Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.0% → 89.8%

Time: 25.8s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -5e-181)
     (fma (- y z) t_1 x)
     (if (<= t_2 0.0) (+ t (/ (- a y) (/ z (- t x)))) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -5e-181) {
		tmp = fma((y - z), t_1, x);
	} else if (t_2 <= 0.0) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -5e-181)
		tmp = fma(Float64(y - z), t_1, x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-181], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000001e-181

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. fma-def 93.0%

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

   3. Simplified 93.0%

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

   if -5.0000000000000001e-181 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

      1. *-commutative 3.1%

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

      2. clear-num 3.7%

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

      3. flip-- 2.3%

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

      4. frac-times 1.7%

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

      5. *-un-lft-identity 1.7%

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

      6. pow2 1.7%

         \[\leadsto x + \frac{\color{blue}{{y}^{2}} - z \cdot z}{\frac{a - z}{t - x} \cdot \left(y + z\right)} \]

      7. pow2 1.7%

         \[\leadsto x + \frac{{y}^{2} - \color{blue}{{z}^{2}}}{\frac{a - z}{t - x} \cdot \left(y + z\right)} \]

   4. Applied egg-rr 1.7%

      \[\leadsto x + \color{blue}{\frac{{y}^{2} - {z}^{2}}{\frac{a - z}{t - x} \cdot \left(y + z\right)}} \]

   5. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 96.6%

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

      2. mul-1-neg 96.6%

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

      3. unsub-neg 96.6%

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

   7. Simplified 96.6%

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

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

   1. Initial program 92.2%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 45.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -5.2e+50)
     t
     (if (<= z -4.3e-116)
       t_1
       (if (<= z -2.65e-217)
         (/ y (/ a (- t x)))
         (if (<= z -3.3e-235)
           t_1
           (if (<= z 9.2e-265)
             (+ x (/ (* y t) a))
             (if (<= z 2.4e-24)
               (- x (/ x (/ a y)))
               (if (<= z 1.3e+125)
                 t
                 (if (<= z 5.3e+190) (/ t (/ a (- y z))) t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5.2e+50) {
		tmp = t;
	} else if (z <= -4.3e-116) {
		tmp = t_1;
	} else if (z <= -2.65e-217) {
		tmp = y / (a / (t - x));
	} else if (z <= -3.3e-235) {
		tmp = t_1;
	} else if (z <= 9.2e-265) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.4e-24) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.3e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t / (a / (y - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-5.2d+50)) then
        tmp = t
    else if (z <= (-4.3d-116)) then
        tmp = t_1
    else if (z <= (-2.65d-217)) then
        tmp = y / (a / (t - x))
    else if (z <= (-3.3d-235)) then
        tmp = t_1
    else if (z <= 9.2d-265) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.4d-24) then
        tmp = x - (x / (a / y))
    else if (z <= 1.3d+125) then
        tmp = t
    else if (z <= 5.3d+190) then
        tmp = t / (a / (y - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5.2e+50) {
		tmp = t;
	} else if (z <= -4.3e-116) {
		tmp = t_1;
	} else if (z <= -2.65e-217) {
		tmp = y / (a / (t - x));
	} else if (z <= -3.3e-235) {
		tmp = t_1;
	} else if (z <= 9.2e-265) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.4e-24) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.3e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t / (a / (y - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5.2e+50:
		tmp = t
	elif z <= -4.3e-116:
		tmp = t_1
	elif z <= -2.65e-217:
		tmp = y / (a / (t - x))
	elif z <= -3.3e-235:
		tmp = t_1
	elif z <= 9.2e-265:
		tmp = x + ((y * t) / a)
	elif z <= 2.4e-24:
		tmp = x - (x / (a / y))
	elif z <= 1.3e+125:
		tmp = t
	elif z <= 5.3e+190:
		tmp = t / (a / (y - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -5.2e+50)
		tmp = t;
	elseif (z <= -4.3e-116)
		tmp = t_1;
	elseif (z <= -2.65e-217)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= -3.3e-235)
		tmp = t_1;
	elseif (z <= 9.2e-265)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.4e-24)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 1.3e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -5.2e+50)
		tmp = t;
	elseif (z <= -4.3e-116)
		tmp = t_1;
	elseif (z <= -2.65e-217)
		tmp = y / (a / (t - x));
	elseif (z <= -3.3e-235)
		tmp = t_1;
	elseif (z <= 9.2e-265)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.4e-24)
		tmp = x - (x / (a / y));
	elseif (z <= 1.3e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = t / (a / (y - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+50], t, If[LessEqual[z, -4.3e-116], t$95$1, If[LessEqual[z, -2.65e-217], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-235], t$95$1, If[LessEqual[z, 9.2e-265], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-24], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+125], t, If[LessEqual[z, 5.3e+190], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.2000000000000004e50 or 2.3999999999999998e-24 < z < 1.30000000000000002e125 or 5.30000000000000015e190 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 53.3%

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

   if -5.2000000000000004e50 < z < -4.2999999999999997e-116 or -2.65e-217 < z < -3.30000000000000028e-235

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 69.4%

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

   4. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

   6. Simplified 62.9%

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

   if -4.2999999999999997e-116 < z < -2.65e-217

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. div-sub 78.6%

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

      2. associate-*r/ 73.1%

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

      3. associate-/l* 78.7%

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

      4. associate-/r/ 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in a around inf 57.5%

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

      1. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if -3.30000000000000028e-235 < z < 9.1999999999999996e-265

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in t around inf 77.0%

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

   if 9.1999999999999996e-265 < z < 2.3999999999999998e-24

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 68.8%

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

   4. Taylor expanded in t around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-/l* 55.4%

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

   6. Simplified 55.4%

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

   if 1.30000000000000002e125 < z < 5.30000000000000015e190

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in a around inf 41.5%

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

      1. associate-/l* 52.4%

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

   8. Simplified 52.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-181} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-181) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (- a y) (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-181) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((a - y) / (z / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-181)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((a - y) / (z / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-181) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((a - y) / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-181) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((a - y) / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-181) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-181) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((a - y) / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-181], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000001e-181 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.7%

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

   if -5.0000000000000001e-181 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

      1. *-commutative 3.1%

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

      2. clear-num 3.7%

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

      3. flip-- 2.3%

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

      4. frac-times 1.7%

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

      5. *-un-lft-identity 1.7%

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

      6. pow2 1.7%

         \[\leadsto x + \frac{\color{blue}{{y}^{2}} - z \cdot z}{\frac{a - z}{t - x} \cdot \left(y + z\right)} \]

      7. pow2 1.7%

         \[\leadsto x + \frac{{y}^{2} - \color{blue}{{z}^{2}}}{\frac{a - z}{t - x} \cdot \left(y + z\right)} \]

   4. Applied egg-rr 1.7%

      \[\leadsto x + \color{blue}{\frac{{y}^{2} - {z}^{2}}{\frac{a - z}{t - x} \cdot \left(y + z\right)}} \]

