Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 91.3%

Time: 28.9s

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: 79.6% 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: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-283} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-283) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

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 <= -2e-283) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-283)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-283) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-283) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	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 <= -2e-283) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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 <= -2e-283) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	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, -2e-283], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $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)))) < -1.99999999999999989e-283 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.0%

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

   if -1.99999999999999989e-283 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 87.1%

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

      1. associate--l+ 87.1%

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

      2. distribute-lft-out-- 87.1%

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

      3. div-sub 87.1%

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

      4. mul-1-neg 87.1%

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

      5. unsub-neg 87.1%

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

      6. distribute-rgt-out-- 87.1%

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

      7. associate-/l* 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-283} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot t}{a}\\ t_2 := x + \frac{y \cdot t}{a}\\ t_3 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_4 := t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-280}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-173}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-106}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* z t) a)))
        (t_2 (+ x (/ (* y t) a)))
        (t_3 (* (- t x) (/ y (- a z))))
        (t_4 (+ t (/ a (/ z (- t x))))))
   (if (<= y -6.6e+66)
     t_3
     (if (<= y -7.3e-211)
       t_1
       (if (<= y -2.2e-280)
         t_4
         (if (<= y 3e-263)
           t_1
           (if (<= y 1.55e-173)
             t_4
             (if (<= y 1.9e-158)
               t_2
               (if (<= y 5.2e-106)
                 t_4
                 (if (<= y 1.05e-38)
                   t_2
                   (if (<= y 5e+87) (* t (/ (- y z) (- a z))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * t) / a);
	double t_2 = x + ((y * t) / a);
	double t_3 = (t - x) * (y / (a - z));
	double t_4 = t + (a / (z / (t - x)));
	double tmp;
	if (y <= -6.6e+66) {
		tmp = t_3;
	} else if (y <= -7.3e-211) {
		tmp = t_1;
	} else if (y <= -2.2e-280) {
		tmp = t_4;
	} else if (y <= 3e-263) {
		tmp = t_1;
	} else if (y <= 1.55e-173) {
		tmp = t_4;
	} else if (y <= 1.9e-158) {
		tmp = t_2;
	} else if (y <= 5.2e-106) {
		tmp = t_4;
	} else if (y <= 1.05e-38) {
		tmp = t_2;
	} else if (y <= 5e+87) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x - ((z * t) / a)
    t_2 = x + ((y * t) / a)
    t_3 = (t - x) * (y / (a - z))
    t_4 = t + (a / (z / (t - x)))
    if (y <= (-6.6d+66)) then
        tmp = t_3
    else if (y <= (-7.3d-211)) then
        tmp = t_1
    else if (y <= (-2.2d-280)) then
        tmp = t_4
    else if (y <= 3d-263) then
        tmp = t_1
    else if (y <= 1.55d-173) then
        tmp = t_4
    else if (y <= 1.9d-158) then
        tmp = t_2
    else if (y <= 5.2d-106) then
        tmp = t_4
    else if (y <= 1.05d-38) then
        tmp = t_2
    else if (y <= 5d+87) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * t) / a);
	double t_2 = x + ((y * t) / a);
	double t_3 = (t - x) * (y / (a - z));
	double t_4 = t + (a / (z / (t - x)));
	double tmp;
	if (y <= -6.6e+66) {
		tmp = t_3;
	} else if (y <= -7.3e-211) {
		tmp = t_1;
	} else if (y <= -2.2e-280) {
		tmp = t_4;
	} else if (y <= 3e-263) {
		tmp = t_1;
	} else if (y <= 1.55e-173) {
		tmp = t_4;
	} else if (y <= 1.9e-158) {
		tmp = t_2;
	} else if (y <= 5.2e-106) {
		tmp = t_4;
	} else if (y <= 1.05e-38) {
		tmp = t_2;
	} else if (y <= 5e+87) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z * t) / a)
	t_2 = x + ((y * t) / a)
	t_3 = (t - x) * (y / (a - z))
	t_4 = t + (a / (z / (t - x)))
	tmp = 0
	if y <= -6.6e+66:
		tmp = t_3
	elif y <= -7.3e-211:
		tmp = t_1
	elif y <= -2.2e-280:
		tmp = t_4
	elif y <= 3e-263:
		tmp = t_1
	elif y <= 1.55e-173:
		tmp = t_4
	elif y <= 1.9e-158:
		tmp = t_2
	elif y <= 5.2e-106:
		tmp = t_4
	elif y <= 1.05e-38:
		tmp = t_2
	elif y <= 5e+87:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z * t) / a))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	t_3 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_4 = Float64(t + Float64(a / Float64(z / Float64(t - x))))
	tmp = 0.0
	if (y <= -6.6e+66)
		tmp = t_3;
	elseif (y <= -7.3e-211)
		tmp = t_1;
	elseif (y <= -2.2e-280)
		tmp = t_4;
	elseif (y <= 3e-263)
		tmp = t_1;
	elseif (y <= 1.55e-173)
		tmp = t_4;
	elseif (y <= 1.9e-158)
		tmp = t_2;
	elseif (y <= 5.2e-106)
		tmp = t_4;
	elseif (y <= 1.05e-38)
		tmp = t_2;
	elseif (y <= 5e+87)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z * t) / a);
	t_2 = x + ((y * t) / a);
	t_3 = (t - x) * (y / (a - z));
	t_4 = t + (a / (z / (t - x)));
	tmp = 0.0;
	if (y <= -6.6e+66)
		tmp = t_3;
	elseif (y <= -7.3e-211)
		tmp = t_1;
	elseif (y <= -2.2e-280)
		tmp = t_4;
	elseif (y <= 3e-263)
		tmp = t_1;
	elseif (y <= 1.55e-173)
		tmp = t_4;
	elseif (y <= 1.9e-158)
		tmp = t_2;
	elseif (y <= 5.2e-106)
		tmp = t_4;
	elseif (y <= 1.05e-38)
		tmp = t_2;
	elseif (y <= 5e+87)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+66], t$95$3, If[LessEqual[y, -7.3e-211], t$95$1, If[LessEqual[y, -2.2e-280], t$95$4, If[LessEqual[y, 3e-263], t$95$1, If[LessEqual[y, 1.55e-173], t$95$4, If[LessEqual[y, 1.9e-158], t$95$2, If[LessEqual[y, 5.2e-106], t$95$4, If[LessEqual[y, 1.05e-38], t$95$2, If[LessEqual[y, 5e+87], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.6000000000000003e66 or 4.9999999999999998e87 < y

