp = x
    else if (t <= (-4.6d-240)) then
        tmp = y * (z / -t)
    else if (t <= 2.5d-244) then
        tmp = x
    else if (t <= 4.3d-5) then
        tmp = y * (z / a)
    else if (t <= 3.2d+71) then
        tmp = x / (t / z)
    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 <= -1.25e+57) {
		tmp = y;
	} else if (t <= -7.5e-157) {
		tmp = x;
	} else if (t <= -4.6e-240) {
		tmp = y * (z / -t);
	} else if (t <= 2.5e-244) {
		tmp = x;
	} else if (t <= 4.3e-5) {
		tmp = y * (z / a);
	} else if (t <= 3.2e+71) {
		tmp = x / (t / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+57:
		tmp = y
	elif t <= -7.5e-157:
		tmp = x
	elif t <= -4.6e-240:
		tmp = y * (z / -t)
	elif t <= 2.5e-244:
		tmp = x
	elif t <= 4.3e-5:
		tmp = y * (z / a)
	elif t <= 3.2e+71:
		tmp = x / (t / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+57)
		tmp = y;
	elseif (t <= -7.5e-157)
		tmp = x;
	elseif (t <= -4.6e-240)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (t <= 2.5e-244)
		tmp = x;
	elseif (t <= 4.3e-5)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.2e+71)
		tmp = Float64(x / Float64(t / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+57)
		tmp = y;
	elseif (t <= -7.5e-157)
		tmp = x;
	elseif (t <= -4.6e-240)
		tmp = y * (z / -t);
	elseif (t <= 2.5e-244)
		tmp = x;
	elseif (t <= 4.3e-5)
		tmp = y * (z / a);
	elseif (t <= 3.2e+71)
		tmp = x / (t / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+57], y, If[LessEqual[t, -7.5e-157], x, If[LessEqual[t, -4.6e-240], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-244], x, If[LessEqual[t, 4.3e-5], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+71], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.24999999999999993e57 or 3.20000000000000023e71 < t

   1. Initial program 50.6%

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

   3. Taylor expanded in t around inf 54.5%

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

   if -1.24999999999999993e57 < t < -7.500000000000001e-157 or -4.59999999999999986e-240 < t < 2.49999999999999999e-244

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf 46.1%

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

   if -7.500000000000001e-157 < t < -4.59999999999999986e-240

   1. Initial program 95.1%

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

   3. Taylor expanded in a around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

      3. associate-/l* 52.1%

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

      4. div-sub 52.1%

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

      5. sub-neg 52.1%

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

      6. *-inverses 52.1%

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

      7. metadata-eval 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in y around inf 42.4%

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

   7. Taylor expanded in z around inf 32.3%

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

      1. mul-1-neg 32.3%

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

      2. associate-/l* 42.3%

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

      3. distribute-lft-neg-in 42.3%

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

   9. Simplified 42.3%

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

   if 2.49999999999999999e-244 < t < 4.3000000000000002e-5

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 66.7%

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

   4. Taylor expanded in y around inf 54.2%

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

   5. Taylor expanded in x around 0 37.1%

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

      1. associate-*r/ 42.0%

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

   7. Simplified 42.0%

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

   if 4.3000000000000002e-5 < t < 3.20000000000000023e71

   1. Initial program 61.0%

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

   3. Taylor expanded in a around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. unsub-neg 41.6%

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

      3. associate-/l* 46.5%

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

      4. div-sub 46.5%

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

      5. sub-neg 46.5%

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

      6. *-inverses 46.5%

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

      7. metadata-eval 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in x around -inf 44.6%

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

      1. associate-/l* 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in x around 0 44.6%

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

       1. remove-double-neg 44.6%

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

       2. distribute-neg-frac2 44.6%

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

       3. neg-mul-1 44.6%

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

       4. *-commutative 44.6%

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

       5. times-frac 49.7%

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

       6. metadata-eval 49.7%

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

       7. distribute-neg-frac2 49.7%

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

       8. /-rgt-identity 49.7%

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

       9. distribute-rgt-neg-out 49.7%

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

       10. remove-double-neg 49.7%

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

       11. associate-/r/ 49.7%

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

   11. Simplified 49.7%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+57}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+56)
   y
   (if (<= t -7.6e-135)
     x
     (if (<= t -1.6e-185)
       (* x (/ z t))
       (if (<= t 1.08e-246)
         x
         (if (<= t 7.8e-10)
           (* y (/ z a))
           (if (<= t 6.4e+70) (/ x (/ t z)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+56) {
		tmp = y;
	} else if (t <= -7.6e-135) {
		tmp = x;
	} else if (t <= -1.6e-185) {
		tmp = x * (z / t);
	} else if (t <= 1.08e-246) {
		tmp = x;
	} else if (t <= 7.8e-10) {
		tmp = y * (z / a);
	} else if (t <= 6.4e+70) {
		tmp = x / (t / z);
	} 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 <= (-2.1d+56)) then
        tmp = y
    else if (t <= (-7.6d-135)) then
        tmp = x
    else if (t <= (-1.6d-185)) then
        tmp = x * (z / t)
    else if (t <= 1.08d-246) then
        tmp = x
    else if (t <= 7.8d-10) then
        tmp = y * (z / a)
    else if (t <= 6.4d+70) then
        tmp = x / (t / z)
    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 <= -2.1e+56) {
		tmp = y;
	} else if (t <= -7.6e-135) {
		tmp = x;
	} else if (t <= -1.6e-185) {
		tmp = x * (z / t);
	} else if (t <= 1.08e-246) {
		tmp = x;
	} else if (t <= 7.8e-10) {
		tmp = y * (z / a);
	} else if (t <= 6.4e+70) {
		tmp = x / (t / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+56:
		tmp = y
	elif t <= -7.6e-135:
		tmp = x
	elif t <= -1.6e-185:
		tmp = x * (z / t)
	elif t <= 1.08e-246:
		tmp = x
	elif t <= 7.8e-10:
		tmp = y * (z / a)
	elif t <= 6.4e+70:
		tmp = x / (t / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+56)
		tmp = y;
	elseif (t <= -7.6e-135)
		tmp = x;
	elseif (t <= -1.6e-185)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.08e-246)
		tmp = x;
	elseif (t <= 7.8e-10)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 6.4e+70)
		tmp = Float64(x / Float64(t / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+56)
		tmp = y;
	elseif (t <= -7.6e-135)
		tmp = x;
	elseif (t <= -1.6e-185)
		tmp = x * (z / t);
	elseif (t <= 1.08e-246)
		tmp = x;
	elseif (t <= 7.8e-10)
		tmp = y * (z / a);
	elseif (t <= 6.4e+70)
		tmp = x / (t / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+56], y, If[LessEqual[t, -7.6e-135], x, If[LessEqual[t, -1.6e-185], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e-246], x, If[LessEqual[t, 7.8e-10], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e+70], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.10000000000000017e56 or 6.4000000000000005e70 < t

