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

Percentage Accurate: 67.4% → 87.1%

Time: 16.7s

Alternatives: 19

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.4% 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: 87.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+120} \lor \neg \left(t \leq 3.6 \cdot 10^{+274}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+120) (not (<= t 3.6e+274)))
   (+ y (* (/ (- y x) t) (- a z)))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+120) || !(t <= 3.6e+274)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+120) || !(t <= 3.6e+274))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+120], N[Not[LessEqual[t, 3.6e+274]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e120 or 3.59999999999999995e274 < t

   1. Initial program 24.7%

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

   3. Taylor expanded in t around inf 64.8%

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

      1. associate--l+ 64.8%

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

      2. distribute-lft-out-- 64.8%

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

      3. div-sub 64.8%

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

      4. mul-1-neg 64.8%

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

      5. unsub-neg 64.8%

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

      6. div-sub 64.8%

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

      7. associate-/l* 71.0%

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

      8. associate-/l* 93.6%

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

      9. distribute-rgt-out-- 93.7%

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

   5. Simplified 93.7%

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

   if -1.05e120 < t < 3.59999999999999995e274

   1. Initial program 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.5%

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

   3. Simplified 93.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+120} \lor \neg \left(t \leq 3.6 \cdot 10^{+274}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 56.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := x + y \cdot \frac{z}{a}\\ t_3 := y \cdot \frac{z - t}{a - t}\\ t_4 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+180}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-254}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-43}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 0.00036:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+74}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a))))
        (t_2 (+ x (* y (/ z a))))
        (t_3 (* y (/ (- z t) (- a t))))
        (t_4 (* z (/ (- y x) (- a t)))))
   (if (<= t -8e+180)
     t_3
     (if (<= t -7.4e+41)
       (* x (/ (- z a) t))
       (if (<= t -5.4e-254)
         (+ x (* z (/ y a)))
         (if (<= t -3.1e-306)
           t_1
           (if (<= t 7.2e-87)
             t_2
             (if (<= t 2e-43)
               t_4
               (if (<= t 0.00036)
                 t_2
                 (if (<= t 8.8e+74) t_4 (if (<= t 1.1e+110) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = x + (y * (z / a));
	double t_3 = y * ((z - t) / (a - t));
	double t_4 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -8e+180) {
		tmp = t_3;
	} else if (t <= -7.4e+41) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.4e-254) {
		tmp = x + (z * (y / a));
	} else if (t <= -3.1e-306) {
		tmp = t_1;
	} else if (t <= 7.2e-87) {
		tmp = t_2;
	} else if (t <= 2e-43) {
		tmp = t_4;
	} else if (t <= 0.00036) {
		tmp = t_2;
	} else if (t <= 8.8e+74) {
		tmp = t_4;
	} else if (t <= 1.1e+110) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = x + (y * (z / a))
    t_3 = y * ((z - t) / (a - t))
    t_4 = z * ((y - x) / (a - t))
    if (t <= (-8d+180)) then
        tmp = t_3
    else if (t <= (-7.4d+41)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-5.4d-254)) then
        tmp = x + (z * (y / a))
    else if (t <= (-3.1d-306)) then
        tmp = t_1
    else if (t <= 7.2d-87) then
        tmp = t_2
    else if (t <= 2d-43) then
        tmp = t_4
    else if (t <= 0.00036d0) then
        tmp = t_2
    else if (t <= 8.8d+74) then
        tmp = t_4
    else if (t <= 1.1d+110) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = x + (y * (z / a));
	double t_3 = y * ((z - t) / (a - t));
	double t_4 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -8e+180) {
		tmp = t_3;
	} else if (t <= -7.4e+41) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.4e-254) {
		tmp = x + (z * (y / a));
	} else if (t <= -3.1e-306) {
		tmp = t_1;
	} else if (t <= 7.2e-87) {
		tmp = t_2;
	} else if (t <= 2e-43) {
		tmp = t_4;
	} else if (t <= 0.00036) {
		tmp = t_2;
	} else if (t <= 8.8e+74) {
		tmp = t_4;
	} else if (t <= 1.1e+110) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = x + (y * (z / a))
	t_3 = y * ((z - t) / (a - t))
	t_4 = z * ((y - x) / (a - t))
	tmp = 0
	if t <= -8e+180:
		tmp = t_3
	elif t <= -7.4e+41:
		tmp = x * ((z - a) / t)
	elif t <= -5.4e-254:
		tmp = x + (z * (y / a))
	elif t <= -3.1e-306:
		tmp = t_1
	elif t <= 7.2e-87:
		tmp = t_2
	elif t <= 2e-43:
		tmp = t_4
	elif t <= 0.00036:
		tmp = t_2
	elif t <= 8.8e+74:
		tmp = t_4
	elif t <= 1.1e+110:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	t_3 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_4 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (t <= -8e+180)
		tmp = t_3;
	elseif (t <= -7.4e+41)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -5.4e-254)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= -3.1e-306)
		tmp = t_1;
	elseif (t <= 7.2e-87)
		tmp = t_2;
	elseif (t <= 2e-43)
		tmp = t_4;
	elseif (t <= 0.00036)
		tmp = t_2;
	elseif (t <= 8.8e+74)
		tmp = t_4;
	elseif (t <= 1.1e+110)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = x + (y * (z / a));
	t_3 = y * ((z - t) / (a - t));
	t_4 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (t <= -8e+180)
		tmp = t_3;
	elseif (t <= -7.4e+41)
		tmp = x * ((z - a) / t);
	elseif (t <= -5.4e-254)
		tmp = x + (z * (y / a));
	elseif (t <= -3.1e-306)
		tmp = t_1;
	elseif (t <= 7.2e-87)
		tmp = t_2;
	elseif (t <= 2e-43)
		tmp = t_4;
	elseif (t <= 0.00036)
		tmp = t_2;
	elseif (t <= 8.8e+74)
		tmp = t_4;
	elseif (t <= 1.1e+110)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+180], t$95$3, If[LessEqual[t, -7.4e+41], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e-254], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e-306], t$95$1, If[LessEqual[t, 7.2e-87], t$95$2, If[LessEqual[t, 2e-43], t$95$4, If[LessEqual[t, 0.00036], t$95$2, If[LessEqual[t, 8.8e+74], t$95$4, If[LessEqual[t, 1.1e+110], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -8.0000000000000001e180 or 1.09999999999999996e110 < t