   5. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 96.6%

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

      2. mul-1-neg 96.6%

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

      3. unsub-neg 96.6%

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

   7. Simplified 96.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-181} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := \frac{-x}{\frac{a - z}{y}}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+123}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-188}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-157}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 0.0033:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (/ (- x) (/ (- a z) y))))
   (if (<= a -1.45e+153)
     t_2
     (if (<= a -2e+123)
       (/ (- t) (+ (/ a z) -1.0))
       (if (<= a -7e-77)
         t_2
         (if (<= a -4.2e-188)
           t_3
           (if (<= a 9.5e-219)
             t_1
             (if (<= a 1.06e-157) t_3 (if (<= a 0.0033) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x + (t / (a / y));
	double t_3 = -x / ((a - z) / y);
	double tmp;
	if (a <= -1.45e+153) {
		tmp = t_2;
	} else if (a <= -2e+123) {
		tmp = -t / ((a / z) + -1.0);
	} else if (a <= -7e-77) {
		tmp = t_2;
	} else if (a <= -4.2e-188) {
		tmp = t_3;
	} else if (a <= 9.5e-219) {
		tmp = t_1;
	} else if (a <= 1.06e-157) {
		tmp = t_3;
	} else if (a <= 0.0033) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x + (t / (a / y))
    t_3 = -x / ((a - z) / y)
    if (a <= (-1.45d+153)) then
        tmp = t_2
    else if (a <= (-2d+123)) then
        tmp = -t / ((a / z) + (-1.0d0))
    else if (a <= (-7d-77)) then
        tmp = t_2
    else if (a <= (-4.2d-188)) then
        tmp = t_3
    else if (a <= 9.5d-219) then
        tmp = t_1
    else if (a <= 1.06d-157) then
        tmp = t_3
    else if (a <= 0.0033d0) 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 = -t / (z / (y - z));
	double t_2 = x + (t / (a / y));
	double t_3 = -x / ((a - z) / y);
	double tmp;
	if (a <= -1.45e+153) {
		tmp = t_2;
	} else if (a <= -2e+123) {
		tmp = -t / ((a / z) + -1.0);
	} else if (a <= -7e-77) {
		tmp = t_2;
	} else if (a <= -4.2e-188) {
		tmp = t_3;
	} else if (a <= 9.5e-219) {
		tmp = t_1;
	} else if (a <= 1.06e-157) {
		tmp = t_3;
	} else if (a <= 0.0033) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x + (t / (a / y))
	t_3 = -x / ((a - z) / y)
	tmp = 0
	if a <= -1.45e+153:
		tmp = t_2
	elif a <= -2e+123:
		tmp = -t / ((a / z) + -1.0)
	elif a <= -7e-77:
		tmp = t_2
	elif a <= -4.2e-188:
		tmp = t_3
	elif a <= 9.5e-219:
		tmp = t_1
	elif a <= 1.06e-157:
		tmp = t_3
	elif a <= 0.0033:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(Float64(-x) / Float64(Float64(a - z) / y))
	tmp = 0.0
	if (a <= -1.45e+153)
		tmp = t_2;
	elseif (a <= -2e+123)
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	elseif (a <= -7e-77)
		tmp = t_2;
	elseif (a <= -4.2e-188)
		tmp = t_3;
	elseif (a <= 9.5e-219)
		tmp = t_1;
	elseif (a <= 1.06e-157)
		tmp = t_3;
	elseif (a <= 0.0033)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x + (t / (a / y));
	t_3 = -x / ((a - z) / y);
	tmp = 0.0;
	if (a <= -1.45e+153)
		tmp = t_2;
	elseif (a <= -2e+123)
		tmp = -t / ((a / z) + -1.0);
	elseif (a <= -7e-77)
		tmp = t_2;
	elseif (a <= -4.2e-188)
		tmp = t_3;
	elseif (a <= 9.5e-219)
		tmp = t_1;
	elseif (a <= 1.06e-157)
		tmp = t_3;
	elseif (a <= 0.0033)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+153], t$95$2, If[LessEqual[a, -2e+123], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-77], t$95$2, If[LessEqual[a, -4.2e-188], t$95$3, If[LessEqual[a, 9.5e-219], t$95$1, If[LessEqual[a, 1.06e-157], t$95$3, If[LessEqual[a, 0.0033], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45000000000000001e153 or -1.99999999999999996e123 < a < -7.00000000000000026e-77 or 0.0033 < a

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 59.1%

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

   4. Taylor expanded in t around inf 51.3%

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

      1. associate-/l* 55.8%

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

   6. Simplified 55.8%

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

   if -1.45000000000000001e153 < a < -1.99999999999999996e123

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 31.8%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around 0 31.8%

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

      1. mul-1-neg 31.8%

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

      2. associate-/l* 72.3%

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

      3. distribute-neg-frac 72.3%

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

      4. div-sub 72.3%

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

      5. sub-neg 72.3%

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

      6. *-inverses 72.3%

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

      7. metadata-eval 72.3%

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

   8. Simplified 72.3%

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

   if -7.00000000000000026e-77 < a < -4.1999999999999998e-188 or 9.4999999999999997e-219 < a < 1.06e-157

   1. Initial program 69.6%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. div-sub 66.8%

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

      2. associate-*r/ 63.7%

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

      3. associate-/l* 68.0%

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

      4. associate-/r/ 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. associate-/l* 60.8%

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

      3. distribute-neg-frac 60.8%

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

   8. Simplified 60.8%

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

   if -4.1999999999999998e-188 < a < 9.4999999999999997e-219 or 1.06e-157 < a < 0.0033

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 51.6%

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

      1. associate-/l* 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in a around 0 45.8%

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

      1. mul-1-neg 45.8%

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

      2. associate-/l* 71.9%

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

      3. distribute-neg-frac 71.9%

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

   8. Simplified 71.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+123}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-219}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-157}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 0.0033:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-61}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= z -6.8e+50)
     (* t (/ (- y z) (- a z)))
     (if (<= z -9.2e-108)
       (+ x (/ (* y (- t x)) a))
       (if (<= z -2.5e-203)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 3.2e-133)
           t_1
           (if (<= z 1.12e-61)
             (* (- t x) (/ y (- a z)))
             (if (<= z 5.7e-5) t_1 (+ t (/ (- a y) (/ z (- t x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (z <= -6.8e+50) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -9.2e-108) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= -2.5e-203) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 3.2e-133) {
		tmp = t_1;
	} else if (z <= 1.12e-61) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 5.7e-5) {
		tmp = t_1;
	} else {
		tmp = t + ((a - y) / (z / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (z <= (-6.8d+50)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-9.2d-108)) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= (-2.5d-203)) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 3.2d-133) then
        tmp = t_1
    else if (z <= 1.12d-61) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 5.7d-5) then
        tmp = t_1
    else
        tmp = t + ((a - y) / (z / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (z <= -6.8e+50) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -9.2e-108) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= -2.5e-203) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 3.2e-133) {
		tmp = t_1;
	} else if (z <= 1.12e-61) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 5.7e-5) {
		tmp = t_1;
	} else {
		tmp = t + ((a - y) / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if z <= -6.8e+50:
		tmp = t * ((y - z) / (a - z))
	elif z <= -9.2e-108:
		tmp = x + ((y * (t - x)) / a)
	elif z <= -2.5e-203:
		tmp = y / ((a - z) / (t - x))
	elif z <= 3.2e-133:
		tmp = t_1
	elif z <= 1.12e-61:
		tmp = (t - x) * (y / (a - z))
	elif z <= 5.7e-5:
		tmp = t_1
	else:
		tmp = t + ((a - y) / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (z <= -6.8e+50)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -9.2e-108)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= -2.5e-203)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 3.2e-133)
		tmp = t_1;
	elseif (z <= 1.12e-61)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 5.7e-5)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (z <= -6.8e+50)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -9.2e-108)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= -2.5e-203)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 3.2e-133)
		tmp = t_1;
	elseif (z <= 1.12e-61)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 5.7e-5)
		tmp = t_1;
	else
		tmp = t + ((a - y) / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+50], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e-108], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-203], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-133], t$95$1, If[LessEqual[z, 1.12e-61], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-5], t$95$1, N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.7999999999999997e50