   1. Initial program 50.6%

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

   3. Taylor expanded in t around inf 54.5%

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

   if -2.10000000000000017e56 < t < -7.6000000000000005e-135 or -1.5999999999999999e-185 < t < 1.08000000000000003e-246

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 44.0%

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

   if -7.6000000000000005e-135 < t < -1.5999999999999999e-185

   1. Initial program 82.5%

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

   3. Taylor expanded in a around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

      3. associate-/l* 55.7%

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

      4. div-sub 55.7%

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

      5. sub-neg 55.7%

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

      6. *-inverses 55.7%

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

      7. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in x around -inf 47.8%

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

      1. associate-/l* 50.3%

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

   8. Simplified 50.3%

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

   if 1.08000000000000003e-246 < t < 7.7999999999999999e-10

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 66.7%

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

   4. Taylor expanded in y around inf 54.2%

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

   5. Taylor expanded in x around 0 37.1%

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

      1. associate-*r/ 42.0%

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

   7. Simplified 42.0%

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

   if 7.7999999999999999e-10 < t < 6.4000000000000005e70

   1. Initial program 61.0%

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

   3. Taylor expanded in a around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. unsub-neg 41.6%

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

      3. associate-/l* 46.5%

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

      4. div-sub 46.5%

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

      5. sub-neg 46.5%

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

      6. *-inverses 46.5%

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

      7. metadata-eval 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in x around -inf 44.6%

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

      1. associate-/l* 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in x around 0 44.6%

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

       1. remove-double-neg 44.6%

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

       2. distribute-neg-frac2 44.6%

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

       3. neg-mul-1 44.6%

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

       4. *-commutative 44.6%

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

       5. times-frac 49.7%

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

       6. metadata-eval 49.7%

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

       7. distribute-neg-frac2 49.7%

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

       8. /-rgt-identity 49.7%

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

       9. distribute-rgt-neg-out 49.7%

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

       10. remove-double-neg 49.7%

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

       11. associate-/r/ 49.7%

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

   11. Simplified 49.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 36.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= t -4.2e+56)
     y
     (if (<= t -7.5e-136)
       x
       (if (<= t -1.15e-183)
         t_1
         (if (<= t 1.25e-247)
           x
           (if (<= t 4.2e-5) (* y (/ z a)) (if (<= t 5.5e+71) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (t <= -4.2e+56) {
		tmp = y;
	} else if (t <= -7.5e-136) {
		tmp = x;
	} else if (t <= -1.15e-183) {
		tmp = t_1;
	} else if (t <= 1.25e-247) {
		tmp = x;
	} else if (t <= 4.2e-5) {
		tmp = y * (z / a);
	} else if (t <= 5.5e+71) {
		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 * (z / t)
    if (t <= (-4.2d+56)) then
        tmp = y
    else if (t <= (-7.5d-136)) then
        tmp = x
    else if (t <= (-1.15d-183)) then
        tmp = t_1
    else if (t <= 1.25d-247) then
        tmp = x
    else if (t <= 4.2d-5) then
        tmp = y * (z / a)
    else if (t <= 5.5d+71) 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 * (z / t);
	double tmp;
	if (t <= -4.2e+56) {
		tmp = y;
	} else if (t <= -7.5e-136) {
		tmp = x;
	} else if (t <= -1.15e-183) {
		tmp = t_1;
	} else if (t <= 1.25e-247) {
		tmp = x;
	} else if (t <= 4.2e-5) {
		tmp = y * (z / a);
	} else if (t <= 5.5e+71) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if t <= -4.2e+56:
		tmp = y
	elif t <= -7.5e-136:
		tmp = x
	elif t <= -1.15e-183:
		tmp = t_1
	elif t <= 1.25e-247:
		tmp = x
	elif t <= 4.2e-5:
		tmp = y * (z / a)
	elif t <= 5.5e+71:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (t <= -4.2e+56)
		tmp = y;
	elseif (t <= -7.5e-136)
		tmp = x;
	elseif (t <= -1.15e-183)
		tmp = t_1;
	elseif (t <= 1.25e-247)
		tmp = x;
	elseif (t <= 4.2e-5)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 5.5e+71)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (t <= -4.2e+56)
		tmp = y;
	elseif (t <= -7.5e-136)
		tmp = x;
	elseif (t <= -1.15e-183)
		tmp = t_1;
	elseif (t <= 1.25e-247)
		tmp = x;
	elseif (t <= 4.2e-5)
		tmp = y * (z / a);
	elseif (t <= 5.5e+71)
		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[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+56], y, If[LessEqual[t, -7.5e-136], x, If[LessEqual[t, -1.15e-183], t$95$1, If[LessEqual[t, 1.25e-247], x, If[LessEqual[t, 4.2e-5], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+71], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.20000000000000034e56 or 5.5e71 < t

   1. Initial program 50.6%

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

   3. Taylor expanded in t around inf 54.5%

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

   if -4.20000000000000034e56 < t < -7.5000000000000003e-136 or -1.15000000000000008e-183 < t < 1.24999999999999994e-247

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 44.0%

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

   if -7.5000000000000003e-136 < t < -1.15000000000000008e-183 or 4.19999999999999977e-5 < t < 5.5e71

   1. Initial program 69.5%

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

   3. Taylor expanded in a around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. unsub-neg 43.9%

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

      3. associate-/l* 50.1%

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

      4. div-sub 50.1%

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

      5. sub-neg 50.1%

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

      6. *-inverses 50.1%

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

      7. metadata-eval 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in x around -inf 45.8%