   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 85.0%

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

      1. div-sub 85.0%

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

      2. associate-*r/ 69.3%

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

      3. associate-/l* 85.1%

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

      4. associate-/r/ 88.9%

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

   5. Simplified 88.9%

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

   if -6.6000000000000003e66 < y < -7.29999999999999968e-211 or -2.2000000000000001e-280 < y < 3e-263

   1. Initial program 82.5%

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

   3. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

      3. associate-/l* 77.5%

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

      4. associate-/r/ 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in z around 0 60.5%

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

   7. Taylor expanded in t around inf 61.7%

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

      1. *-commutative 61.7%

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

   9. Simplified 61.7%

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

   if -7.29999999999999968e-211 < y < -2.2000000000000001e-280 or 3e-263 < y < 1.55000000000000003e-173 or 1.8999999999999999e-158 < y < 5.2000000000000001e-106

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. div-sub 63.5%

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

      4. mul-1-neg 63.5%

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

      5. unsub-neg 63.5%

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

      6. distribute-rgt-out-- 63.5%

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

      7. associate-/l* 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. sub-neg 57.2%

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

      2. mul-1-neg 57.2%

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

      3. remove-double-neg 57.2%

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

      4. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

   if 1.55000000000000003e-173 < y < 1.8999999999999999e-158 or 5.2000000000000001e-106 < y < 1.05000000000000006e-38

   1. Initial program 77.1%

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

   3. Taylor expanded in z around 0 72.3%

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

   4. Taylor expanded in t around inf 72.9%

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

      1. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   if 1.05000000000000006e-38 < y < 4.9999999999999998e87