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 44.9%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in t around 0 44.9%

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

      1. associate-*r/ 81.2%

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

   8. Simplified 81.2%

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

   if -6.7999999999999997e50 < z < -9.19999999999999983e-108

   1. Initial program 88.8%

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

   3. Taylor expanded in z around 0 67.1%

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

   if -9.19999999999999983e-108 < z < -2.5000000000000001e-203

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 78.0%

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

      1. div-sub 78.0%

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

      2. associate-*r/ 72.5%

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

      3. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   if -2.5000000000000001e-203 < z < 3.20000000000000013e-133 or 1.12000000000000001e-61 < z < 5.7000000000000003e-5

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   if 3.20000000000000013e-133 < z < 1.12000000000000001e-61

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. div-sub 75.4%

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

      2. associate-*r/ 75.6%

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

      3. associate-/l* 77.9%

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

      4. associate-/r/ 80.0%

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

   5. Simplified 80.0%

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

   if 5.7000000000000003e-5 < z

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. clear-num 73.7%

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

      3. flip-- 40.8%

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

      4. frac-times 39.9%

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

      5. *-un-lft-identity 39.9%

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

      6. pow2 39.9%

         \[\leadsto x + \frac{\color{blue}{{y}^{2}} - z \cdot z}{\frac{a - z}{t - x} \cdot \left(y + z\right)} \]

      7. pow2 39.9%

         \[\leadsto x + \frac{{y}^{2} - \color{blue}{{z}^{2}}}{\frac{a - z}{t - x} \cdot \left(y + z\right)} \]

   4. Applied egg-rr 39.9%

      \[\leadsto x + \color{blue}{\frac{{y}^{2} - {z}^{2}}{\frac{a - z}{t - x} \cdot \left(y + z\right)}} \]

   5. Taylor expanded in z around inf 64.1%

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

      1. associate-/l* 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

   7. Simplified 76.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-61}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 12000000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (/ a y))))
   (if (<= z -1.75e+20)
     t
     (if (<= z -6.6e-108)
       x
       (if (<= z -9.8e-233)
         t_1
         (if (<= z 1.25e-288)
           x
           (if (<= z 1.1e-144)
             t_1
             (if (<= z 6e-135) x (if (<= z 12000000.0) (/ (* x y) z) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (a / y);
	double tmp;
	if (z <= -1.75e+20) {
		tmp = t;
	} else if (z <= -6.6e-108) {
		tmp = x;
	} else if (z <= -9.8e-233) {
		tmp = t_1;
	} else if (z <= 1.25e-288) {
		tmp = x;
	} else if (z <= 1.1e-144) {
		tmp = t_1;
	} else if (z <= 6e-135) {
		tmp = x;
	} else if (z <= 12000000.0) {
		tmp = (x * y) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (a / y)
    if (z <= (-1.75d+20)) then
        tmp = t
    else if (z <= (-6.6d-108)) then
        tmp = x
    else if (z <= (-9.8d-233)) then
        tmp = t_1
    else if (z <= 1.25d-288) then
        tmp = x
    else if (z <= 1.1d-144) then
        tmp = t_1
    else if (z <= 6d-135) then
        tmp = x
    else if (z <= 12000000.0d0) then
        tmp = (x * y) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (a / y);
	double tmp;
	if (z <= -1.75e+20) {
		tmp = t;
	} else if (z <= -6.6e-108) {
		tmp = x;
	} else if (z <= -9.8e-233) {
		tmp = t_1;
	} else if (z <= 1.25e-288) {
		tmp = x;
	} else if (z <= 1.1e-144) {
		tmp = t_1;
	} else if (z <= 6e-135) {
		tmp = x;
	} else if (z <= 12000000.0) {
		tmp = (x * y) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (a / y)
	tmp = 0
	if z <= -1.75e+20:
		tmp = t
	elif z <= -6.6e-108:
		tmp = x
	elif z <= -9.8e-233:
		tmp = t_1
	elif z <= 1.25e-288:
		tmp = x
	elif z <= 1.1e-144:
		tmp = t_1
	elif z <= 6e-135:
		tmp = x
	elif z <= 12000000.0:
		tmp = (x * y) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(a / y))
	tmp = 0.0
	if (z <= -1.75e+20)
		tmp = t;
	elseif (z <= -6.6e-108)
		tmp = x;
	elseif (z <= -9.8e-233)
		tmp = t_1;
	elseif (z <= 1.25e-288)
		tmp = x;
	elseif (z <= 1.1e-144)
		tmp = t_1;
	elseif (z <= 6e-135)
		tmp = x;
	elseif (z <= 12000000.0)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (a / y);
	tmp = 0.0;
	if (z <= -1.75e+20)
		tmp = t;
	elseif (z <= -6.6e-108)
		tmp = x;
	elseif (z <= -9.8e-233)
		tmp = t_1;
	elseif (z <= 1.25e-288)
		tmp = x;
	elseif (z <= 1.1e-144)
		tmp = t_1;
	elseif (z <= 6e-135)
		tmp = x;
	elseif (z <= 12000000.0)
		tmp = (x * y) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+20], t, If[LessEqual[z, -6.6e-108], x, If[LessEqual[z, -9.8e-233], t$95$1, If[LessEqual[z, 1.25e-288], x, If[LessEqual[z, 1.1e-144], t$95$1, If[LessEqual[z, 6e-135], x, If[LessEqual[z, 12000000.0], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.75e20 or 1.2e7 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 47.8%

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

   if -1.75e20 < z < -6.6000000000000004e-108 or -9.7999999999999999e-233 < z < 1.25000000000000003e-288 or 1.10000000000000003e-144 < z < 6.00000000000000024e-135

   1. Initial program 90.5%

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

   3. Taylor expanded in a around inf 52.6%

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

   if -6.6000000000000004e-108 < z < -9.7999999999999999e-233 or 1.25000000000000003e-288 < z < 1.10000000000000003e-144