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

      1. associate-/l* 49.7%

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

   8. Simplified 49.7%

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

   if 1.24999999999999994e-247 < t < 4.19999999999999977e-5

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 66.7%

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

   4. Taylor expanded in y around inf 54.2%

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

   5. Taylor expanded in x around 0 37.1%

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

      1. associate-*r/ 42.0%

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

   7. Simplified 42.0%

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

Alternative 8: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -80:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- z t) (/ y (- a t))))))
   (if (<= a -80.0)
     t_2
     (if (<= a -8.5e-163)
       t_1
       (if (<= a -2.3e-225)
         (/ (* z (- x y)) t)
         (if (<= a 2.6e+32) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -80.0) {
		tmp = t_2;
	} else if (a <= -8.5e-163) {
		tmp = t_1;
	} else if (a <= -2.3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 2.6e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((z - t) * (y / (a - t)))
    if (a <= (-80.0d0)) then
        tmp = t_2
    else if (a <= (-8.5d-163)) then
        tmp = t_1
    else if (a <= (-2.3d-225)) then
        tmp = (z * (x - y)) / t
    else if (a <= 2.6d+32) 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 * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -80.0) {
		tmp = t_2;
	} else if (a <= -8.5e-163) {
		tmp = t_1;
	} else if (a <= -2.3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 2.6e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((z - t) * (y / (a - t)))
	tmp = 0
	if a <= -80.0:
		tmp = t_2
	elif a <= -8.5e-163:
		tmp = t_1
	elif a <= -2.3e-225:
		tmp = (z * (x - y)) / t
	elif a <= 2.6e+32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (a <= -80.0)
		tmp = t_2;
	elseif (a <= -8.5e-163)
		tmp = t_1;
	elseif (a <= -2.3e-225)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 2.6e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((z - t) * (y / (a - t)));
	tmp = 0.0;
	if (a <= -80.0)
		tmp = t_2;
	elseif (a <= -8.5e-163)
		tmp = t_1;
	elseif (a <= -2.3e-225)
		tmp = (z * (x - y)) / t;
	elseif (a <= 2.6e+32)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -80.0], t$95$2, If[LessEqual[a, -8.5e-163], t$95$1, If[LessEqual[a, -2.3e-225], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 2.6e+32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -80 or 2.6000000000000002e32 < a

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. *-lft-identity 77.4%

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

      3. times-frac 87.0%

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

      4. /-rgt-identity 87.0%

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

   5. Simplified 87.0%

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

   if -80 < a < -8.5e-163 or -2.2999999999999999e-225 < a < 2.6000000000000002e32

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. distribute-rgt-in 76.7%

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

      2. *-lft-identity 76.7%

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

      3. mul-1-neg 76.7%

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

      4. distribute-lft-neg-out 76.7%

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

      5. /-rgt-identity 76.7%

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

      6. times-frac 74.1%

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

      7. *-commutative 74.1%

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

      8. *-rgt-identity 74.1%

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

      9. mul-1-neg 74.1%

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

      10. associate-/l* 77.9%

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

      11. div-sub 77.9%

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

      12. associate-+r+ 70.8%

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

      13. +-commutative 70.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around inf 69.3%

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

      1. div-sub 69.3%

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

   8. Simplified 69.3%

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

   if -8.5e-163 < a < -2.2999999999999999e-225

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 66.3%

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

      4. div-sub 66.4%

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

      5. sub-neg 66.4%

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

      6. *-inverses 66.4%

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

      7. metadata-eval 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around -inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*r* 83.5%

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

      3. neg-mul-1 83.5%

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

   8. Simplified 83.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -80:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -19000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- y x) (/ (- z t) a)))))
   (if (<= a -19000.0)
     t_2
     (if (<= a -9.5e-163)
       t_1
       (if (<= a -1.65e-225)
         (/ (* z (- x y)) t)
         (if (<= a 3.6e+155) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) * ((z - t) / a));
	double tmp;
	if (a <= -19000.0) {
		tmp = t_2;
	} else if (a <= -9.5e-163) {
		tmp = t_1;
	} else if (a <= -1.65e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 3.6e+155) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((y - x) * ((z - t) / a))
    if (a <= (-19000.0d0)) then
        tmp = t_2
    else if (a <= (-9.5d-163)) then
        tmp = t_1
    else if (a <= (-1.65d-225)) then
        tmp = (z * (x - y)) / t
    else if (a <= 3.6d+155) 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 * ((z - t) / (a - t));
	double t_2 = x + ((y - x) * ((z - t) / a));
	double tmp;
	if (a <= -19000.0) {
		tmp = t_2;
	} else if (a <= -9.5e-163) {
		tmp = t_1;
	} else if (a <= -1.65e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 3.6e+155) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((y - x) * ((z - t) / a))
	tmp = 0
	if a <= -19000.0:
		tmp = t_2
	elif a <= -9.5e-163:
		tmp = t_1
	elif a <= -1.65e-225:
		tmp = (z * (x - y)) / t
	elif a <= 3.6e+155:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -19000.0)
		tmp = t_2;
	elseif (a <= -9.5e-163)
		tmp = t_1;
	elseif (a <= -1.65e-225)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 3.6e+155)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((y - x) * ((z - t) / a));
	tmp = 0.0;
	if (a <= -19000.0)
		tmp = t_2;
	elseif (a <= -9.5e-163)
		tmp = t_1;
	elseif (a <= -1.65e-225)
		tmp = (z * (x - y)) / t;
	elseif (a <= 3.6e+155)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -19000.0], t$95$2, If[LessEqual[a, -9.5e-163], t$95$1, If[LessEqual[a, -1.65e-225], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 3.6e+155], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -19000 or 3.60000000000000007e155 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 75.2%

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

      1. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   if -19000 < a < -9.50000000000000012e-163 or -1.6500000000000001e-225 < a < 3.60000000000000007e155

   1. Initial program 69.2%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. distribute-rgt-in 74.7%

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

      2. *-lft-identity 74.7%

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

      3. mul-1-neg 74.7%

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

      4. distribute-lft-neg-out 74.7%

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

      5. /-rgt-identity 74.7%

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

      6. times-frac 72.4%

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

      7. *-commutative 72.4%

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

      8. *-rgt-identity 72.4%

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

      9. mul-1-neg 72.4%

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

      10. associate-/l* 76.9%

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

      11. div-sub 76.9%

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

      12. associate-+r+ 70.8%

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

      13. +-commutative 70.8%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in y around inf 67.0%