   1. Initial program 27.7%

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

      1. add-cube-cbrt 27.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 27.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 27.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 65.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 65.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 74.5%

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

      1. div-sub 74.5%

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

   7. Simplified 74.5%

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

   if -8.0000000000000001e180 < t < -7.39999999999999962e41

   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 x around -inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

      3. +-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in t around -inf 56.7%

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

      1. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

   if -7.39999999999999962e41 < t < -5.40000000000000013e-254

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 65.1%

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

   4. Taylor expanded in y around inf 53.6%

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

      1. *-commutative 53.6%

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

   6. Simplified 53.6%

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

      1. associate-/l* 56.8%

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

   8. Applied egg-rr 56.8%

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

   if -5.40000000000000013e-254 < t < -3.09999999999999998e-306 or 8.8000000000000005e74 < t < 1.09999999999999996e110

   1. Initial program 89.7%

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

   3. Taylor expanded in x around -inf 75.5%

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

      1. associate-*r* 75.5%

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

      2. neg-mul-1 75.5%

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

      3. +-commutative 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in t around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. sub-neg 76.0%

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

      3. metadata-eval 76.0%

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

   8. Simplified 76.0%

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

   if -3.09999999999999998e-306 < t < 7.19999999999999986e-87 or 2.00000000000000015e-43 < t < 3.60000000000000023e-4

   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 t around 0 79.8%

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

   4. Taylor expanded in y around inf 79.6%

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

      1. associate-/l* 85.6%

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

   6. Simplified 85.6%

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

   if 7.19999999999999986e-87 < t < 2.00000000000000015e-43 or 3.60000000000000023e-4 < t < 8.8000000000000005e74

   1. Initial program 94.9%

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

      1. add-cube-cbrt 94.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 94.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 94.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 98.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 98.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 80.9%

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

      1. div-sub 80.9%

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

   7. Simplified 80.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-254}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 0.00036:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-255}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-44} \lor \neg \left(t \leq 1.35 \cdot 10^{+32}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* z (/ y a)))))
   (if (<= t -7.8e+180)
     t_1
     (if (<= t -6.8e+41)
       (* x (/ (- z a) t))
       (if (<= t -5.2e-255)
         t_2
         (if (<= t -2.6e-305)
           (* x (- 1.0 (/ z a)))
           (if (<= t 2.7e-87)
             (+ x (* y (/ z a)))
             (if (or (<= t 8.2e-44) (not (<= t 1.35e+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 * (y / a));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = t_1;
	} else if (t <= -6.8e+41) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.2e-255) {
		tmp = t_2;
	} else if (t <= -2.6e-305) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.7e-87) {
		tmp = x + (y * (z / a));
	} else if ((t <= 8.2e-44) || !(t <= 1.35e+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 * (y / a))
    if (t <= (-7.8d+180)) then
        tmp = t_1
    else if (t <= (-6.8d+41)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-5.2d-255)) then
        tmp = t_2
    else if (t <= (-2.6d-305)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 2.7d-87) then
        tmp = x + (y * (z / a))
    else if ((t <= 8.2d-44) .or. (.not. (t <= 1.35d+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 * (y / a));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = t_1;
	} else if (t <= -6.8e+41) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.2e-255) {
		tmp = t_2;
	} else if (t <= -2.6e-305) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.7e-87) {
		tmp = x + (y * (z / a));
	} else if ((t <= 8.2e-44) || !(t <= 1.35e+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 * (y / a))
	tmp = 0
	if t <= -7.8e+180:
		tmp = t_1
	elif t <= -6.8e+41:
		tmp = x * ((z - a) / t)
	elif t <= -5.2e-255:
		tmp = t_2
	elif t <= -2.6e-305:
		tmp = x * (1.0 - (z / a))
	elif t <= 2.7e-87:
		tmp = x + (y * (z / a))
	elif (t <= 8.2e-44) or not (t <= 1.35e+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(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -7.8e+180)
		tmp = t_1;
	elseif (t <= -6.8e+41)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -5.2e-255)
		tmp = t_2;
	elseif (t <= -2.6e-305)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 2.7e-87)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif ((t <= 8.2e-44) || !(t <= 1.35e+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 * (y / a));
	tmp = 0.0;
	if (t <= -7.8e+180)
		tmp = t_1;
	elseif (t <= -6.8e+41)
		tmp = x * ((z - a) / t);
	elseif (t <= -5.2e-255)
		tmp = t_2;
	elseif (t <= -2.6e-305)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 2.7e-87)
		tmp = x + (y * (z / a));
	elseif ((t <= 8.2e-44) || ~((t <= 1.35e+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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+180], t$95$1, If[LessEqual[t, -6.8e+41], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-255], t$95$2, If[LessEqual[t, -2.6e-305], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-87], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.2e-44], N[Not[LessEqual[t, 1.35e+32]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.8000000000000002e180 or 2.69999999999999984e-87 < t < 8.19999999999999984e-44 or 1.35000000000000006e32 < t

   1. Initial program 42.7%

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

      1. add-cube-cbrt 42.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 42.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 42.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 72.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 72.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 70.4%

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

      1. div-sub 70.4%

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

   7. Simplified 70.4%

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

   if -7.8000000000000002e180 < t < -6.79999999999999996e41

   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 x around -inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

      3. +-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in t around -inf 56.7%

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

      1. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

   if -6.79999999999999996e41 < t < -5.20000000000000041e-255 or 8.19999999999999984e-44 < t < 1.35000000000000006e32