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 68.6%

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

   4. Taylor expanded in x around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

   6. Simplified 52.1%

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

   7. Taylor expanded in y around inf 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/l* 41.5%

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

      3. distribute-neg-frac 41.5%

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

   9. Simplified 41.5%

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

   if 6.00000000000000024e-135 < z < 1.2e7

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

      2. associate-*r/ 66.0%

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

      3. associate-/l* 67.4%

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

      4. associate-/r/ 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 44.5%

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

      3. distribute-neg-frac 44.5%

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

   8. Simplified 44.5%

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

   9. Taylor expanded in a around 0 41.1%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-144}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 12000000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-48}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+51)
   (* t (/ (- y z) (- a z)))
   (if (<= z -2e-108)
     (+ x (/ (* y (- t x)) a))
     (if (<= z -5.3e-204)
       (/ y (/ (- a z) (- t x)))
       (if (<= z 1.45e-133)
         (+ x (/ y (/ a (- t x))))
         (if (<= z 6e-48)
           (* (- t x) (/ y (- a z)))
           (if (<= z 2.25e-29)
             (- x (/ x (/ a y)))
             (- t (/ (- t x) (/ z y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+51) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -2e-108) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= -5.3e-204) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.45e-133) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 6e-48) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 2.25e-29) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+51)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-2d-108)) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= (-5.3d-204)) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 1.45d-133) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 6d-48) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 2.25d-29) then
        tmp = x - (x / (a / y))
    else
        tmp = t - ((t - x) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+51) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -2e-108) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= -5.3e-204) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.45e-133) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 6e-48) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 2.25e-29) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+51:
		tmp = t * ((y - z) / (a - z))
	elif z <= -2e-108:
		tmp = x + ((y * (t - x)) / a)
	elif z <= -5.3e-204:
		tmp = y / ((a - z) / (t - x))
	elif z <= 1.45e-133:
		tmp = x + (y / (a / (t - x)))
	elif z <= 6e-48:
		tmp = (t - x) * (y / (a - z))
	elif z <= 2.25e-29:
		tmp = x - (x / (a / y))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+51)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -2e-108)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= -5.3e-204)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 1.45e-133)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 6e-48)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 2.25e-29)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+51)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -2e-108)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= -5.3e-204)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 1.45e-133)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 6e-48)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 2.25e-29)
		tmp = x - (x / (a / y));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+51], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-108], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-204], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-133], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-48], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-29], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -4.2000000000000002e51

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 44.9%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in t around 0 44.9%

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

      1. associate-*r/ 81.2%

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

   8. Simplified 81.2%

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

   if -4.2000000000000002e51 < z < -2.00000000000000008e-108

   1. Initial program 88.8%

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

   3. Taylor expanded in z around 0 67.1%

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

   if -2.00000000000000008e-108 < z < -5.2999999999999997e-204

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 78.0%

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

      1. div-sub 78.0%

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

      2. associate-*r/ 72.5%

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

      3. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   if -5.2999999999999997e-204 < z < 1.4499999999999999e-133

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 82.6%

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

      1. associate-/l* 84.9%

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

   5. Simplified 84.9%

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

   if 1.4499999999999999e-133 < z < 5.9999999999999998e-48

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. div-sub 75.4%

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

      2. associate-*r/ 75.6%

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

      3. associate-/l* 77.9%

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

      4. associate-/r/ 80.0%

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

   5. Simplified 80.0%

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

   if 5.9999999999999998e-48 < z < 2.2499999999999999e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 2.2499999999999999e-29 < z

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. distribute-lft-out-- 62.8%

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

      3. div-sub 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. distribute-rgt-out-- 62.8%

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

      7. associate-/l* 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around inf 71.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-48}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := \frac{-t}{\frac{a}{z} + -1}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-223}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (/ (- t) (+ (/ a z) -1.0))))
   (if (<= z -6.6e+50)
     t_2
     (if (<= z -1.8e-114)
       t_1
       (if (<= z -3.15e-223)
         (/ y (/ a (- t x)))
         (if (<= z -1.05e-233)
           t_1
           (if (<= z 2.9e-265)
             (+ x (/ (* y t) a))
             (if (<= z 6.8e-26) (- x (/ x (/ a y))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -6.6e+50) {
		tmp = t_2;
	} else if (z <= -1.8e-114) {
		tmp = t_1;
	} else if (z <= -3.15e-223) {
		tmp = y / (a / (t - x));
	} else if (z <= -1.05e-233) {
		tmp = t_1;
	} else if (z <= 2.9e-265) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.8e-26) {
		tmp = x - (x / (a / y));
	} 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 * (1.0d0 - (y / a))
    t_2 = -t / ((a / z) + (-1.0d0))
    if (z <= (-6.6d+50)) then
        tmp = t_2
    else if (z <= (-1.8d-114)) then
        tmp = t_1
    else if (z <= (-3.15d-223)) then
        tmp = y / (a / (t - x))
    else if (z <= (-1.05d-233)) then
        tmp = t_1
    else if (z <= 2.9d-265) then
        tmp = x + ((y * t) / a)
    else if (z <= 6.8d-26) then
        tmp = x - (x / (a / y))
    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 * (1.0 - (y / a));
	double t_2 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -6.6e+50) {
		tmp = t_2;
	} else if (z <= -1.8e-114) {
		tmp = t_1;
	} else if (z <= -3.15e-223) {
		tmp = y / (a / (t - x));
	} else if (z <= -1.05e-233) {
		tmp = t_1;
	} else if (z <= 2.9e-265) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.8e-26) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = -t / ((a / z) + -1.0)
	tmp = 0
	if z <= -6.6e+50:
		tmp = t_2
	elif z <= -1.8e-114:
		tmp = t_1
	elif z <= -3.15e-223:
		tmp = y / (a / (t - x))
	elif z <= -1.05e-233:
		tmp = t_1
	elif z <= 2.9e-265:
		tmp = x + ((y * t) / a)
	elif z <= 6.8e-26:
		tmp = x - (x / (a / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0))
	tmp = 0.0
	if (z <= -6.6e+50)
		tmp = t_2;
	elseif (z <= -1.8e-114)
		tmp = t_1;
	elseif (z <= -3.15e-223)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= -1.05e-233)
		tmp = t_1;
	elseif (z <= 2.9e-265)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 6.8e-26)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = -t / ((a / z) + -1.0);
	tmp = 0.0;
	if (z <= -6.6e+50)
		tmp = t_2;
	elseif (z <= -1.8e-114)
		tmp = t_1;
	elseif (z <= -3.15e-223)
		tmp = y / (a / (t - x));
	elseif (z <= -1.05e-233)
		tmp = t_1;
	elseif (z <= 2.9e-265)
		tmp = x + ((y * t) / a);
	elseif (z <= 6.8e-26)
		tmp = x - (x / (a / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+50], t$95$2, If[LessEqual[z, -1.8e-114], t$95$1, If[LessEqual[z, -3.15e-223], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e-233], t$95$1, If[LessEqual[z, 2.9e-265], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-26], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.6000000000000001e50 or 6.80000000000000026e-26 < z

   1. Initial program 71.7%

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

   3. Taylor expanded in x around 0 39.6%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around 0 33.6%

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

      1. mul-1-neg 33.6%

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

      2. associate-/l* 60.0%

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

      3. distribute-neg-frac 60.0%

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

      4. div-sub 60.0%

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

      5. sub-neg 60.0%

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

      6. *-inverses 60.0%

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

      7. metadata-eval 60.0%

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

   8. Simplified 60.0%

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

   if -6.6000000000000001e50 < z < -1.80000000000000009e-114 or -3.14999999999999993e-223 < z < -1.0499999999999999e-233