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

      1. div-sub 67.0%

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

   8. Simplified 67.0%

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

   if -9.50000000000000012e-163 < a < -1.6500000000000001e-225

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 66.3%

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

      4. div-sub 66.4%

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

      5. sub-neg 66.4%

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

      6. *-inverses 66.4%

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

      7. metadata-eval 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around -inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*r* 83.5%

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

      3. neg-mul-1 83.5%

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

   8. Simplified 83.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -19000:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - z \cdot \frac{x - y}{a}\\ \mathbf{if}\;a \leq -8500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (- x (* z (/ (- x y) a)))))
   (if (<= a -8500.0)
     t_2
     (if (<= a -9.4e-163)
       t_1
       (if (<= a -3e-225) (/ (* z (- x y)) t) (if (<= a 4.2e+156) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - (z * ((x - y) / a));
	double tmp;
	if (a <= -8500.0) {
		tmp = t_2;
	} else if (a <= -9.4e-163) {
		tmp = t_1;
	} else if (a <= -3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 4.2e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x - (z * ((x - y) / a))
    if (a <= (-8500.0d0)) then
        tmp = t_2
    else if (a <= (-9.4d-163)) then
        tmp = t_1
    else if (a <= (-3d-225)) then
        tmp = (z * (x - y)) / t
    else if (a <= 4.2d+156) 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 * ((z - t) / (a - t));
	double t_2 = x - (z * ((x - y) / a));
	double tmp;
	if (a <= -8500.0) {
		tmp = t_2;
	} else if (a <= -9.4e-163) {
		tmp = t_1;
	} else if (a <= -3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 4.2e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - (z * ((x - y) / a))
	tmp = 0
	if a <= -8500.0:
		tmp = t_2
	elif a <= -9.4e-163:
		tmp = t_1
	elif a <= -3e-225:
		tmp = (z * (x - y)) / t
	elif a <= 4.2e+156:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(z * Float64(Float64(x - y) / a)))
	tmp = 0.0
	if (a <= -8500.0)
		tmp = t_2;
	elseif (a <= -9.4e-163)
		tmp = t_1;
	elseif (a <= -3e-225)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 4.2e+156)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - (z * ((x - y) / a));
	tmp = 0.0;
	if (a <= -8500.0)
		tmp = t_2;
	elseif (a <= -9.4e-163)
		tmp = t_1;
	elseif (a <= -3e-225)
		tmp = (z * (x - y)) / t;
	elseif (a <= 4.2e+156)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8500.0], t$95$2, If[LessEqual[a, -9.4e-163], t$95$1, If[LessEqual[a, -3e-225], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 4.2e+156], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8500 or 4.19999999999999963e156 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in t around 0 69.0%

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

      1. associate-/l* 75.9%

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

   5. Simplified 75.9%

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

   if -8500 < a < -9.4e-163 or -3.00000000000000018e-225 < a < 4.19999999999999963e156

   1. Initial program 69.2%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. distribute-rgt-in 74.7%

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

      2. *-lft-identity 74.7%

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

      3. mul-1-neg 74.7%

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

      4. distribute-lft-neg-out 74.7%

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

      5. /-rgt-identity 74.7%

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

      6. times-frac 72.4%

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

      7. *-commutative 72.4%

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

      8. *-rgt-identity 72.4%

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

      9. mul-1-neg 72.4%

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

      10. associate-/l* 76.9%

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

      11. div-sub 76.9%

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

      12. associate-+r+ 70.8%

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

      13. +-commutative 70.8%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in y around inf 67.0%

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

      1. div-sub 67.0%

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

   8. Simplified 67.0%

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

   if -9.4e-163 < a < -3.00000000000000018e-225

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 66.3%

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

      4. div-sub 66.4%

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

      5. sub-neg 66.4%

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

      6. *-inverses 66.4%

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

      7. metadata-eval 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around -inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*r* 83.5%

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

      3. neg-mul-1 83.5%

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

   8. Simplified 83.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8500:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -8.2e+113)
     (+ x (* y (/ z a)))
     (if (<= a -9e-163)
       t_1
       (if (<= a -1.3e-225)
         (/ (* z (- x y)) t)
         (if (<= a 4e+155) t_1 (- x (* x (/ z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -8.2e+113) {
		tmp = x + (y * (z / a));
	} else if (a <= -9e-163) {
		tmp = t_1;
	} else if (a <= -1.3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 4e+155) {
		tmp = t_1;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-8.2d+113)) then
        tmp = x + (y * (z / a))
    else if (a <= (-9d-163)) then
        tmp = t_1
    else if (a <= (-1.3d-225)) then
        tmp = (z * (x - y)) / t
    else if (a <= 4d+155) then
        tmp = t_1
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -8.2e+113) {
		tmp = x + (y * (z / a));
	} else if (a <= -9e-163) {
		tmp = t_1;
	} else if (a <= -1.3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 4e+155) {
		tmp = t_1;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -8.2e+113:
		tmp = x + (y * (z / a))
	elif a <= -9e-163:
		tmp = t_1
	elif a <= -1.3e-225:
		tmp = (z * (x - y)) / t
	elif a <= 4e+155:
		tmp = t_1
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -8.2e+113)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= -9e-163)
		tmp = t_1;
	elseif (a <= -1.3e-225)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 4e+155)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -8.2e+113)
		tmp = x + (y * (z / a));
	elseif (a <= -9e-163)
		tmp = t_1;
	elseif (a <= -1.3e-225)
		tmp = (z * (x - y)) / t;
	elseif (a <= 4e+155)
		tmp = t_1;
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+113], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9e-163], t$95$1, If[LessEqual[a, -1.3e-225], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 4e+155], t$95$1, N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.19999999999999985e113

   1. Initial program 75.3%

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

   3. Taylor expanded in t around 0 67.9%

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

   4. Taylor expanded in y around inf 68.7%

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

      1. associate-/l* 75.6%

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

   6. Simplified 75.6%

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

   if -8.19999999999999985e113 < a < -8.9999999999999995e-163 or -1.30000000000000007e-225 < a < 4.00000000000000003e155

   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 x around 0 75.1%

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

      1. distribute-rgt-in 75.1%

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

      2. *-lft-identity 75.1%

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

      3. mul-1-neg 75.1%

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

      4. distribute-lft-neg-out 75.1%

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

      5. /-rgt-identity 75.1%

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

      6. times-frac 73.1%

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

      7. *-commutative 73.1%

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

      8. *-rgt-identity 73.1%

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

      9. mul-1-neg 73.1%

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

      10. associate-/l* 77.5%

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

      11. div-sub 77.5%

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

      12. associate-+r+ 72.3%

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

      13. +-commutative 72.3%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in y around inf 66.7%