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 56.7%

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

      1. div-inv 56.5%

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

      2. associate-*l* 70.7%

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

      3. un-div-inv 71.0%

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

   5. Applied egg-rr 71.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-211}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-280}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-263}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-173}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-106}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.45:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))) (t_2 (+ t (/ (- x t) (/ z y)))))
   (if (<= z -1.55e+21)
     t_2
     (if (<= z -1.95e-17)
       (+ x (* (- t x) (/ y a)))
       (if (<= z -3.8e-52)
         (* t (/ (- y z) (- a z)))
         (if (<= z 1.45)
           t_1
           (if (<= z 1.7e+48)
             t_2
             (if (<= z 1.45e+70)
               t_1
               (if (<= z 1.25e+86)
                 (/ (- x) (/ (- a z) y))
                 (- t (/ y (/ z (- t x)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double t_2 = t + ((x - t) / (z / y));
	double tmp;
	if (z <= -1.55e+21) {
		tmp = t_2;
	} else if (z <= -1.95e-17) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= -3.8e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.45) {
		tmp = t_1;
	} else if (z <= 1.7e+48) {
		tmp = t_2;
	} else if (z <= 1.45e+70) {
		tmp = t_1;
	} else if (z <= 1.25e+86) {
		tmp = -x / ((a - z) / y);
	} else {
		tmp = t - (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) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    t_2 = t + ((x - t) / (z / y))
    if (z <= (-1.55d+21)) then
        tmp = t_2
    else if (z <= (-1.95d-17)) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= (-3.8d-52)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.45d0) then
        tmp = t_1
    else if (z <= 1.7d+48) then
        tmp = t_2
    else if (z <= 1.45d+70) then
        tmp = t_1
    else if (z <= 1.25d+86) then
        tmp = -x / ((a - z) / y)
    else
        tmp = t - (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 + ((t - x) / (a / (y - z)));
	double t_2 = t + ((x - t) / (z / y));
	double tmp;
	if (z <= -1.55e+21) {
		tmp = t_2;
	} else if (z <= -1.95e-17) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= -3.8e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.45) {
		tmp = t_1;
	} else if (z <= 1.7e+48) {
		tmp = t_2;
	} else if (z <= 1.45e+70) {
		tmp = t_1;
	} else if (z <= 1.25e+86) {
		tmp = -x / ((a - z) / y);
	} else {
		tmp = t - (y / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	t_2 = t + ((x - t) / (z / y))
	tmp = 0
	if z <= -1.55e+21:
		tmp = t_2
	elif z <= -1.95e-17:
		tmp = x + ((t - x) * (y / a))
	elif z <= -3.8e-52:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.45:
		tmp = t_1
	elif z <= 1.7e+48:
		tmp = t_2
	elif z <= 1.45e+70:
		tmp = t_1
	elif z <= 1.25e+86:
		tmp = -x / ((a - z) / y)
	else:
		tmp = t - (y / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	t_2 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	tmp = 0.0
	if (z <= -1.55e+21)
		tmp = t_2;
	elseif (z <= -1.95e-17)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= -3.8e-52)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.45)
		tmp = t_1;
	elseif (z <= 1.7e+48)
		tmp = t_2;
	elseif (z <= 1.45e+70)
		tmp = t_1;
	elseif (z <= 1.25e+86)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	else
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	t_2 = t + ((x - t) / (z / y));
	tmp = 0.0;
	if (z <= -1.55e+21)
		tmp = t_2;
	elseif (z <= -1.95e-17)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= -3.8e-52)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.45)
		tmp = t_1;
	elseif (z <= 1.7e+48)
		tmp = t_2;
	elseif (z <= 1.45e+70)
		tmp = t_1;
	elseif (z <= 1.25e+86)
		tmp = -x / ((a - z) / y);
	else
		tmp = t - (y / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+21], t$95$2, If[LessEqual[z, -1.95e-17], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-52], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45], t$95$1, If[LessEqual[z, 1.7e+48], t$95$2, If[LessEqual[z, 1.45e+70], t$95$1, If[LessEqual[z, 1.25e+86], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.55e21 or 1.44999999999999996 < z < 1.7000000000000002e48

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. distribute-lft-out-- 60.0%

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

      3. div-sub 60.0%

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

      4. mul-1-neg 60.0%

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

      5. unsub-neg 60.0%

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

      6. distribute-rgt-out-- 60.3%

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

      7. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 69.8%

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

   if -1.55e21 < z < -1.94999999999999995e-17

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. expm1-log1p-u 72.3%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)\right)} \]

      2. expm1-udef 58.8%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)} - 1\right)} \]

      3. associate-/l* 58.8%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t - x}}}\right)} - 1\right) \]

   5. Applied egg-rr 58.8%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 58.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)\right)} \]

      2. expm1-log1p 73.1%

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

      3. associate-/r/ 86.6%

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

      4. *-commutative 86.6%

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

   7. Simplified 86.6%

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

   if -1.94999999999999995e-17 < z < -3.8000000000000003e-52

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. div-inv 64.2%

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

      2. associate-*l* 87.9%

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

      3. un-div-inv 87.9%

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

   5. Applied egg-rr 87.9%

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

   if -3.8000000000000003e-52 < z < 1.44999999999999996 or 1.7000000000000002e48 < z < 1.4499999999999999e70