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 69.4%

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

   4. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

   6. Simplified 62.9%

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

   if -1.80000000000000009e-114 < z < -3.14999999999999993e-223

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. div-sub 78.6%

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

      2. associate-*r/ 73.1%

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

      3. associate-/l* 78.7%

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

      4. associate-/r/ 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in a around inf 57.5%

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

      1. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if -1.0499999999999999e-233 < z < 2.89999999999999975e-265

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in t around inf 77.0%

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

   if 2.89999999999999975e-265 < z < 6.80000000000000026e-26

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 68.8%

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

   4. Taylor expanded in t around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-/l* 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-223}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.1e+50)
   t
   (if (<= z -4.4e-234)
     (* x (- 1.0 (/ y a)))
     (if (<= z 8.2e-266)
       (+ x (/ (* y t) a))
       (if (<= z 2.25e-24)
         (- x (/ x (/ a y)))
         (if (<= z 1.65e+125)
           t
           (if (<= z 5.3e+190) (/ t (/ a (- y z))) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.1e+50) {
		tmp = t;
	} else if (z <= -4.4e-234) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.2e-266) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.25e-24) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.65e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t / (a / (y - z));
	} else {
		tmp = 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 <= (-6.1d+50)) then
        tmp = t
    else if (z <= (-4.4d-234)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8.2d-266) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.25d-24) then
        tmp = x - (x / (a / y))
    else if (z <= 1.65d+125) then
        tmp = t
    else if (z <= 5.3d+190) then
        tmp = t / (a / (y - z))
    else
        tmp = 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 <= -6.1e+50) {
		tmp = t;
	} else if (z <= -4.4e-234) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.2e-266) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.25e-24) {
		tmp = x - (x / (a / y));
	} else if (z <= 1.65e+125) {
		tmp = t;
	} else if (z <= 5.3e+190) {
		tmp = t / (a / (y - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.1e+50:
		tmp = t
	elif z <= -4.4e-234:
		tmp = x * (1.0 - (y / a))
	elif z <= 8.2e-266:
		tmp = x + ((y * t) / a)
	elif z <= 2.25e-24:
		tmp = x - (x / (a / y))
	elif z <= 1.65e+125:
		tmp = t
	elif z <= 5.3e+190:
		tmp = t / (a / (y - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.1e+50)
		tmp = t;
	elseif (z <= -4.4e-234)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8.2e-266)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.25e-24)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 1.65e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.1e+50)
		tmp = t;
	elseif (z <= -4.4e-234)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8.2e-266)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.25e-24)
		tmp = x - (x / (a / y));
	elseif (z <= 1.65e+125)
		tmp = t;
	elseif (z <= 5.3e+190)
		tmp = t / (a / (y - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.1e+50], t, If[LessEqual[z, -4.4e-234], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-266], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-24], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+125], t, If[LessEqual[z, 5.3e+190], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.10000000000000026e50 or 2.2499999999999999e-24 < z < 1.65000000000000003e125 or 5.30000000000000015e190 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 53.3%

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

   if -6.10000000000000026e50 < z < -4.3999999999999998e-234

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 67.3%

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

   4. Taylor expanded in x around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   6. Simplified 56.0%

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

   if -4.3999999999999998e-234 < z < 8.2000000000000006e-266

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in t around inf 77.0%

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

   if 8.2000000000000006e-266 < z < 2.2499999999999999e-24

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 68.8%

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

   4. Taylor expanded in t around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-/l* 55.4%

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

   6. Simplified 55.4%

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

   if 1.65000000000000003e125 < z < 5.30000000000000015e190

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in a around inf 41.5%

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

      1. associate-/l* 52.4%

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

   8. Simplified 52.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-271}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 135000000:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+14)
   t
   (if (<= z -1.3e-115)
     x
     (if (<= z -2.8e-271)
       (/ t (/ a y))
       (if (<= z 5.8e-135) x (if (<= z 135000000.0) (/ x (/ z y)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+14) {
		tmp = t;
	} else if (z <= -1.3e-115) {
		tmp = x;
	} else if (z <= -2.8e-271) {
		tmp = t / (a / y);
	} else if (z <= 5.8e-135) {
		tmp = x;
	} else if (z <= 135000000.0) {
		tmp = x / (z / y);
	} else {
		tmp = 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 <= (-4.3d+14)) then
        tmp = t
    else if (z <= (-1.3d-115)) then
        tmp = x
    else if (z <= (-2.8d-271)) then
        tmp = t / (a / y)
    else if (z <= 5.8d-135) then
        tmp = x
    else if (z <= 135000000.0d0) then
        tmp = x / (z / y)
    else
        tmp = 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 <= -4.3e+14) {
		tmp = t;
	} else if (z <= -1.3e-115) {
		tmp = x;
	} else if (z <= -2.8e-271) {
		tmp = t / (a / y);
	} else if (z <= 5.8e-135) {
		tmp = x;
	} else if (z <= 135000000.0) {
		tmp = x / (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+14:
		tmp = t
	elif z <= -1.3e-115:
		tmp = x
	elif z <= -2.8e-271:
		tmp = t / (a / y)
	elif z <= 5.8e-135:
		tmp = x
	elif z <= 135000000.0:
		tmp = x / (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+14)
		tmp = t;
	elseif (z <= -1.3e-115)
		tmp = x;
	elseif (z <= -2.8e-271)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 5.8e-135)
		tmp = x;
	elseif (z <= 135000000.0)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+14)
		tmp = t;
	elseif (z <= -1.3e-115)
		tmp = x;
	elseif (z <= -2.8e-271)
		tmp = t / (a / y);
	elseif (z <= 5.8e-135)
		tmp = x;
	elseif (z <= 135000000.0)
		tmp = x / (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+14], t, If[LessEqual[z, -1.3e-115], x, If[LessEqual[z, -2.8e-271], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-135], x, If[LessEqual[z, 135000000.0], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3e14 or 1.35e8 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 47.8%

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

   if -4.3e14 < z < -1.30000000000000002e-115 or -2.7999999999999997e-271 < z < 5.8000000000000004e-135