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

      1. div-sub 66.7%

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

   8. Simplified 66.7%

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

   if -8.9999999999999995e-163 < a < -1.30000000000000007e-225

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 66.3%

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

      4. div-sub 66.4%

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

      5. sub-neg 66.4%

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

      6. *-inverses 66.4%

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

      7. metadata-eval 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around -inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*r* 83.5%

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

      3. neg-mul-1 83.5%

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

   8. Simplified 83.5%

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

   if 4.00000000000000003e155 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 73.4%

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

   4. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

      3. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-229}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y (- a t))))))
   (if (<= a -2.5e-33)
     t_1
     (if (<= a 3.1e-229)
       (+ y (/ (+ (* (- y x) a) (* z (- x y))) t))
       (if (<= a 5.1e+60) (+ x (/ (* (- y x) (- z t)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -2.5e-33) {
		tmp = t_1;
	} else if (a <= 3.1e-229) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (a <= 5.1e+60) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / (a - t)))
    if (a <= (-2.5d-33)) then
        tmp = t_1
    else if (a <= 3.1d-229) then
        tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
    else if (a <= 5.1d+60) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -2.5e-33) {
		tmp = t_1;
	} else if (a <= 3.1e-229) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (a <= 5.1e+60) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / (a - t)))
	tmp = 0
	if a <= -2.5e-33:
		tmp = t_1
	elif a <= 3.1e-229:
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
	elif a <= 5.1e+60:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (a <= -2.5e-33)
		tmp = t_1;
	elseif (a <= 3.1e-229)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	elseif (a <= 5.1e+60)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / (a - t)));
	tmp = 0.0;
	if (a <= -2.5e-33)
		tmp = t_1;
	elseif (a <= 3.1e-229)
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	elseif (a <= 5.1e+60)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-33], t$95$1, If[LessEqual[a, 3.1e-229], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e+60], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.50000000000000014e-33 or 5.09999999999999996e60 < a

   1. Initial program 76.7%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. *-lft-identity 78.6%

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

      3. times-frac 89.4%

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

      4. /-rgt-identity 89.4%

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

   5. Simplified 89.4%

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

   if -2.50000000000000014e-33 < a < 3.1000000000000001e-229

   1. Initial program 72.2%

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

   3. Taylor expanded in t around -inf 88.1%

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

   if 3.1000000000000001e-229 < a < 5.09999999999999996e60

   1. Initial program 72.4%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-229}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-229}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y (- a t))))))
   (if (<= a -1.85e-26)
     t_1
     (if (<= a 2.45e-229)
       (+ y (/ (* (- y x) (- a z)) t))
       (if (<= a 7.2e+56) (+ x (/ (* (- y x) (- z t)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -1.85e-26) {
		tmp = t_1;
	} else if (a <= 2.45e-229) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 7.2e+56) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / (a - t)))
    if (a <= (-1.85d-26)) then
        tmp = t_1
    else if (a <= 2.45d-229) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (a <= 7.2d+56) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double tmp;
	if (a <= -1.85e-26) {
		tmp = t_1;
	} else if (a <= 2.45e-229) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 7.2e+56) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / (a - t)))
	tmp = 0
	if a <= -1.85e-26:
		tmp = t_1
	elif a <= 2.45e-229:
		tmp = y + (((y - x) * (a - z)) / t)
	elif a <= 7.2e+56:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (a <= -1.85e-26)
		tmp = t_1;
	elseif (a <= 2.45e-229)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (a <= 7.2e+56)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / (a - t)));
	tmp = 0.0;
	if (a <= -1.85e-26)
		tmp = t_1;
	elseif (a <= 2.45e-229)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (a <= 7.2e+56)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e-26], t$95$1, If[LessEqual[a, 2.45e-229], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+56], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8499999999999999e-26 or 7.19999999999999996e56 < a

   1. Initial program 76.7%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. *-lft-identity 78.6%

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

      3. times-frac 89.4%

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

      4. /-rgt-identity 89.4%

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

   5. Simplified 89.4%

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

   if -1.8499999999999999e-26 < a < 2.44999999999999987e-229

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf 88.1%

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

      1. associate--l+ 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*r/ 88.1%

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

      4. mul-1-neg 88.1%

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

      5. div-sub 88.1%

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

      6. mul-1-neg 88.1%

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

      7. distribute-lft-out-- 88.1%

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

      8. associate-*r/ 88.1%

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

      9. mul-1-neg 88.1%

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

      10. unsub-neg 88.1%

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

      11. distribute-rgt-out-- 88.1%

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

   5. Simplified 88.1%

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

   if 2.44999999999999987e-229 < a < 7.19999999999999996e56

   1. Initial program 72.4%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-26}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-229}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0092:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0092)
   (+ x (* y (/ z a)))
   (if (<= a -2e-167)
     (* y (- 1.0 (/ z t)))
     (if (<= a -1.3e-225)
       (/ (* z (- x y)) t)
       (if (<= a 3.6e+155) (* y (/ (- t z) t)) (- x (* x (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0092) {
		tmp = x + (y * (z / a));
	} else if (a <= -2e-167) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= -1.3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.0092d0)) then
        tmp = x + (y * (z / a))
    else if (a <= (-2d-167)) then
        tmp = y * (1.0d0 - (z / t))
    else if (a <= (-1.3d-225)) then
        tmp = (z * (x - y)) / t
    else if (a <= 3.6d+155) then
        tmp = y * ((t - z) / t)
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0092) {
		tmp = x + (y * (z / a));
	} else if (a <= -2e-167) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= -1.3e-225) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0092:
		tmp = x + (y * (z / a))
	elif a <= -2e-167:
		tmp = y * (1.0 - (z / t))
	elif a <= -1.3e-225:
		tmp = (z * (x - y)) / t
	elif a <= 3.6e+155:
		tmp = y * ((t - z) / t)
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0092)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= -2e-167)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (a <= -1.3e-225)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 3.6e+155)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0092)
		tmp = x + (y * (z / a));
	elseif (a <= -2e-167)
		tmp = y * (1.0 - (z / t));
	elseif (a <= -1.3e-225)
		tmp = (z * (x - y)) / t;
	elseif (a <= 3.6e+155)
		tmp = y * ((t - z) / t);
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0092], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-167], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-225], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 3.6e+155], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -0.0091999999999999998