   1. Initial program 89.1%

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

   3. Taylor expanded in a around inf 79.4%

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

      1. associate-/l* 82.6%

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

   5. Simplified 82.6%

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

   if 1.4499999999999999e70 < z < 1.2499999999999999e86

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. unsub-neg 40.2%

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

      3. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 40.2%

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

      1. associate-*r/ 40.2%

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

      2. associate-*r* 40.2%

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

      3. neg-mul-1 40.2%

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

   10. Simplified 40.2%

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

   11. Taylor expanded in x around 0 40.2%

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

       1. mul-1-neg 40.2%

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

       2. associate-/l* 100.0%

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

       3. distribute-neg-frac 100.0%

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

   13. Simplified 100.0%

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

   if 1.2499999999999999e86 < z

   1. Initial program 68.4%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. associate--l+ 71.0%

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

      2. distribute-lft-out-- 71.0%

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

      3. div-sub 71.0%

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

      4. mul-1-neg 71.0%

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

      5. unsub-neg 71.0%

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

      6. distribute-rgt-out-- 71.0%

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

      7. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in y around inf 68.0%

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

      1. associate-/l* 78.3%

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

   8. Simplified 78.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.45:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+48}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ t_2 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-160}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 8.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))) (t_2 (- t (* t (/ y z)))))
   (if (<= z -3.1e+48)
     t_2
     (if (<= z -1.95e-17)
       t_1
       (if (<= z -6.8e-52)
         t_2
         (if (<= z -1.18e-178)
           t_1
           (if (<= z 8.5e-160)
             (+ x (/ (* y t) a))
             (if (<= z 8.2) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -3.1e+48) {
		tmp = t_2;
	} else if (z <= -1.95e-17) {
		tmp = t_1;
	} else if (z <= -6.8e-52) {
		tmp = t_2;
	} else if (z <= -1.18e-178) {
		tmp = t_1;
	} else if (z <= 8.5e-160) {
		tmp = x + ((y * t) / a);
	} else if (z <= 8.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    t_2 = t - (t * (y / z))
    if (z <= (-3.1d+48)) then
        tmp = t_2
    else if (z <= (-1.95d-17)) then
        tmp = t_1
    else if (z <= (-6.8d-52)) then
        tmp = t_2
    else if (z <= (-1.18d-178)) then
        tmp = t_1
    else if (z <= 8.5d-160) then
        tmp = x + ((y * t) / a)
    else if (z <= 8.2d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -3.1e+48) {
		tmp = t_2;
	} else if (z <= -1.95e-17) {
		tmp = t_1;
	} else if (z <= -6.8e-52) {
		tmp = t_2;
	} else if (z <= -1.18e-178) {
		tmp = t_1;
	} else if (z <= 8.5e-160) {
		tmp = x + ((y * t) / a);
	} else if (z <= 8.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	t_2 = t - (t * (y / z))
	tmp = 0
	if z <= -3.1e+48:
		tmp = t_2
	elif z <= -1.95e-17:
		tmp = t_1
	elif z <= -6.8e-52:
		tmp = t_2
	elif z <= -1.18e-178:
		tmp = t_1
	elif z <= 8.5e-160:
		tmp = x + ((y * t) / a)
	elif z <= 8.2:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	t_2 = Float64(t - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -3.1e+48)
		tmp = t_2;
	elseif (z <= -1.95e-17)
		tmp = t_1;
	elseif (z <= -6.8e-52)
		tmp = t_2;
	elseif (z <= -1.18e-178)
		tmp = t_1;
	elseif (z <= 8.5e-160)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 8.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	t_2 = t - (t * (y / z));
	tmp = 0.0;
	if (z <= -3.1e+48)
		tmp = t_2;
	elseif (z <= -1.95e-17)
		tmp = t_1;
	elseif (z <= -6.8e-52)
		tmp = t_2;
	elseif (z <= -1.18e-178)
		tmp = t_1;
	elseif (z <= 8.5e-160)
		tmp = x + ((y * t) / a);
	elseif (z <= 8.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+48], t$95$2, If[LessEqual[z, -1.95e-17], t$95$1, If[LessEqual[z, -6.8e-52], t$95$2, If[LessEqual[z, -1.18e-178], t$95$1, If[LessEqual[z, 8.5e-160], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000005e48 or -1.94999999999999995e-17 < z < -6.80000000000000035e-52 or 8.1999999999999993 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in z around inf 61.0%