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 40.0%

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

   if -1.30000000000000002e-115 < z < -2.7999999999999997e-271

   1. Initial program 94.0%

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

   3. Taylor expanded in y around -inf 71.1%

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

   4. Taylor expanded in t around inf 38.9%

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

   5. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 45.7%

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

   7. Simplified 45.7%

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

   if 5.8000000000000004e-135 < z < 1.35e8

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

      2. associate-*r/ 66.0%

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

      3. associate-/l* 67.4%

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

      4. associate-/r/ 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 44.5%

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

      3. distribute-neg-frac 44.5%

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

   8. Simplified 44.5%

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

   9. Taylor expanded in a around 0 41.1%

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

       1. associate-/l* 41.1%

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

   11. Simplified 41.1%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-271}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 135000000:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -76000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-274}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 255000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -76000.0)
   t
   (if (<= z -2.9e-117)
     x
     (if (<= z -6e-274)
       (/ t (/ a y))
       (if (<= z 7.8e-135) x (if (<= z 255000.0) (/ (* x y) z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -76000.0) {
		tmp = t;
	} else if (z <= -2.9e-117) {
		tmp = x;
	} else if (z <= -6e-274) {
		tmp = t / (a / y);
	} else if (z <= 7.8e-135) {
		tmp = x;
	} else if (z <= 255000.0) {
		tmp = (x * y) / z;
	} else {
		tmp = 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 <= (-76000.0d0)) then
        tmp = t
    else if (z <= (-2.9d-117)) then
        tmp = x
    else if (z <= (-6d-274)) then
        tmp = t / (a / y)
    else if (z <= 7.8d-135) then
        tmp = x
    else if (z <= 255000.0d0) then
        tmp = (x * y) / z
    else
        tmp = 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 <= -76000.0) {
		tmp = t;
	} else if (z <= -2.9e-117) {
		tmp = x;
	} else if (z <= -6e-274) {
		tmp = t / (a / y);
	} else if (z <= 7.8e-135) {
		tmp = x;
	} else if (z <= 255000.0) {
		tmp = (x * y) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -76000.0:
		tmp = t
	elif z <= -2.9e-117:
		tmp = x
	elif z <= -6e-274:
		tmp = t / (a / y)
	elif z <= 7.8e-135:
		tmp = x
	elif z <= 255000.0:
		tmp = (x * y) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -76000.0)
		tmp = t;
	elseif (z <= -2.9e-117)
		tmp = x;
	elseif (z <= -6e-274)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 7.8e-135)
		tmp = x;
	elseif (z <= 255000.0)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -76000.0)
		tmp = t;
	elseif (z <= -2.9e-117)
		tmp = x;
	elseif (z <= -6e-274)
		tmp = t / (a / y);
	elseif (z <= 7.8e-135)
		tmp = x;
	elseif (z <= 255000.0)
		tmp = (x * y) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -76000.0], t, If[LessEqual[z, -2.9e-117], x, If[LessEqual[z, -6e-274], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-135], x, If[LessEqual[z, 255000.0], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -76000 or 255000 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 47.8%

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

   if -76000 < z < -2.9000000000000001e-117 or -5.99999999999999954e-274 < z < 7.80000000000000043e-135

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 40.0%

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

   if -2.9000000000000001e-117 < z < -5.99999999999999954e-274

   1. Initial program 94.0%

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

   3. Taylor expanded in y around -inf 71.1%

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

   4. Taylor expanded in t around inf 38.9%

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

   5. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 45.7%

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

   7. Simplified 45.7%

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

   if 7.80000000000000043e-135 < z < 255000

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

      2. associate-*r/ 66.0%

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

      3. associate-/l* 67.4%

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

      4. associate-/r/ 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 44.5%

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

      3. distribute-neg-frac 44.5%

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

   8. Simplified 44.5%

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

   9. Taylor expanded in a around 0 41.1%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -76000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-274}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 255000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -3.4e+58)
     t_2
     (if (<= t -2.45e-235)
       t_1
       (if (<= t 8.5e-231)
         (* x (- 1.0 (/ y a)))
         (if (<= t 1.3e+42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.4e+58) {
		tmp = t_2;
	} else if (t <= -2.45e-235) {
		tmp = t_1;
	} else if (t <= 8.5e-231) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.3e+42) {
		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 = (t - x) * (y / (a - z))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-3.4d+58)) then
        tmp = t_2
    else if (t <= (-2.45d-235)) then
        tmp = t_1
    else if (t <= 8.5d-231) then
        tmp = x * (1.0d0 - (y / a))
    else if (t <= 1.3d+42) 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 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.4e+58) {
		tmp = t_2;
	} else if (t <= -2.45e-235) {
		tmp = t_1;
	} else if (t <= 8.5e-231) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.3e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3.4e+58:
		tmp = t_2
	elif t <= -2.45e-235:
		tmp = t_1
	elif t <= 8.5e-231:
		tmp = x * (1.0 - (y / a))
	elif t <= 1.3e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3.4e+58)
		tmp = t_2;
	elseif (t <= -2.45e-235)
		tmp = t_1;
	elseif (t <= 8.5e-231)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (t <= 1.3e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3.4e+58)
		tmp = t_2;
	elseif (t <= -2.45e-235)
		tmp = t_1;
	elseif (t <= 8.5e-231)
		tmp = x * (1.0 - (y / a));
	elseif (t <= 1.3e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+58], t$95$2, If[LessEqual[t, -2.45e-235], t$95$1, If[LessEqual[t, 8.5e-231], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4000000000000001e58 or 1.29999999999999995e42 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0 49.1%

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

      1. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around 0 49.1%

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

      1. associate-*r/ 81.5%

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

   8. Simplified 81.5%

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

   if -3.4000000000000001e58 < t < -2.44999999999999983e-235 or 8.5e-231 < t < 1.29999999999999995e42

   1. Initial program 73.8%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. div-sub 59.0%

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

      2. associate-*r/ 55.8%

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

      3. associate-/l* 59.6%

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

      4. associate-/r/ 59.1%

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

   5. Simplified 59.1%

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

   if -2.44999999999999983e-235 < t < 8.5e-231

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0 68.2%

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

   4. Taylor expanded in x around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-235}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+42}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-57}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -9e+52)
     t_1
     (if (<= z 3.1e-133)
       (+ x (/ y (/ a (- t x))))
       (if (<= z 1.95e-57)
         (* (- t x) (/ y (- a z)))
         (if (<= z 2.2e-29) (- x (/ x (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9e+52) {
		tmp = t_1;
	} else if (z <= 3.1e-133) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1.95e-57) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 2.2e-29) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-9d+52)) then
        tmp = t_1
    else if (z <= 3.1d-133) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 1.95d-57) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 2.2d-29) then
        tmp = x - (x / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9e+52) {
		tmp = t_1;
	} else if (z <= 3.1e-133) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1.95e-57) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 2.2e-29) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -9e+52:
		tmp = t_1
	elif z <= 3.1e-133:
		tmp = x + (y / (a / (t - x)))
	elif z <= 1.95e-57:
		tmp = (t - x) * (y / (a - z))
	elif z <= 2.2e-29:
		tmp = x - (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -9e+52)
		tmp = t_1;
	elseif (z <= 3.1e-133)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 1.95e-57)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 2.2e-29)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -9e+52)
		tmp = t_1;
	elseif (z <= 3.1e-133)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 1.95e-57)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 2.2e-29)
		tmp = x - (x / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+52], t$95$1, If[LessEqual[z, 3.1e-133], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-57], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-29], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999999e52 or 2.1999999999999999e-29 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in x around 0 39.1%

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

      1. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in t around 0 39.1%

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

      1. associate-*r/ 70.2%

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

   8. Simplified 70.2%

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

   if -8.9999999999999999e52 < z < 3.10000000000000016e-133

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 73.0%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   if 3.10000000000000016e-133 < z < 1.95000000000000003e-57