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0 63.3%

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

   4. Taylor expanded in y around inf 54.8%

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

      1. *-commutative 54.8%

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

   6. Simplified 54.8%

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

      1. associate-/l* 58.6%

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

   8. Applied egg-rr 58.6%

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

   if -5.20000000000000041e-255 < t < -2.6000000000000002e-305

   1. Initial program 92.0%

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

   3. Taylor expanded in x around -inf 84.6%

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

      1. associate-*r* 84.6%

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

      2. neg-mul-1 84.6%

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

      3. +-commutative 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

   8. Simplified 84.6%

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

   if -2.6000000000000002e-305 < t < 2.69999999999999984e-87

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0 82.9%

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

   4. Taylor expanded in y around inf 82.7%

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

      1. associate-/l* 88.1%

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

   6. Simplified 88.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-255}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-44} \lor \neg \left(t \leq 1.35 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{a - t}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+274}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) (- a t))))))
   (if (<= t -7.8e+180)
     (* y (/ (- z t) (- a t)))
     (if (<= t -2.1e+109)
       (* x (/ (- z a) t))
       (if (<= t -1.7e+42)
         (- y (/ (* (- y x) z) t))
         (if (<= t -5.4e-110)
           t_1
           (if (<= t 2.8e+68)
             (+ x (* z (/ (- y x) (- a t))))
             (if (<= t 3.3e+274) t_1 (+ y (* (/ (- y x) t) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / (a - t)));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -2.1e+109) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.7e+42) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -5.4e-110) {
		tmp = t_1;
	} else if (t <= 2.8e+68) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 3.3e+274) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((t - z) / (a - t)))
    if (t <= (-7.8d+180)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-2.1d+109)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.7d+42)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= (-5.4d-110)) then
        tmp = t_1
    else if (t <= 2.8d+68) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if (t <= 3.3d+274) then
        tmp = t_1
    else
        tmp = y + (((y - x) / t) * 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 = x - (y * ((t - z) / (a - t)));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -2.1e+109) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.7e+42) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -5.4e-110) {
		tmp = t_1;
	} else if (t <= 2.8e+68) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 3.3e+274) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / (a - t)))
	tmp = 0
	if t <= -7.8e+180:
		tmp = y * ((z - t) / (a - t))
	elif t <= -2.1e+109:
		tmp = x * ((z - a) / t)
	elif t <= -1.7e+42:
		tmp = y - (((y - x) * z) / t)
	elif t <= -5.4e-110:
		tmp = t_1
	elif t <= 2.8e+68:
		tmp = x + (z * ((y - x) / (a - t)))
	elif t <= 3.3e+274:
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t - z) / Float64(a - t))))
	tmp = 0.0
	if (t <= -7.8e+180)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -2.1e+109)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.7e+42)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= -5.4e-110)
		tmp = t_1;
	elseif (t <= 2.8e+68)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t <= 3.3e+274)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t - z) / (a - t)));
	tmp = 0.0;
	if (t <= -7.8e+180)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -2.1e+109)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.7e+42)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= -5.4e-110)
		tmp = t_1;
	elseif (t <= 2.8e+68)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif (t <= 3.3e+274)
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+180], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e+109], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e+42], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e-110], t$95$1, If[LessEqual[t, 2.8e+68], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+274], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.8000000000000002e180

   1. Initial program 21.0%

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

      1. add-cube-cbrt 20.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 20.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 20.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 58.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 58.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 80.1%

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

      1. div-sub 80.1%

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

   7. Simplified 80.1%

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

   if -7.8000000000000002e180 < t < -2.1000000000000001e109

   1. Initial program 52.3%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 42.7%

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

      1. associate-/l* 69.2%

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

   8. Simplified 69.2%

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

   if -2.1000000000000001e109 < t < -1.69999999999999988e42

   1. Initial program 83.8%

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

   3. Taylor expanded in t around inf 92.2%

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

      1. associate--l+ 92.2%

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

      2. distribute-lft-out-- 92.2%

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

      3. div-sub 92.2%

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

      4. mul-1-neg 92.2%

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

      5. unsub-neg 92.2%

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

      6. div-sub 92.2%

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

      7. associate-/l* 92.1%

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

      8. associate-/l* 92.1%

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

      9. distribute-rgt-out-- 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in z around inf 83.7%

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

   if -1.69999999999999988e42 < t < -5.3999999999999996e-110 or 2.8e68 < t < 3.30000000000000014e274

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -5.3999999999999996e-110 < t < 2.8e68

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 92.4%

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

   5. Simplified 92.4%

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

   if 3.30000000000000014e274 < t

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.6%

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

      4. mul-1-neg 61.6%

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

      5. unsub-neg 61.6%

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

      6. div-sub 61.6%

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

      7. associate-/l* 61.6%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 98.7%

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

      3. distribute-rgt-neg-in 98.7%

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

      4. distribute-neg-frac2 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+274}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+42}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.00039:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -8e+180)
     t_1
     (if (<= t -2.1e+109)
       (* x (/ (- z a) t))
       (if (<= t -2.15e+42)
         (- y (/ (* (- y x) z) t))
         (if (<= t 0.00039)
           (+ x (* z (/ (- y x) a)))
           (if (<= t 3.2e+74)
             (* z (/ (- y x) (- a t)))
             (if (<= t 1.05e+110) (* x (- 1.0 (/ z a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8e+180) {
		tmp = t_1;
	} else if (t <= -2.1e+109) {
		tmp = x * ((z - a) / t);
	} else if (t <= -2.15e+42) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= 0.00039) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 3.2e+74) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.05e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-8d+180)) then
        tmp = t_1
    else if (t <= (-2.1d+109)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-2.15d+42)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= 0.00039d0) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 3.2d+74) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.05d+110) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8e+180) {
		tmp = t_1;
	} else if (t <= -2.1e+109) {
		tmp = x * ((z - a) / t);
	} else if (t <= -2.15e+42) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= 0.00039) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 3.2e+74) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.05e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -8e+180:
		tmp = t_1
	elif t <= -2.1e+109:
		tmp = x * ((z - a) / t)
	elif t <= -2.15e+42:
		tmp = y - (((y - x) * z) / t)
	elif t <= 0.00039:
		tmp = x + (z * ((y - x) / a))
	elif t <= 3.2e+74:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.05e+110:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	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 (t <= -8e+180)
		tmp = t_1;
	elseif (t <= -2.1e+109)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -2.15e+42)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= 0.00039)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 3.2e+74)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.05e+110)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	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 (t <= -8e+180)
		tmp = t_1;
	elseif (t <= -2.1e+109)
		tmp = x * ((z - a) / t);
	elseif (t <= -2.15e+42)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= 0.00039)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 3.2e+74)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.05e+110)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+180], t$95$1, If[LessEqual[t, -2.1e+109], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e+42], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00039], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+74], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+110], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -8.0000000000000001e180 or 1.05000000000000007e110 < t