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

      1. associate--l+ 61.0%

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

      2. distribute-lft-out-- 61.0%

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

      3. div-sub 61.0%

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

      4. mul-1-neg 61.0%

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

      5. unsub-neg 61.0%

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

      6. distribute-rgt-out-- 61.1%

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

      7. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in y around inf 69.2%

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

   7. Taylor expanded in t around inf 46.7%

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

      1. associate-*r/ 51.8%

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

   9. Simplified 51.8%

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

   if -3.10000000000000005e48 < z < -1.94999999999999995e-17 or -6.80000000000000035e-52 < z < -1.18000000000000006e-178 or 8.49999999999999959e-160 < z < 8.1999999999999993

   1. Initial program 84.8%

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

      1. clear-num 84.8%

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

      2. associate-/r/ 84.8%

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in t around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

      3. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 66.5%

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

   10. Simplified 66.5%

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

   if -1.18000000000000006e-178 < z < 8.49999999999999959e-160

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 81.9%

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

   4. Taylor expanded in t around inf 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+48}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-178}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-160}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 8.2:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y}}\\ t_2 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+48}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 0.7:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z y)))) (t_2 (- x (/ x (/ a y)))))
   (if (<= z -2.6e+157)
     t_1
     (if (<= z -1.1e+68)
       (/ (- y) (/ z (- t x)))
       (if (<= z -3.1e+48)
         (- t (* t (/ y z)))
         (if (<= z -4.2e-178)
           t_2
           (if (<= z 3.5e-161)
             (+ x (/ (* y t) a))
             (if (<= z 0.7) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (z <= -2.6e+157) {
		tmp = t_1;
	} else if (z <= -1.1e+68) {
		tmp = -y / (z / (t - x));
	} else if (z <= -3.1e+48) {
		tmp = t - (t * (y / z));
	} else if (z <= -4.2e-178) {
		tmp = t_2;
	} else if (z <= 3.5e-161) {
		tmp = x + ((y * t) / a);
	} else if (z <= 0.7) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x / (z / y))
    t_2 = x - (x / (a / y))
    if (z <= (-2.6d+157)) then
        tmp = t_1
    else if (z <= (-1.1d+68)) then
        tmp = -y / (z / (t - x))
    else if (z <= (-3.1d+48)) then
        tmp = t - (t * (y / z))
    else if (z <= (-4.2d-178)) then
        tmp = t_2
    else if (z <= 3.5d-161) then
        tmp = x + ((y * t) / a)
    else if (z <= 0.7d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (z <= -2.6e+157) {
		tmp = t_1;
	} else if (z <= -1.1e+68) {
		tmp = -y / (z / (t - x));
	} else if (z <= -3.1e+48) {
		tmp = t - (t * (y / z));
	} else if (z <= -4.2e-178) {
		tmp = t_2;
	} else if (z <= 3.5e-161) {
		tmp = x + ((y * t) / a);
	} else if (z <= 0.7) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / y))
	t_2 = x - (x / (a / y))
	tmp = 0
	if z <= -2.6e+157:
		tmp = t_1
	elif z <= -1.1e+68:
		tmp = -y / (z / (t - x))
	elif z <= -3.1e+48:
		tmp = t - (t * (y / z))
	elif z <= -4.2e-178:
		tmp = t_2
	elif z <= 3.5e-161:
		tmp = x + ((y * t) / a)
	elif z <= 0.7:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / y)))
	t_2 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (z <= -2.6e+157)
		tmp = t_1;
	elseif (z <= -1.1e+68)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= -3.1e+48)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= -4.2e-178)
		tmp = t_2;
	elseif (z <= 3.5e-161)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 0.7)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / y));
	t_2 = x - (x / (a / y));
	tmp = 0.0;
	if (z <= -2.6e+157)
		tmp = t_1;
	elseif (z <= -1.1e+68)
		tmp = -y / (z / (t - x));
	elseif (z <= -3.1e+48)
		tmp = t - (t * (y / z));
	elseif (z <= -4.2e-178)
		tmp = t_2;
	elseif (z <= 3.5e-161)
		tmp = x + ((y * t) / a);
	elseif (z <= 0.7)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+157], t$95$1, If[LessEqual[z, -1.1e+68], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e+48], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-178], t$95$2, If[LessEqual[z, 3.5e-161], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.7], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.60000000000000011e157 or 0.69999999999999996 < z