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 67.3%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 70.7%

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

   6. Simplified 70.7%

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

   if -0.0091999999999999998 < a < -2e-167

   1. Initial program 71.6%

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

   3. Taylor expanded in a around 0 48.8%

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

      1. mul-1-neg 48.8%

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

      2. unsub-neg 48.8%

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

      3. associate-/l* 55.3%

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

      4. div-sub 55.3%

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

      5. sub-neg 55.3%

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

      6. *-inverses 55.3%

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

      7. metadata-eval 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around inf 67.5%

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

   if -2e-167 < a < -1.30000000000000007e-225

   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 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. associate-/l* 70.5%

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

      4. div-sub 70.6%

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

      5. sub-neg 70.6%

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

      6. *-inverses 70.6%

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

      7. metadata-eval 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around -inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*r* 88.7%

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

      3. neg-mul-1 88.7%

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

   8. Simplified 88.7%

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

   if -1.30000000000000007e-225 < a < 3.60000000000000007e155

   1. Initial program 68.6%

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

   3. Taylor expanded in a around 0 50.9%

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

      1. mul-1-neg 50.9%

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

      2. unsub-neg 50.9%

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

      3. associate-/l* 61.8%

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

      4. div-sub 61.7%

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

      5. sub-neg 61.7%

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

      6. *-inverses 61.7%

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

      7. metadata-eval 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in y around inf 55.1%

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

   7. Taylor expanded in t around 0 55.1%

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

   if 3.60000000000000007e155 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 73.4%

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

   4. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

      3. associate-/l* 79.4%

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

   6. Simplified 79.4%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0092:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e-5)
   (+ x (* y (/ z a)))
   (if (<= a 3.3e-230)
     (* y (- 1.0 (/ z t)))
     (if (<= a 9.5e-197)
       (* x (/ z (- t a)))
       (if (<= a 3.6e+155) (* y (/ (- t z) t)) (- x (* x (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-5) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.3e-230) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 9.5e-197) {
		tmp = x * (z / (t - a));
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d-5)) then
        tmp = x + (y * (z / a))
    else if (a <= 3.3d-230) then
        tmp = y * (1.0d0 - (z / t))
    else if (a <= 9.5d-197) then
        tmp = x * (z / (t - a))
    else if (a <= 3.6d+155) then
        tmp = y * ((t - z) / t)
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-5) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.3e-230) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 9.5e-197) {
		tmp = x * (z / (t - a));
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e-5:
		tmp = x + (y * (z / a))
	elif a <= 3.3e-230:
		tmp = y * (1.0 - (z / t))
	elif a <= 9.5e-197:
		tmp = x * (z / (t - a))
	elif a <= 3.6e+155:
		tmp = y * ((t - z) / t)
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e-5)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 3.3e-230)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (a <= 9.5e-197)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (a <= 3.6e+155)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e-5)
		tmp = x + (y * (z / a));
	elseif (a <= 3.3e-230)
		tmp = y * (1.0 - (z / t));
	elseif (a <= 9.5e-197)
		tmp = x * (z / (t - a));
	elseif (a <= 3.6e+155)
		tmp = y * ((t - z) / t);
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e-5], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-230], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-197], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+155], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.5000000000000002e-5

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 67.3%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 70.7%

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

   6. Simplified 70.7%

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

   if -5.5000000000000002e-5 < a < 3.29999999999999994e-230

   1. Initial program 72.1%

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

   3. Taylor expanded in a around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. unsub-neg 61.8%

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

      3. associate-/l* 69.6%

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

      4. div-sub 69.6%

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

      5. sub-neg 69.6%

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

      6. *-inverses 69.6%

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

      7. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in y around inf 67.2%

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

   if 3.29999999999999994e-230 < a < 9.5000000000000003e-197

   1. Initial program 85.9%

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

   3. Taylor expanded in x around -inf 77.9%

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

      1. associate-*r* 77.9%

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

      2. neg-mul-1 77.9%

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

      3. +-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in z around inf 77.9%

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

   if 9.5000000000000003e-197 < a < 3.60000000000000007e155

   1. Initial program 68.1%

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

   3. Taylor expanded in a around 0 39.6%

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

      1. mul-1-neg 39.6%

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

      2. unsub-neg 39.6%

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

      3. associate-/l* 49.7%

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

      4. div-sub 49.6%

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

      5. sub-neg 49.6%

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

      6. *-inverses 49.6%

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

      7. metadata-eval 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in y around inf 45.4%

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

   7. Taylor expanded in t around 0 45.4%

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

   if 3.60000000000000007e155 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 73.4%

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

   4. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

      3. associate-/l* 79.4%

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

   6. Simplified 79.4%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -17000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+192)
   x
   (if (<= a -1.15e+65)
     (* y (/ (- z t) a))
     (if (<= a -17000.0) x (if (<= a 6.8e+155) (* y (/ (- t z) t)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+192) {
		tmp = x;
	} else if (a <= -1.15e+65) {
		tmp = y * ((z - t) / a);
	} else if (a <= -17000.0) {
		tmp = x;
	} else if (a <= 6.8e+155) {
		tmp = y * ((t - z) / t);
	} 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 <= (-6d+192)) then
        tmp = x
    else if (a <= (-1.15d+65)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-17000.0d0)) then
        tmp = x
    else if (a <= 6.8d+155) then
        tmp = y * ((t - z) / t)
    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 <= -6e+192) {
		tmp = x;
	} else if (a <= -1.15e+65) {
		tmp = y * ((z - t) / a);
	} else if (a <= -17000.0) {
		tmp = x;
	} else if (a <= 6.8e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+192:
		tmp = x
	elif a <= -1.15e+65:
		tmp = y * ((z - t) / a)
	elif a <= -17000.0:
		tmp = x
	elif a <= 6.8e+155:
		tmp = y * ((t - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+192)
		tmp = x;
	elseif (a <= -1.15e+65)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -17000.0)
		tmp = x;
	elseif (a <= 6.8e+155)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+192)
		tmp = x;
	elseif (a <= -1.15e+65)
		tmp = y * ((z - t) / a);
	elseif (a <= -17000.0)
		tmp = x;
	elseif (a <= 6.8e+155)
		tmp = y * ((t - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+192], x, If[LessEqual[a, -1.15e+65], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -17000.0], x, If[LessEqual[a, 6.8e+155], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6e192 or -1.15e65 < a < -17000 or 6.8000000000000002e155 < a