   1. Initial program 27.7%

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

      1. add-cube-cbrt 27.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 27.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 27.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 65.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 65.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 74.5%

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

      1. div-sub 74.5%

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

   7. Simplified 74.5%

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

   if -8.0000000000000001e180 < t < -2.1000000000000001e109

   1. Initial program 52.3%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 42.7%

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

      1. associate-/l* 69.2%

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

   8. Simplified 69.2%

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

   if -2.1000000000000001e109 < t < -2.1499999999999999e42

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf 91.5%

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

      1. associate--l+ 91.5%

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

      2. distribute-lft-out-- 91.5%

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

      3. div-sub 91.5%

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

      4. mul-1-neg 91.5%

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

      5. unsub-neg 91.5%

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

      6. div-sub 91.5%

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

      7. associate-/l* 91.3%

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

      8. associate-/l* 91.3%

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

      9. distribute-rgt-out-- 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf 82.2%

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

   if -2.1499999999999999e42 < t < 3.89999999999999993e-4

   1. Initial program 90.4%

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

   3. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

   if 3.89999999999999993e-4 < t < 3.19999999999999995e74

   1. Initial program 99.0%

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

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 99.5%

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

      1. div-sub 99.5%

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

   7. Simplified 99.5%

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

   if 3.19999999999999995e74 < t < 1.05000000000000007e110

   1. Initial program 84.8%

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

   3. Taylor expanded in x around -inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. neg-mul-1 55.7%

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

      3. +-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. sub-neg 57.3%

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

      3. metadata-eval 57.3%

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

   8. Simplified 57.3%

      \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a} + -1\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+42}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.00039:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.00038:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7.8e+180)
     t_1
     (if (<= t -2.1e+109)
       (* x (/ (- z a) t))
       (if (<= t -2.3e+42)
         (- y (/ (* (- y x) z) t))
         (if (<= t 0.00038)
           (+ x (* z (/ (- y x) a)))
           (if (<= t 8.8e+71)
             (/ z (/ (- a t) (- y x)))
             (if (<= t 1.18e+110) (* x (- 1.0 (/ z a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = t_1;
	} else if (t <= -2.1e+109) {
		tmp = x * ((z - a) / t);
	} else if (t <= -2.3e+42) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= 0.00038) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 8.8e+71) {
		tmp = z / ((a - t) / (y - x));
	} else if (t <= 1.18e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-7.8d+180)) then
        tmp = t_1
    else if (t <= (-2.1d+109)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-2.3d+42)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= 0.00038d0) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 8.8d+71) then
        tmp = z / ((a - t) / (y - x))
    else if (t <= 1.18d+110) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = t_1;
	} else if (t <= -2.1e+109) {
		tmp = x * ((z - a) / t);
	} else if (t <= -2.3e+42) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= 0.00038) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 8.8e+71) {
		tmp = z / ((a - t) / (y - x));
	} else if (t <= 1.18e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7.8e+180:
		tmp = t_1
	elif t <= -2.1e+109:
		tmp = x * ((z - a) / t)
	elif t <= -2.3e+42:
		tmp = y - (((y - x) * z) / t)
	elif t <= 0.00038:
		tmp = x + (z * ((y - x) / a))
	elif t <= 8.8e+71:
		tmp = z / ((a - t) / (y - x))
	elif t <= 1.18e+110:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	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 (t <= -7.8e+180)
		tmp = t_1;
	elseif (t <= -2.1e+109)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -2.3e+42)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= 0.00038)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 8.8e+71)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (t <= 1.18e+110)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	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 (t <= -7.8e+180)
		tmp = t_1;
	elseif (t <= -2.1e+109)
		tmp = x * ((z - a) / t);
	elseif (t <= -2.3e+42)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= 0.00038)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 8.8e+71)
		tmp = z / ((a - t) / (y - x));
	elseif (t <= 1.18e+110)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+180], t$95$1, If[LessEqual[t, -2.1e+109], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e+42], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00038], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+71], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e+110], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.8000000000000002e180 or 1.1799999999999999e110 < t

   1. Initial program 27.7%

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

      1. add-cube-cbrt 27.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 27.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 27.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 65.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 65.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 74.5%

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

      1. div-sub 74.5%

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

   7. Simplified 74.5%

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

   if -7.8000000000000002e180 < t < -2.1000000000000001e109

   1. Initial program 52.3%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 42.7%

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

      1. associate-/l* 69.2%

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

   8. Simplified 69.2%

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

   if -2.1000000000000001e109 < t < -2.3e42

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf 91.5%

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

      1. associate--l+ 91.5%

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

      2. distribute-lft-out-- 91.5%

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

      3. div-sub 91.5%

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

      4. mul-1-neg 91.5%

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

      5. unsub-neg 91.5%

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

      6. div-sub 91.5%

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

      7. associate-/l* 91.3%

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

      8. associate-/l* 91.3%

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

      9. distribute-rgt-out-- 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf 82.2%