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. distribute-lft-out-- 62.5%

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

      3. div-sub 62.5%

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

      4. mul-1-neg 62.5%

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

      5. unsub-neg 62.5%

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

      6. distribute-rgt-out-- 62.7%

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

      7. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf 72.7%

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

   7. Taylor expanded in t around 0 55.0%

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

      1. associate-/l* 65.1%

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

      2. neg-mul-1 65.1%

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

      3. distribute-neg-frac 65.1%

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

   9. Simplified 65.1%

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

   if -2.60000000000000011e157 < z < -1.09999999999999994e68

   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 inf 53.0%

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

      1. associate--l+ 53.0%

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

      2. distribute-lft-out-- 53.0%

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

      3. div-sub 53.0%

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

      4. mul-1-neg 53.0%

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

      5. unsub-neg 53.0%

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

      6. distribute-rgt-out-- 53.0%

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

      7. associate-/l* 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around -inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. associate-/l* 53.5%

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

      3. distribute-neg-frac 53.5%

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

   8. Simplified 53.5%

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

   if -1.09999999999999994e68 < z < -3.10000000000000005e48

   1. Initial program 83.9%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. distribute-lft-out-- 66.8%

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

      3. div-sub 66.8%

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

      4. mul-1-neg 66.8%

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

      5. unsub-neg 66.8%

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

      6. distribute-rgt-out-- 68.0%

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

      7. associate-/l* 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in y around inf 52.8%

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

   7. Taylor expanded in t around inf 52.9%

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

      1. associate-*r/ 52.9%

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

   9. Simplified 52.9%

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

   if -3.10000000000000005e48 < z < -4.2e-178 or 3.5000000000000002e-161 < z < 0.69999999999999996

   1. Initial program 86.2%

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

      1. clear-num 86.1%

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

      2. associate-/r/ 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. associate-/l* 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. associate-/l* 59.2%

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

   10. Simplified 59.2%

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

   if -4.2e-178 < z < 3.5000000000000002e-161

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 83.5%

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

   4. Taylor expanded in t around inf 69.1%

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

      1. *-commutative 69.1%

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

   6. Simplified 69.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+157}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+48}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 0.7:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{a - z} \cdot \left(x - t\right)\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -3.85 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-174}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+175}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ z (- a z)) (- x t)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= y -3.85e+67)
     t_2
     (if (<= y 6.1e-217)
       t_1
       (if (<= y 1.65e-174)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= y 2.55e-45)
           t_1
           (if (<= y 2.5e+175) (+ t (/ (- x t) (/ z (- y a)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z / (a - z)) * (x - t));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -3.85e+67) {
		tmp = t_2;
	} else if (y <= 6.1e-217) {
		tmp = t_1;
	} else if (y <= 1.65e-174) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (y <= 2.55e-45) {
		tmp = t_1;
	} else if (y <= 2.5e+175) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / (a - z)) * (x - t))
    t_2 = (t - x) * (y / (a - z))
    if (y <= (-3.85d+67)) then
        tmp = t_2
    else if (y <= 6.1d-217) then
        tmp = t_1
    else if (y <= 1.65d-174) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (y <= 2.55d-45) then
        tmp = t_1
    else if (y <= 2.5d+175) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z / (a - z)) * (x - t));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -3.85e+67) {
		tmp = t_2;
	} else if (y <= 6.1e-217) {
		tmp = t_1;
	} else if (y <= 1.65e-174) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (y <= 2.55e-45) {
		tmp = t_1;
	} else if (y <= 2.5e+175) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z / (a - z)) * (x - t))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -3.85e+67:
		tmp = t_2
	elif y <= 6.1e-217:
		tmp = t_1
	elif y <= 1.65e-174:
		tmp = t + (((t - x) * (a - y)) / z)
	elif y <= 2.55e-45:
		tmp = t_1
	elif y <= 2.5e+175:
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z / Float64(a - z)) * Float64(x - t)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.85e+67)
		tmp = t_2;
	elseif (y <= 6.1e-217)
		tmp = t_1;
	elseif (y <= 1.65e-174)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (y <= 2.55e-45)
		tmp = t_1;
	elseif (y <= 2.5e+175)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z / (a - z)) * (x - t));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -3.85e+67)
		tmp = t_2;
	elseif (y <= 6.1e-217)
		tmp = t_1;
	elseif (y <= 1.65e-174)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (y <= 2.55e-45)
		tmp = t_1;
	elseif (y <= 2.5e+175)
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.85e+67], t$95$2, If[LessEqual[y, 6.1e-217], t$95$1, If[LessEqual[y, 1.65e-174], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e-45], t$95$1, If[LessEqual[y, 2.5e+175], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8500000000000001e67 or 2.5e175 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 88.5%