   1. Initial program 81.5%

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

   3. Taylor expanded in a around inf 68.3%

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

   if -6e192 < a < -1.15e65

   1. Initial program 72.7%

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

   3. Taylor expanded in x around 0 72.5%

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

      1. distribute-rgt-in 72.5%

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

      2. *-lft-identity 72.5%

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

      3. mul-1-neg 72.5%

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

      4. distribute-lft-neg-out 72.5%

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

      5. /-rgt-identity 72.5%

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

      6. times-frac 72.0%

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

      7. *-commutative 72.0%

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

      8. *-rgt-identity 72.0%

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

      9. mul-1-neg 72.0%

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

      10. associate-/l* 79.6%

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

      11. div-sub 79.6%

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

      12. associate-+r+ 79.7%

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

      13. +-commutative 79.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in y around inf 64.0%

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

      1. div-sub 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in a around inf 41.1%

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

       1. associate-/l* 44.8%

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

   11. Simplified 44.8%

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

   if -17000 < a < 6.8000000000000002e155

   1. Initial program 71.2%

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

   3. Taylor expanded in a around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

      3. associate-/l* 61.1%

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

      4. div-sub 61.1%

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

      5. sub-neg 61.1%

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

      6. *-inverses 61.1%

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

      7. metadata-eval 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 55.6%

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

   7. Taylor expanded in t around 0 55.6%

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

Alternative 17: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4800:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-163}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4800.0)
   x
   (if (<= a -2.8e-163)
     y
     (if (<= a -7.8e-304) (* x (/ z t)) (if (<= a 3.6e+155) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4800.0) {
		tmp = x;
	} else if (a <= -2.8e-163) {
		tmp = y;
	} else if (a <= -7.8e-304) {
		tmp = x * (z / t);
	} else if (a <= 3.6e+155) {
		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 <= (-4800.0d0)) then
        tmp = x
    else if (a <= (-2.8d-163)) then
        tmp = y
    else if (a <= (-7.8d-304)) then
        tmp = x * (z / t)
    else if (a <= 3.6d+155) 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 <= -4800.0) {
		tmp = x;
	} else if (a <= -2.8e-163) {
		tmp = y;
	} else if (a <= -7.8e-304) {
		tmp = x * (z / t);
	} else if (a <= 3.6e+155) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4800.0:
		tmp = x
	elif a <= -2.8e-163:
		tmp = y
	elif a <= -7.8e-304:
		tmp = x * (z / t)
	elif a <= 3.6e+155:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4800.0)
		tmp = x;
	elseif (a <= -2.8e-163)
		tmp = y;
	elseif (a <= -7.8e-304)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 3.6e+155)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4800.0)
		tmp = x;
	elseif (a <= -2.8e-163)
		tmp = y;
	elseif (a <= -7.8e-304)
		tmp = x * (z / t);
	elseif (a <= 3.6e+155)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4800.0], x, If[LessEqual[a, -2.8e-163], y, If[LessEqual[a, -7.8e-304], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+155], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4800 or 3.60000000000000007e155 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 57.3%

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

   if -4800 < a < -2.8e-163 or -7.79999999999999949e-304 < a < 3.60000000000000007e155

   1. Initial program 67.9%

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

   3. Taylor expanded in t around inf 37.5%

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

   if -2.8e-163 < a < -7.79999999999999949e-304

   1. Initial program 81.8%

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

   3. Taylor expanded in a around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. unsub-neg 76.7%

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

      3. associate-/l* 74.3%

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

      4. div-sub 74.3%

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

      5. sub-neg 74.3%

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

      6. *-inverses 74.3%

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

      7. metadata-eval 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in x around -inf 49.2%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

Alternative 18: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-27} \lor \neg \left(a \leq 5.5 \cdot 10^{-147}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e-27) (not (<= a 5.5e-147)))
   (+ x (* (- z t) (/ y (- a t))))
   (+ y (/ (* (- y x) (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-27) || !(a <= 5.5e-147)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.1d-27)) .or. (.not. (a <= 5.5d-147))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-27) || !(a <= 5.5e-147)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e-27) or not (a <= 5.5e-147):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e-27) || !(a <= 5.5e-147))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e-27) || ~((a <= 5.5e-147)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e-27], N[Not[LessEqual[a, 5.5e-147]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0999999999999998e-27 or 5.5e-147 < a

   1. Initial program 74.4%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. *-commutative 71.8%

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

      2. *-lft-identity 71.8%

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

      3. times-frac 81.4%

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

      4. /-rgt-identity 81.4%

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

   5. Simplified 81.4%

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

   if -3.0999999999999998e-27 < a < 5.5e-147

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 85.2%

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

      1. associate--l+ 85.2%

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

      2. associate-*r/ 85.2%

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

      3. associate-*r/ 85.2%

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

      4. mul-1-neg 85.2%

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

      5. div-sub 86.2%

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

      6. mul-1-neg 86.2%

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

      7. distribute-lft-out-- 86.2%

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

      8. associate-*r/ 86.2%

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

      9. mul-1-neg 86.2%

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

      10. unsub-neg 86.2%

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

      11. distribute-rgt-out-- 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-27} \lor \neg \left(a \leq 5.5 \cdot 10^{-147}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.16 \lor \neg \left(a \leq 3.6 \cdot 10^{+155}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.16) (not (<= a 3.6e+155)))
   (+ x (* y (/ z a)))
   (* y (/ (- t z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.16) || !(a <= 3.6e+155)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.16d0)) .or. (.not. (a <= 3.6d+155))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * ((t - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.16) || !(a <= 3.6e+155)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.16) or not (a <= 3.6e+155):
		tmp = x + (y * (z / a))
	else:
		tmp = y * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.16) || !(a <= 3.6e+155))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.16) || ~((a <= 3.6e+155)))
		tmp = x + (y * (z / a));
	else
		tmp = y * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.16], N[Not[LessEqual[a, 3.6e+155]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.160000000000000003 or 3.60000000000000007e155 < a