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

   if -2.3e42 < t < 3.8000000000000002e-4

   1. Initial program 90.4%

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

   3. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

   if 3.8000000000000002e-4 < t < 8.79999999999999978e71

   1. Initial program 99.0%

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

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 99.5%

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

      1. div-sub 99.5%

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

   7. Simplified 99.5%

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

      1. clear-num 99.2%

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

      2. un-div-inv 100.0%

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

   9. Applied egg-rr 100.0%

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

   if 8.79999999999999978e71 < t < 1.1799999999999999e110

   1. Initial program 84.8%

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

   3. Taylor expanded in x around -inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. neg-mul-1 55.7%

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

      3. +-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. sub-neg 57.3%

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

      3. metadata-eval 57.3%

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

   8. Simplified 57.3%

      \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a} + -1\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 0.00038:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7.8e+180)
     t_1
     (if (<= t -2.45e+42)
       (* x (/ (- z a) t))
       (if (<= t 0.00055)
         (+ x (* z (/ (- y x) a)))
         (if (<= t 6.2e+70)
           (* z (/ (- y x) (- a t)))
           (if (<= t 1.3e+110) (* x (- 1.0 (/ z a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = t_1;
	} else if (t <= -2.45e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= 0.00055) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 6.2e+70) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.3e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-7.8d+180)) then
        tmp = t_1
    else if (t <= (-2.45d+42)) then
        tmp = x * ((z - a) / t)
    else if (t <= 0.00055d0) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 6.2d+70) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.3d+110) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.8e+180) {
		tmp = t_1;
	} else if (t <= -2.45e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= 0.00055) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 6.2e+70) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.3e+110) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7.8e+180:
		tmp = t_1
	elif t <= -2.45e+42:
		tmp = x * ((z - a) / t)
	elif t <= 0.00055:
		tmp = x + (z * ((y - x) / a))
	elif t <= 6.2e+70:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.3e+110:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	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 (t <= -7.8e+180)
		tmp = t_1;
	elseif (t <= -2.45e+42)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 0.00055)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 6.2e+70)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.3e+110)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	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 (t <= -7.8e+180)
		tmp = t_1;
	elseif (t <= -2.45e+42)
		tmp = x * ((z - a) / t);
	elseif (t <= 0.00055)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 6.2e+70)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.3e+110)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+180], t$95$1, If[LessEqual[t, -2.45e+42], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00055], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+70], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+110], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.8000000000000002e180 or 1.3e110 < t

   1. Initial program 27.7%

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

      1. add-cube-cbrt 27.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 27.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 27.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 65.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 65.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 74.5%

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

      1. div-sub 74.5%

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

   7. Simplified 74.5%

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

   if -7.8000000000000002e180 < t < -2.4500000000000001e42

   1. Initial program 68.0%

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

   3. Taylor expanded in x around -inf 59.0%

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

      1. associate-*r* 59.0%

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

      2. neg-mul-1 59.0%

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

      3. +-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in t around -inf 54.7%

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

      1. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

   if -2.4500000000000001e42 < t < 5.50000000000000033e-4

   1. Initial program 90.4%

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

   3. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

   if 5.50000000000000033e-4 < t < 6.2000000000000006e70

   1. Initial program 99.0%

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

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 99.5%

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

      1. div-sub 99.5%

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

   7. Simplified 99.5%

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

   if 6.2000000000000006e70 < t < 1.3e110

   1. Initial program 84.8%

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

   3. Taylor expanded in x around -inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. neg-mul-1 55.7%

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

      3. +-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. sub-neg 57.3%

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

      3. metadata-eval 57.3%

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

   8. Simplified 57.3%

      \[\leadsto \color{blue}{-x \cdot \left(\frac{z}{a} + -1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ t_2 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t))))
        (t_2 (+ y (* (/ (- y x) t) (- a z)))))
   (if (<= t -1.45e+58)
     t_2
     (if (<= t -4.8e-110)
       t_1
       (if (<= t 1.85e-155)
         (+ x (* z (/ (- y x) (- a t))))
         (if (<= t 7.8e+104) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double t_2 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -1.45e+58) {
		tmp = t_2;
	} else if (t <= -4.8e-110) {
		tmp = t_1;
	} else if (t <= 1.85e-155) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 7.8e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    t_2 = y + (((y - x) / t) * (a - z))
    if (t <= (-1.45d+58)) then
        tmp = t_2
    else if (t <= (-4.8d-110)) then
        tmp = t_1
    else if (t <= 1.85d-155) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if (t <= 7.8d+104) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double t_2 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -1.45e+58) {
		tmp = t_2;
	} else if (t <= -4.8e-110) {
		tmp = t_1;
	} else if (t <= 1.85e-155) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 7.8e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	t_2 = y + (((y - x) / t) * (a - z))
	tmp = 0
	if t <= -1.45e+58:
		tmp = t_2
	elif t <= -4.8e-110:
		tmp = t_1
	elif t <= 1.85e-155:
		tmp = x + (z * ((y - x) / (a - t)))
	elif t <= 7.8e+104:
		tmp = t_1
	else:
		tmp = t_2
	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)))
	t_2 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -1.45e+58)
		tmp = t_2;
	elseif (t <= -4.8e-110)
		tmp = t_1;
	elseif (t <= 1.85e-155)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t <= 7.8e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	t_2 = y + (((y - x) / t) * (a - z));
	tmp = 0.0;
	if (t <= -1.45e+58)
		tmp = t_2;
	elseif (t <= -4.8e-110)
		tmp = t_1;
	elseif (t <= 1.85e-155)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif (t <= 7.8e+104)
		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[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+58], t$95$2, If[LessEqual[t, -4.8e-110], t$95$1, If[LessEqual[t, 1.85e-155], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+104], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45000000000000001e58 or 7.80000000000000033e104 < t

   1. Initial program 35.8%

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

   3. Taylor expanded in t around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. distribute-lft-out-- 63.4%

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

      3. div-sub 63.4%

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

      4. mul-1-neg 63.4%

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

      5. unsub-neg 63.4%

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

      6. div-sub 63.4%

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

      7. associate-/l* 71.4%

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

      8. associate-/l* 85.6%

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

      9. distribute-rgt-out-- 85.7%

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

   5. Simplified 85.7%

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

   if -1.45000000000000001e58 < t < -4.80000000000000013e-110 or 1.85e-155 < t < 7.80000000000000033e104