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

      1. div-sub 88.5%

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

      2. associate-*r/ 72.6%

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

      3. associate-/l* 88.6%

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

      4. associate-/r/ 93.1%

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

   5. Simplified 93.1%

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

   if -3.8500000000000001e67 < y < 6.1000000000000003e-217 or 1.65e-174 < y < 2.5499999999999999e-45

   1. Initial program 81.4%

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

   3. Taylor expanded in y around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. associate-/l* 76.2%

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

      4. associate-/r/ 78.9%

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

   5. Simplified 78.9%

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

   if 6.1000000000000003e-217 < y < 1.65e-174

   1. Initial program 42.9%

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

      1. clear-num 43.1%

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

      2. associate-/r/ 42.9%

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

   4. Applied egg-rr 42.9%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate--l+ 80.6%

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

      2. associate-*r/ 80.6%

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

      3. associate-*r/ 80.6%

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

      4. div-sub 80.6%

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

      5. distribute-lft-out-- 80.6%

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

      6. associate-*r/ 80.6%

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

      7. mul-1-neg 80.6%

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

      8. unsub-neg 80.6%

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

      9. distribute-rgt-out-- 80.6%

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

   7. Simplified 80.6%

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

   if 2.5499999999999999e-45 < y < 2.5e175

   1. Initial program 77.1%

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

   3. Taylor expanded in z around inf 55.6%

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

      1. associate--l+ 55.6%

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

      2. distribute-lft-out-- 55.6%

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

      3. div-sub 58.5%

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

      4. mul-1-neg 58.5%

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

      5. unsub-neg 58.5%

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

      6. distribute-rgt-out-- 58.8%

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

      7. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.85 \cdot 10^{+67}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-174}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+175}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y}}\\ t_2 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z y)))) (t_2 (- x (/ x (/ a y)))))
   (if (<= x -5.5e+219)
     t_2
     (if (<= x -6.4e+150)
       t_1
       (if (<= x -3.7e-13)
         t_2
         (if (<= x 2.25e-5)
           (* t (/ (- y z) (- a z)))
           (if (<= x 2.6e+190) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (x <= -5.5e+219) {
		tmp = t_2;
	} else if (x <= -6.4e+150) {
		tmp = t_1;
	} else if (x <= -3.7e-13) {
		tmp = t_2;
	} else if (x <= 2.25e-5) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 2.6e+190) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x / (z / y))
    t_2 = x - (x / (a / y))
    if (x <= (-5.5d+219)) then
        tmp = t_2
    else if (x <= (-6.4d+150)) then
        tmp = t_1
    else if (x <= (-3.7d-13)) then
        tmp = t_2
    else if (x <= 2.25d-5) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 2.6d+190) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (x <= -5.5e+219) {
		tmp = t_2;
	} else if (x <= -6.4e+150) {
		tmp = t_1;
	} else if (x <= -3.7e-13) {
		tmp = t_2;
	} else if (x <= 2.25e-5) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 2.6e+190) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / y))
	t_2 = x - (x / (a / y))
	tmp = 0
	if x <= -5.5e+219:
		tmp = t_2
	elif x <= -6.4e+150:
		tmp = t_1
	elif x <= -3.7e-13:
		tmp = t_2
	elif x <= 2.25e-5:
		tmp = t * ((y - z) / (a - z))
	elif x <= 2.6e+190:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / y)))
	t_2 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -5.5e+219)
		tmp = t_2;
	elseif (x <= -6.4e+150)
		tmp = t_1;
	elseif (x <= -3.7e-13)
		tmp = t_2;
	elseif (x <= 2.25e-5)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 2.6e+190)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / y));
	t_2 = x - (x / (a / y));
	tmp = 0.0;
	if (x <= -5.5e+219)
		tmp = t_2;
	elseif (x <= -6.4e+150)
		tmp = t_1;
	elseif (x <= -3.7e-13)
		tmp = t_2;
	elseif (x <= 2.25e-5)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 2.6e+190)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+219], t$95$2, If[LessEqual[x, -6.4e+150], t$95$1, If[LessEqual[x, -3.7e-13], t$95$2, If[LessEqual[x, 2.25e-5], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+190], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.49999999999999973e219 or -6.40000000000000031e150 < x < -3.69999999999999989e-13 or 2.25000000000000014e-5 < x < 2.60000000000000011e190