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. div-sub 75.4%

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

      2. associate-*r/ 75.6%

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

      3. associate-/l* 77.9%

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

      4. associate-/r/ 80.0%

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

   5. Simplified 80.0%

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

   if 1.95000000000000003e-57 < z < 2.1999999999999999e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-57}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+51)
   (* t (/ (- y z) (- a z)))
   (if (<= z 2.9e-133)
     (+ x (/ y (/ a (- t x))))
     (if (<= z 2.6e-45)
       (* (- t x) (/ y (- a z)))
       (if (<= z 4.4e-30) (- x (/ x (/ a y))) (- t (/ (- t x) (/ z y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+51) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.9e-133) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 2.6e-45) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 4.4e-30) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+51)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.9d-133) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 2.6d-45) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 4.4d-30) then
        tmp = x - (x / (a / y))
    else
        tmp = t - ((t - x) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+51) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.9e-133) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 2.6e-45) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 4.4e-30) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+51:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.9e-133:
		tmp = x + (y / (a / (t - x)))
	elif z <= 2.6e-45:
		tmp = (t - x) * (y / (a - z))
	elif z <= 4.4e-30:
		tmp = x - (x / (a / y))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+51)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.9e-133)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 2.6e-45)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 4.4e-30)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+51)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.9e-133)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 2.6e-45)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 4.4e-30)
		tmp = x - (x / (a / y));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+51], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-133], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-45], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-30], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.25e51

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 44.9%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in t around 0 44.9%

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

      1. associate-*r/ 81.2%

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

   8. Simplified 81.2%

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

   if -1.25e51 < z < 2.8999999999999998e-133

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 73.0%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   if 2.8999999999999998e-133 < z < 2.59999999999999987e-45

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. div-sub 75.4%

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

      2. associate-*r/ 75.6%

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

      3. associate-/l* 77.9%

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

      4. associate-/r/ 80.0%

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

   5. Simplified 80.0%

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

   if 2.59999999999999987e-45 < z < 4.39999999999999967e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 4.39999999999999967e-30 < z

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. distribute-lft-out-- 62.8%

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

      3. div-sub 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. distribute-rgt-out-- 62.8%

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

      7. associate-/l* 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around inf 71.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -6.1e+50)
     t
     (if (<= z -1.15e-233)
       t_1
       (if (<= z 1.7e-265) (+ x (/ (* y t) a)) (if (<= z 2.4e-24) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.1e+50) {
		tmp = t;
	} else if (z <= -1.15e-233) {
		tmp = t_1;
	} else if (z <= 1.7e-265) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.4e-24) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-6.1d+50)) then
        tmp = t
    else if (z <= (-1.15d-233)) then
        tmp = t_1
    else if (z <= 1.7d-265) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.4d-24) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.1e+50) {
		tmp = t;
	} else if (z <= -1.15e-233) {
		tmp = t_1;
	} else if (z <= 1.7e-265) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.4e-24) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6.1e+50:
		tmp = t
	elif z <= -1.15e-233:
		tmp = t_1
	elif z <= 1.7e-265:
		tmp = x + ((y * t) / a)
	elif z <= 2.4e-24:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6.1e+50)
		tmp = t;
	elseif (z <= -1.15e-233)
		tmp = t_1;
	elseif (z <= 1.7e-265)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.4e-24)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6.1e+50)
		tmp = t;
	elseif (z <= -1.15e-233)
		tmp = t_1;
	elseif (z <= 1.7e-265)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.4e-24)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.1e+50], t, If[LessEqual[z, -1.15e-233], t$95$1, If[LessEqual[z, 1.7e-265], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-24], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.10000000000000026e50 or 2.3999999999999998e-24 < z

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 47.7%

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

   if -6.10000000000000026e50 < z < -1.1500000000000001e-233 or 1.7e-265 < z < 2.3999999999999998e-24

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 68.0%

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

   4. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   6. Simplified 55.7%

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

   if -1.1500000000000001e-233 < z < 1.7e-265

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in t around inf 77.0%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+50)
   t
   (if (<= z -4.8e-234)
     (* x (- 1.0 (/ y a)))
     (if (<= z 5.6e-266)
       (+ x (/ (* y t) a))
       (if (<= z 1.9e-25) (- x (/ x (/ a y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+50) {
		tmp = t;
	} else if (z <= -4.8e-234) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.6e-266) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.9e-25) {
		tmp = x - (x / (a / y));
	} else {
		tmp = 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 <= (-5.6d+50)) then
        tmp = t
    else if (z <= (-4.8d-234)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.6d-266) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.9d-25) then
        tmp = x - (x / (a / y))
    else
        tmp = 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 <= -5.6e+50) {
		tmp = t;
	} else if (z <= -4.8e-234) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.6e-266) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.9e-25) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+50:
		tmp = t
	elif z <= -4.8e-234:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.6e-266:
		tmp = x + ((y * t) / a)
	elif z <= 1.9e-25:
		tmp = x - (x / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+50)
		tmp = t;
	elseif (z <= -4.8e-234)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.6e-266)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.9e-25)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+50)
		tmp = t;
	elseif (z <= -4.8e-234)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.6e-266)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.9e-25)
		tmp = x - (x / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+50], t, If[LessEqual[z, -4.8e-234], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-266], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-25], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5999999999999996e50 or 1.8999999999999999e-25 < z

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 47.7%

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

   if -5.5999999999999996e50 < z < -4.7999999999999998e-234

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 67.3%

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

   4. Taylor expanded in x around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   6. Simplified 56.0%

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

   if -4.7999999999999998e-234 < z < 5.5999999999999999e-266

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in t around inf 77.0%

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

   if 5.5999999999999999e-266 < z < 1.8999999999999999e-25

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 68.8%

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

   4. Taylor expanded in t around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-/l* 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+259}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.7e+259)
   (/ (- x) (/ (- a z) y))
   (if (<= x -2.5e+74)
     (- x (/ x (/ a y)))
     (if (<= x 4.6e+89) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e+259) {
		tmp = -x / ((a - z) / y);
	} else if (x <= -2.5e+74) {
		tmp = x - (x / (a / y));
	} else if (x <= 4.6e+89) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.7d+259)) then
        tmp = -x / ((a - z) / y)
    else if (x <= (-2.5d+74)) then
        tmp = x - (x / (a / y))
    else if (x <= 4.6d+89) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e+259) {
		tmp = -x / ((a - z) / y);
	} else if (x <= -2.5e+74) {
		tmp = x - (x / (a / y));
	} else if (x <= 4.6e+89) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.7e+259:
		tmp = -x / ((a - z) / y)
	elif x <= -2.5e+74:
		tmp = x - (x / (a / y))
	elif x <= 4.6e+89:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.7e+259)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (x <= -2.5e+74)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (x <= 4.6e+89)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.7e+259)
		tmp = -x / ((a - z) / y);
	elseif (x <= -2.5e+74)
		tmp = x - (x / (a / y));
	elseif (x <= 4.6e+89)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.7e+259], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e+74], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+89], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.69999999999999988e259

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 89.6%

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

      1. div-sub 89.6%

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

      2. associate-*r/ 79.2%

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

      3. associate-/l* 89.6%

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

      4. associate-/r/ 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in t around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. associate-/l* 89.6%