   1. Initial program 90.2%

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

   if -4.80000000000000013e-110 < t < 1.85e-155

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 96.3%

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

   5. Simplified 96.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+58}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-255}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.9e+181)
   y
   (if (<= t -8.5e+39)
     (* x (/ (- z a) t))
     (if (<= t -6.2e-255)
       (+ x (* z (/ y a)))
       (if (<= t 2.1e-308)
         (* x (- 1.0 (/ z a)))
         (if (<= t 2.9e+114) (+ x (* y (/ z a))) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.9e+181) {
		tmp = y;
	} else if (t <= -8.5e+39) {
		tmp = x * ((z - a) / t);
	} else if (t <= -6.2e-255) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.1e-308) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.9e+114) {
		tmp = x + (y * (z / a));
	} 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 <= (-4.9d+181)) then
        tmp = y
    else if (t <= (-8.5d+39)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-6.2d-255)) then
        tmp = x + (z * (y / a))
    else if (t <= 2.1d-308) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 2.9d+114) then
        tmp = x + (y * (z / a))
    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 <= -4.9e+181) {
		tmp = y;
	} else if (t <= -8.5e+39) {
		tmp = x * ((z - a) / t);
	} else if (t <= -6.2e-255) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.1e-308) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.9e+114) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.9e+181:
		tmp = y
	elif t <= -8.5e+39:
		tmp = x * ((z - a) / t)
	elif t <= -6.2e-255:
		tmp = x + (z * (y / a))
	elif t <= 2.1e-308:
		tmp = x * (1.0 - (z / a))
	elif t <= 2.9e+114:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.9e+181)
		tmp = y;
	elseif (t <= -8.5e+39)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -6.2e-255)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 2.1e-308)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 2.9e+114)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.9e+181)
		tmp = y;
	elseif (t <= -8.5e+39)
		tmp = x * ((z - a) / t);
	elseif (t <= -6.2e-255)
		tmp = x + (z * (y / a));
	elseif (t <= 2.1e-308)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 2.9e+114)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.9e+181], y, If[LessEqual[t, -8.5e+39], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e-255], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-308], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+114], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.89999999999999981e181 or 2.9e114 < t

   1. Initial program 27.0%

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

   3. Taylor expanded in t around inf 58.4%

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

   if -4.89999999999999981e181 < t < -8.49999999999999971e39

   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 x around -inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

      3. +-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in t around -inf 56.7%

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

      1. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

   if -8.49999999999999971e39 < t < -6.19999999999999995e-255

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 65.1%

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

   4. Taylor expanded in y around inf 53.6%

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

      1. *-commutative 53.6%

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

   6. Simplified 53.6%

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

      1. associate-/l* 56.8%

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

   8. Applied egg-rr 56.8%

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

   if -6.19999999999999995e-255 < t < 2.1e-308

   1. Initial program 92.0%

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

   3. Taylor expanded in x around -inf 84.6%

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

      1. associate-*r* 84.6%

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

      2. neg-mul-1 84.6%

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

      3. +-commutative 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

   8. Simplified 84.6%

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

   if 2.1e-308 < t < 2.9e114

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 65.6%

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

   4. Taylor expanded in y around inf 63.0%

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

      1. associate-/l* 69.1%

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

   6. Simplified 69.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-255}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-110}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+102}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- y x) t) (- a z)))))
   (if (<= t -1.05e+42)
     t_1
     (if (<= t -5.2e-110)
       (- x (* y (/ (- t z) (- a t))))
       (if (<= t 7.8e+102) (+ x (* z (/ (- y x) (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -1.05e+42) {
		tmp = t_1;
	} else if (t <= -5.2e-110) {
		tmp = x - (y * ((t - z) / (a - t)));
	} else if (t <= 7.8e+102) {
		tmp = x + (z * ((y - x) / (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 = y + (((y - x) / t) * (a - z))
    if (t <= (-1.05d+42)) then
        tmp = t_1
    else if (t <= (-5.2d-110)) then
        tmp = x - (y * ((t - z) / (a - t)))
    else if (t <= 7.8d+102) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -1.05e+42) {
		tmp = t_1;
	} else if (t <= -5.2e-110) {
		tmp = x - (y * ((t - z) / (a - t)));
	} else if (t <= 7.8e+102) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) / t) * (a - z))
	tmp = 0
	if t <= -1.05e+42:
		tmp = t_1
	elif t <= -5.2e-110:
		tmp = x - (y * ((t - z) / (a - t)))
	elif t <= 7.8e+102:
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -1.05e+42)
		tmp = t_1;
	elseif (t <= -5.2e-110)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	elseif (t <= 7.8e+102)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) / t) * (a - z));
	tmp = 0.0;
	if (t <= -1.05e+42)
		tmp = t_1;
	elseif (t <= -5.2e-110)
		tmp = x - (y * ((t - z) / (a - t)));
	elseif (t <= 7.8e+102)
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+42], t$95$1, If[LessEqual[t, -5.2e-110], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+102], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.04999999999999998e42 or 7.7999999999999997e102 < t

   1. Initial program 37.8%

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

   3. Taylor expanded in t around inf 64.5%

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

      1. associate--l+ 64.5%

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

      2. distribute-lft-out-- 64.5%

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

      3. div-sub 64.5%

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

      4. mul-1-neg 64.5%

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

      5. unsub-neg 64.5%

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

      6. div-sub 64.5%

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

      7. associate-/l* 72.2%

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

      8. associate-/l* 86.1%

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

      9. distribute-rgt-out-- 86.1%

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

   5. Simplified 86.1%

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

   if -1.04999999999999998e42 < t < -5.19999999999999979e-110

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 87.3%

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

      1. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   if -5.19999999999999979e-110 < t < 7.7999999999999997e102