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 69.3%

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

   4. Taylor expanded in y around inf 70.5%

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

      1. associate-/l* 73.4%

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

   6. Simplified 73.4%

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

   if -0.160000000000000003 < a < 3.60000000000000007e155

   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 0 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

      3. associate-/l* 61.4%

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

      4. div-sub 61.4%

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

      5. sub-neg 61.4%

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

      6. *-inverses 61.4%

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

      7. metadata-eval 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around inf 55.9%

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

   7. Taylor expanded in t around 0 56.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.16 \lor \neg \left(a \leq 3.6 \cdot 10^{+155}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00031:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.00031)
   (+ x (* y (/ z a)))
   (if (<= a 3.6e+155) (* y (/ (- t z) t)) (- x (* x (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00031) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.00031d0)) then
        tmp = x + (y * (z / a))
    else if (a <= 3.6d+155) then
        tmp = y * ((t - z) / t)
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00031) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00031:
		tmp = x + (y * (z / a))
	elif a <= 3.6e+155:
		tmp = y * ((t - z) / t)
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00031)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 3.6e+155)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00031)
		tmp = x + (y * (z / a));
	elseif (a <= 3.6e+155)
		tmp = y * ((t - z) / t);
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00031], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+155], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1e-4

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 67.3%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 70.7%

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

   6. Simplified 70.7%

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

   if -3.1e-4 < a < 3.60000000000000007e155

   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 0 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

      3. associate-/l* 61.4%

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

      4. div-sub 61.4%

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

      5. sub-neg 61.4%

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

      6. *-inverses 61.4%

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

      7. metadata-eval 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around inf 55.9%

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

   7. Taylor expanded in t around 0 56.0%

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

   if 3.60000000000000007e155 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 73.4%

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

   4. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

      3. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

Alternative 21: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00265:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.00265)
   (+ x (* y (/ z a)))
   (if (<= a 3.6e+155) (* y (/ (- t z) t)) (+ x (/ (* y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00265) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.00265d0)) then
        tmp = x + (y * (z / a))
    else if (a <= 3.6d+155) then
        tmp = y * ((t - z) / t)
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00265) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00265:
		tmp = x + (y * (z / a))
	elif a <= 3.6e+155:
		tmp = y * ((t - z) / t)
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00265)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 3.6e+155)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00265)
		tmp = x + (y * (z / a));
	elseif (a <= 3.6e+155)
		tmp = y * ((t - z) / t);
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00265], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+155], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.00265000000000000001

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 67.3%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 70.7%

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

   6. Simplified 70.7%

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

   if -0.00265000000000000001 < a < 3.60000000000000007e155

   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 0 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

      3. associate-/l* 61.4%

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

      4. div-sub 61.4%

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

      5. sub-neg 61.4%

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

      6. *-inverses 61.4%

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

      7. metadata-eval 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around inf 55.9%

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

   7. Taylor expanded in t around 0 56.0%

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

   if 3.60000000000000007e155 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 73.4%

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

   4. Taylor expanded in y around inf 79.2%

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

Alternative 22: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -21000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -21000.0) x (if (<= a 3.6e+155) (* y (/ (- t z) t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -21000.0) {
		tmp = x;
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} 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 <= (-21000.0d0)) then
        tmp = x
    else if (a <= 3.6d+155) then
        tmp = y * ((t - z) / t)
    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 <= -21000.0) {
		tmp = x;
	} else if (a <= 3.6e+155) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -21000.0:
		tmp = x
	elif a <= 3.6e+155:
		tmp = y * ((t - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -21000.0)
		tmp = x;
	elseif (a <= 3.6e+155)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -21000.0)
		tmp = x;
	elseif (a <= 3.6e+155)
		tmp = y * ((t - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -21000.0], x, If[LessEqual[a, 3.6e+155], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -21000 or 3.60000000000000007e155 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 57.3%

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

   if -21000 < a < 3.60000000000000007e155

   1. Initial program 71.2%

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

   3. Taylor expanded in a around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

      3. associate-/l* 61.1%

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

      4. div-sub 61.1%

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

      5. sub-neg 61.1%

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

      6. *-inverses 61.1%

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

      7. metadata-eval 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 55.6%

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

   7. Taylor expanded in t around 0 55.6%

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

Alternative 23: 47.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1020:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1020.0) x (if (<= a 1.25e+156) (* y (- 1.0 (/ z t))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1020.0) {
		tmp = x;
	} else if (a <= 1.25e+156) {
		tmp = y * (1.0 - (z / t));
	} 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 <= (-1020.0d0)) then
        tmp = x
    else if (a <= 1.25d+156) then
        tmp = y * (1.0d0 - (z / t))
    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 <= -1020.0) {
		tmp = x;
	} else if (a <= 1.25e+156) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1020.0:
		tmp = x
	elif a <= 1.25e+156:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1020.0)
		tmp = x;
	elseif (a <= 1.25e+156)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1020.0)
		tmp = x;
	elseif (a <= 1.25e+156)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1020.0], x, If[LessEqual[a, 1.25e+156], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1020 or 1.24999999999999998e156 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 57.3%

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

   if -1020 < a < 1.24999999999999998e156

   1. Initial program 71.2%

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

   3. Taylor expanded in a around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

      3. associate-/l* 61.1%

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

      4. div-sub 61.1%

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

      5. sub-neg 61.1%

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

      6. *-inverses 61.1%

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

      7. metadata-eval 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 55.6%

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

Alternative 24: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2200:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+155}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2200.0) x (if (<= a 3.6e+155) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2200.0) {
		tmp = x;
	} else if (a <= 3.6e+155) {
		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 <= (-2200.0d0)) then
        tmp = x
    else if (a <= 3.6d+155) 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 <= -2200.0) {
		tmp = x;
	} else if (a <= 3.6e+155) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2200.0:
		tmp = x
	elif a <= 3.6e+155:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2200.0)
		tmp = x;
	elseif (a <= 3.6e+155)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2200.0)
		tmp = x;
	elseif (a <= 3.6e+155)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2200.0], x, If[LessEqual[a, 3.6e+155], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2200 or 3.60000000000000007e155 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 57.3%

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

   if -2200 < a < 3.60000000000000007e155

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 34.2%

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

Alternative 25: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.2%

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

3. Taylor expanded in a around inf 25.6%

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

Developer target: 87.0% 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 2024110 
(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))))