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

      3. distribute-neg-frac 89.6%

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

   8. Simplified 89.6%

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

   if -2.69999999999999988e259 < x < -2.49999999999999982e74

   1. Initial program 75.4%

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

   3. Taylor expanded in z around 0 61.5%

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

   4. Taylor expanded in t around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

   if -2.49999999999999982e74 < x < 4.5999999999999998e89

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 53.8%

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

      1. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around 0 53.8%

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

      1. associate-*r/ 71.1%

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

   8. Simplified 71.1%

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

   if 4.5999999999999998e89 < x

   1. Initial program 70.5%

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

   3. Taylor expanded in z around 0 55.6%

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

   4. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. unsub-neg 53.3%

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

   6. Simplified 53.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+259}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -31500000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -31500000000000.0)
   t
   (if (<= z -1.25e-116)
     x
     (if (<= z -2.1e-273) (* t (/ y a)) (if (<= z 8.5e-26) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -31500000000000.0) {
		tmp = t;
	} else if (z <= -1.25e-116) {
		tmp = x;
	} else if (z <= -2.1e-273) {
		tmp = t * (y / a);
	} else if (z <= 8.5e-26) {
		tmp = x;
	} else {
		tmp = 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 <= (-31500000000000.0d0)) then
        tmp = t
    else if (z <= (-1.25d-116)) then
        tmp = x
    else if (z <= (-2.1d-273)) then
        tmp = t * (y / a)
    else if (z <= 8.5d-26) then
        tmp = x
    else
        tmp = 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 <= -31500000000000.0) {
		tmp = t;
	} else if (z <= -1.25e-116) {
		tmp = x;
	} else if (z <= -2.1e-273) {
		tmp = t * (y / a);
	} else if (z <= 8.5e-26) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -31500000000000.0:
		tmp = t
	elif z <= -1.25e-116:
		tmp = x
	elif z <= -2.1e-273:
		tmp = t * (y / a)
	elif z <= 8.5e-26:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -31500000000000.0)
		tmp = t;
	elseif (z <= -1.25e-116)
		tmp = x;
	elseif (z <= -2.1e-273)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 8.5e-26)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -31500000000000.0)
		tmp = t;
	elseif (z <= -1.25e-116)
		tmp = x;
	elseif (z <= -2.1e-273)
		tmp = t * (y / a);
	elseif (z <= 8.5e-26)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -31500000000000.0], t, If[LessEqual[z, -1.25e-116], x, If[LessEqual[z, -2.1e-273], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-26], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.15e13 or 8.50000000000000004e-26 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in z around inf 46.4%

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

   if -3.15e13 < z < -1.2500000000000001e-116 or -2.1000000000000002e-273 < z < 8.50000000000000004e-26

   1. Initial program 90.1%

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

   3. Taylor expanded in a around inf 35.2%

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

   if -1.2500000000000001e-116 < z < -2.1000000000000002e-273

   1. Initial program 94.0%

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

   3. Taylor expanded in y around -inf 71.1%

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

   4. Taylor expanded in t around inf 38.9%

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

   5. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 45.7%

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

   7. Simplified 45.7%

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

      1. div-inv 45.6%

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

      2. clear-num 45.6%

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

   9. Applied egg-rr 45.6%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31500000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-272}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -20000.0)
   t
   (if (<= z -1.22e-116)
     x
     (if (<= z -1.15e-272) (/ t (/ a y)) (if (<= z 1.9e-25) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -20000.0) {
		tmp = t;
	} else if (z <= -1.22e-116) {
		tmp = x;
	} else if (z <= -1.15e-272) {
		tmp = t / (a / y);
	} else if (z <= 1.9e-25) {
		tmp = x;
	} else {
		tmp = 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 <= (-20000.0d0)) then
        tmp = t
    else if (z <= (-1.22d-116)) then
        tmp = x
    else if (z <= (-1.15d-272)) then
        tmp = t / (a / y)
    else if (z <= 1.9d-25) then
        tmp = x
    else
        tmp = 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 <= -20000.0) {
		tmp = t;
	} else if (z <= -1.22e-116) {
		tmp = x;
	} else if (z <= -1.15e-272) {
		tmp = t / (a / y);
	} else if (z <= 1.9e-25) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -20000.0:
		tmp = t
	elif z <= -1.22e-116:
		tmp = x
	elif z <= -1.15e-272:
		tmp = t / (a / y)
	elif z <= 1.9e-25:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -20000.0)
		tmp = t;
	elseif (z <= -1.22e-116)
		tmp = x;
	elseif (z <= -1.15e-272)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 1.9e-25)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -20000.0)
		tmp = t;
	elseif (z <= -1.22e-116)
		tmp = x;
	elseif (z <= -1.15e-272)
		tmp = t / (a / y);
	elseif (z <= 1.9e-25)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -20000.0], t, If[LessEqual[z, -1.22e-116], x, If[LessEqual[z, -1.15e-272], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-25], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e4 or 1.8999999999999999e-25 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in z around inf 46.4%

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

   if -2e4 < z < -1.22e-116 or -1.14999999999999994e-272 < z < 1.8999999999999999e-25

   1. Initial program 90.1%

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

   3. Taylor expanded in a around inf 35.2%

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

   if -1.22e-116 < z < -1.14999999999999994e-272

   1. Initial program 94.0%

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

   3. Taylor expanded in y around -inf 71.1%

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

   4. Taylor expanded in t around inf 38.9%

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

   5. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 45.7%

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

   7. Simplified 45.7%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-272}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+50) t (if (<= z 2.4e-24) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+50) {
		tmp = t;
	} else if (z <= 2.4e-24) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = 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 <= (-4.9d+50)) then
        tmp = t
    else if (z <= 2.4d-24) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = 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 <= -4.9e+50) {
		tmp = t;
	} else if (z <= 2.4e-24) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.9e+50:
		tmp = t
	elif z <= 2.4e-24:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+50)
		tmp = t;
	elseif (z <= 2.4e-24)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.9e+50)
		tmp = t;
	elseif (z <= 2.4e-24)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+50], t, If[LessEqual[z, 2.4e-24], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9000000000000002e50 or 2.3999999999999998e-24 < z

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 47.7%

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

   if -4.9000000000000002e50 < z < 2.3999999999999998e-24

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 70.9%

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

   4. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   6. Simplified 55.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.12e+16) t (if (<= z 1.32e-24) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+16) {
		tmp = t;
	} else if (z <= 1.32e-24) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.12d+16)) then
        tmp = t
    else if (z <= 1.32d-24) then
        tmp = x
    else
        tmp = 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 <= -1.12e+16) {
		tmp = t;
	} else if (z <= 1.32e-24) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.12e+16:
		tmp = t
	elif z <= 1.32e-24:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.12e+16)
		tmp = t;
	elseif (z <= 1.32e-24)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.12e+16)
		tmp = t;
	elseif (z <= 1.32e-24)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.12e+16], t, If[LessEqual[z, 1.32e-24], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e16 or 1.3199999999999999e-24 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in z around inf 46.4%

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

   if -1.12e16 < z < 1.3199999999999999e-24

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 30.8%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.2%

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

3. Taylor expanded in z around inf 25.1%

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

4. Final simplification 25.1%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))