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-110}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+102}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+120} \lor \neg \left(t \leq 8.8 \cdot 10^{+268}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+120) (not (<= t 8.8e+268)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+120) || !(t <= 8.8e+268)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d+120)) .or. (.not. (t <= 8.8d+268))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x + ((z - t) * ((y - x) * ((-1.0d0) / (t - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+120) || !(t <= 8.8e+268)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+120) or not (t <= 8.8e+268):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+120) || !(t <= 8.8e+268))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+120) || ~((t <= 8.8e+268)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+120], N[Not[LessEqual[t, 8.8e+268]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e120 or 8.79999999999999977e268 < t

   1. Initial program 24.3%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. distribute-lft-out-- 63.6%

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

      3. div-sub 63.6%

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

      4. mul-1-neg 63.6%

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

      5. unsub-neg 63.6%

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

      6. div-sub 63.6%

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

      7. associate-/l* 71.6%

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

      8. associate-/l* 93.7%

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

      9. distribute-rgt-out-- 93.8%

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

   5. Simplified 93.8%

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

   if -2.1e120 < t < 8.79999999999999977e268

   1. Initial program 80.9%

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

      1. div-inv 80.8%

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

      2. *-commutative 80.8%

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

      3. associate-*l* 92.0%

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

   4. Applied egg-rr 92.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+120} \lor \neg \left(t \leq 8.8 \cdot 10^{+268}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+115}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.28e+181)
   y
   (if (<= t -2.35e+42)
     (* x (/ (- z a) t))
     (if (<= t 1.85e+115) (+ x (* y (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.28e+181) {
		tmp = y;
	} else if (t <= -2.35e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.85e+115) {
		tmp = x + (y * (z / a));
	} 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 <= (-1.28d+181)) then
        tmp = y
    else if (t <= (-2.35d+42)) then
        tmp = x * ((z - a) / t)
    else if (t <= 1.85d+115) then
        tmp = x + (y * (z / a))
    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 <= -1.28e+181) {
		tmp = y;
	} else if (t <= -2.35e+42) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.85e+115) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.28e+181:
		tmp = y
	elif t <= -2.35e+42:
		tmp = x * ((z - a) / t)
	elif t <= 1.85e+115:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.28e+181)
		tmp = y;
	elseif (t <= -2.35e+42)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 1.85e+115)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.28e+181)
		tmp = y;
	elseif (t <= -2.35e+42)
		tmp = x * ((z - a) / t);
	elseif (t <= 1.85e+115)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.28e+181], y, If[LessEqual[t, -2.35e+42], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+115], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.27999999999999997e181 or 1.85000000000000003e115 < t

   1. Initial program 27.0%

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

   3. Taylor expanded in t around inf 58.4%

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

   if -1.27999999999999997e181 < t < -2.34999999999999993e42

   1. Initial program 68.0%

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

   3. Taylor expanded in x around -inf 59.0%

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

      1. associate-*r* 59.0%

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

      2. neg-mul-1 59.0%

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

      3. +-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in t around -inf 54.7%

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

      1. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

   if -2.34999999999999993e42 < t < 1.85000000000000003e115

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 67.8%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+115}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-42} \lor \neg \left(y \leq 2.2 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.95e-42) (not (<= y 2.2e-12)))
   (* y (/ (- z t) (- a t)))
   (* x (+ (/ (- t z) (- a t)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.95e-42) || !(y <= 2.2e-12)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.95d-42)) .or. (.not. (y <= 2.2d-12))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.95e-42) || !(y <= 2.2e-12)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.95e-42) or not (y <= 2.2e-12):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.95e-42) || !(y <= 2.2e-12))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.95e-42) || ~((y <= 2.2e-12)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (((t - z) / (a - t)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.95e-42], N[Not[LessEqual[y, 2.2e-12]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9500000000000001e-42 or 2.19999999999999992e-12 < y

   1. Initial program 65.7%

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

      1. add-cube-cbrt 64.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 64.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 64.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 89.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 89.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around inf 72.1%

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

      1. div-sub 72.1%

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

   7. Simplified 72.1%

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

   if -1.9500000000000001e-42 < y < 2.19999999999999992e-12

   1. Initial program 76.3%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   5. Simplified 67.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-42} \lor \neg \left(y \leq 2.2 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-49} \lor \neg \left(a \leq 3.5 \cdot 10^{-152}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.6e-49) (not (<= a 3.5e-152)))
   (- x (* y (/ (- t z) (- a t))))
   (- y (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.6e-49) || !(a <= 3.5e-152)) {
		tmp = x - (y * ((t - z) / (a - t)));
	} else {
		tmp = y - (((y - x) * 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 <= (-8.6d-49)) .or. (.not. (a <= 3.5d-152))) then
        tmp = x - (y * ((t - z) / (a - t)))
    else
        tmp = y - (((y - x) * 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 <= -8.6e-49) || !(a <= 3.5e-152)) {
		tmp = x - (y * ((t - z) / (a - t)));
	} else {
		tmp = y - (((y - x) * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.6e-49) or not (a <= 3.5e-152):
		tmp = x - (y * ((t - z) / (a - t)))
	else:
		tmp = y - (((y - x) * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.6e-49) || !(a <= 3.5e-152))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.6e-49) || ~((a <= 3.5e-152)))
		tmp = x - (y * ((t - z) / (a - t)));
	else
		tmp = y - (((y - x) * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.6e-49], N[Not[LessEqual[a, 3.5e-152]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.60000000000000033e-49 or 3.5000000000000001e-152 < a

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 61.8%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   if -8.60000000000000033e-49 < a < 3.5000000000000001e-152

   1. Initial program 74.0%

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

   3. Taylor expanded in t around inf 86.2%

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

      1. associate--l+ 86.2%

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

      2. distribute-lft-out-- 86.2%

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

      3. div-sub 86.2%

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

      4. mul-1-neg 86.2%

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

      5. unsub-neg 86.2%

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

      6. div-sub 86.2%

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

      7. associate-/l* 87.5%

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

      8. associate-/l* 77.5%

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

      9. distribute-rgt-out-- 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in z around inf 85.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-49} \lor \neg \left(a \leq 3.5 \cdot 10^{-152}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+182}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+182)
   y
   (if (<= t -5.2e+40) (* x (/ (- z a) t)) (if (<= t 1.9e+115) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+182) {
		tmp = y;
	} else if (t <= -5.2e+40) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.9e+115) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.02d+182)) then
        tmp = y
    else if (t <= (-5.2d+40)) then
        tmp = x * ((z - a) / t)
    else if (t <= 1.9d+115) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+182) {
		tmp = y;
	} else if (t <= -5.2e+40) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.9e+115) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+182:
		tmp = y
	elif t <= -5.2e+40:
		tmp = x * ((z - a) / t)
	elif t <= 1.9e+115:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+182)
		tmp = y;
	elseif (t <= -5.2e+40)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 1.9e+115)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+182)
		tmp = y;
	elseif (t <= -5.2e+40)
		tmp = x * ((z - a) / t);
	elseif (t <= 1.9e+115)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+182], y, If[LessEqual[t, -5.2e+40], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+115], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e182 or 1.9e115 < t

   1. Initial program 27.0%

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

   3. Taylor expanded in t around inf 58.4%

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

   if -1.02e182 < t < -5.2000000000000001e40

   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 x around -inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

      3. +-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in t around -inf 56.7%

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

      1. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

   if -5.2000000000000001e40 < t < 1.9e115

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 34.7%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+182}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.34 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.34e+81)
   (* x (/ (- z a) t))
   (if (<= z 2.8e-102) x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.34e+81) {
		tmp = x * ((z - a) / t);
	} else if (z <= 2.8e-102) {
		tmp = x;
	} else {
		tmp = y * (z / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.34d+81)) then
        tmp = x * ((z - a) / t)
    else if (z <= 2.8d-102) then
        tmp = x
    else
        tmp = y * (z / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.34e+81) {
		tmp = x * ((z - a) / t);
	} else if (z <= 2.8e-102) {
		tmp = x;
	} else {
		tmp = y * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.34e+81:
		tmp = x * ((z - a) / t)
	elif z <= 2.8e-102:
		tmp = x
	else:
		tmp = y * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.34e+81)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (z <= 2.8e-102)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.34e+81)
		tmp = x * ((z - a) / t);
	elseif (z <= 2.8e-102)
		tmp = x;
	else
		tmp = y * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.34e+81], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-102], x, N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.33999999999999997e81

   1. Initial program 71.3%

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

   3. Taylor expanded in x around -inf 57.2%

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

      1. associate-*r* 57.2%

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

      2. neg-mul-1 57.2%

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

      3. +-commutative 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in t around -inf 38.3%

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

      1. associate-/l* 49.6%

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

   8. Simplified 49.6%

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

   if -1.33999999999999997e81 < z < 2.80000000000000013e-102

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf 41.2%

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

   if 2.80000000000000013e-102 < z

   1. Initial program 73.3%

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

      1. add-cube-cbrt 72.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right) \cdot \sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}} \]

      2. pow3 72.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}}\right)}^{3}} \]

      3. +-commutative 72.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x}}\right)}^{3} \]

      4. associate-/l* 89.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x}\right)}^{3} \]

      5. fma-undefine 89.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in z around inf 60.7%

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

      1. div-sub 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in y around inf 39.1%

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

      1. associate-/l* 43.7%

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

   10. Simplified 43.7%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.34 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+176)
   y
   (if (<= t -4.8e+38) (* x (/ z t)) (if (<= t 1.3e+115) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+176) {
		tmp = y;
	} else if (t <= -4.8e+38) {
		tmp = x * (z / t);
	} else if (t <= 1.3e+115) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.8d+176)) then
        tmp = y
    else if (t <= (-4.8d+38)) then
        tmp = x * (z / t)
    else if (t <= 1.3d+115) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+176) {
		tmp = y;
	} else if (t <= -4.8e+38) {
		tmp = x * (z / t);
	} else if (t <= 1.3e+115) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+176:
		tmp = y
	elif t <= -4.8e+38:
		tmp = x * (z / t)
	elif t <= 1.3e+115:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+176)
		tmp = y;
	elseif (t <= -4.8e+38)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 1.3e+115)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+176)
		tmp = y;
	elseif (t <= -4.8e+38)
		tmp = x * (z / t);
	elseif (t <= 1.3e+115)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+176], y, If[LessEqual[t, -4.8e+38], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+115], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000003e176 or 1.3e115 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -3.8000000000000003e176 < t < -4.80000000000000035e38

   1. Initial program 72.6%

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

   3. Taylor expanded in x around -inf 63.6%

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

      1. associate-*r* 63.6%

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

      2. neg-mul-1 63.6%

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

      3. +-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in a around 0 50.3%

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

      1. associate-/l* 54.8%

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

   8. Simplified 54.8%

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

   if -4.80000000000000035e38 < t < 1.3e115

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 34.7%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+172) y (if (<= t 1.7e+115) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+172) {
		tmp = y;
	} else if (t <= 1.7e+115) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.7d+172)) then
        tmp = y
    else if (t <= 1.7d+115) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+172) {
		tmp = y;
	} else if (t <= 1.7e+115) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+172:
		tmp = y
	elif t <= 1.7e+115:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+172)
		tmp = y;
	elseif (t <= 1.7e+115)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+172)
		tmp = y;
	elseif (t <= 1.7e+115)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+172], y, If[LessEqual[t, 1.7e+115], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e172 or 1.7e115 < t

   1. Initial program 26.7%

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

   3. Taylor expanded in t around inf 57.7%

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

   if -1.6999999999999999e172 < t < 1.7e115

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 32.3%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in a around inf 24.9%

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

4. Final simplification 24.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.4% 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 2024096 
(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))))