   1. Initial program 81.5%

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

      1. clear-num 81.5%

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

      2. associate-/r/ 81.5%

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

   4. Applied egg-rr 81.5%

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

   5. Taylor expanded in t around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

      3. associate-/l* 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in z around 0 53.5%

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

      1. associate-/l* 59.4%

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

   10. Simplified 59.4%

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

   if -5.49999999999999973e219 < x < -6.40000000000000031e150 or 2.60000000000000011e190 < x

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. associate--l+ 54.5%

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

      2. distribute-lft-out-- 54.5%

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

      3. div-sub 54.7%

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

      4. mul-1-neg 54.7%

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

      5. unsub-neg 54.7%

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

      6. distribute-rgt-out-- 55.1%

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

      7. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around inf 69.5%

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

   7. Taylor expanded in t around 0 50.1%

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

      1. associate-/l* 66.9%

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

      2. neg-mul-1 66.9%

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

      3. distribute-neg-frac 66.9%

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

   9. Simplified 66.9%

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

   if -3.69999999999999989e-13 < x < 2.25000000000000014e-5

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 57.7%

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

      1. div-inv 57.6%

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

      2. associate-*l* 72.3%

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

      3. un-div-inv 72.5%

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

   5. Applied egg-rr 72.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+219}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+190}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -15000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -15000000.0)
     t_1
     (if (<= z -1.95e-17)
       (+ x (* (- t x) (/ y a)))
       (if (<= z -6.8e-52)
         (* t (/ (- y z) (- a z)))
         (if (<= z 0.00065) (+ x (/ (- t x) (/ a (- y z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -15000000.0) {
		tmp = t_1;
	} else if (z <= -1.95e-17) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= -6.8e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 0.00065) {
		tmp = x + ((t - x) / (a / (y - z)));
	} 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 + ((x - t) / (z / (y - a)))
    if (z <= (-15000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.95d-17)) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= (-6.8d-52)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 0.00065d0) then
        tmp = x + ((t - x) / (a / (y - z)))
    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 + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -15000000.0) {
		tmp = t_1;
	} else if (z <= -1.95e-17) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= -6.8e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 0.00065) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -15000000.0:
		tmp = t_1
	elif z <= -1.95e-17:
		tmp = x + ((t - x) * (y / a))
	elif z <= -6.8e-52:
		tmp = t * ((y - z) / (a - z))
	elif z <= 0.00065:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -15000000.0)
		tmp = t_1;
	elseif (z <= -1.95e-17)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= -6.8e-52)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 0.00065)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -15000000.0)
		tmp = t_1;
	elseif (z <= -1.95e-17)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= -6.8e-52)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 0.00065)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -15000000.0], t$95$1, If[LessEqual[z, -1.95e-17], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-52], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00065], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e7 or 6.4999999999999997e-4 < z

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. distribute-rgt-out-- 61.1%

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

      7. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   if -1.5e7 < z < -1.94999999999999995e-17

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. expm1-log1p-u 72.3%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)\right)} \]

      2. expm1-udef 58.8%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)} - 1\right)} \]

      3. associate-/l* 58.8%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t - x}}}\right)} - 1\right) \]

   5. Applied egg-rr 58.8%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 58.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)\right)} \]

      2. expm1-log1p 73.1%

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

      3. associate-/r/ 86.6%

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

      4. *-commutative 86.6%

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

   7. Simplified 86.6%

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

   if -1.94999999999999995e-17 < z < -6.80000000000000035e-52

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. div-inv 64.2%

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

      2. associate-*l* 87.9%

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

      3. un-div-inv 87.9%

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

   5. Applied egg-rr 87.9%

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

   if -6.80000000000000035e-52 < z < 6.4999999999999997e-4

   1. Initial program 88.8%

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

   3. Taylor expanded in a around inf 80.3%

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

      1. associate-/l* 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15000000:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (- t (/ y (/ z (- t x))))))
   (if (<= z -7e+19)
     t_2
     (if (<= z -1.95e-17)
       t_1
       (if (<= z -6.6e-52)
         (* t (/ (- y z) (- a z)))
         (if (<= z 2.4) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t - (y / (z / (t - x)));
	double tmp;
	if (z <= -7e+19) {
		tmp = t_2;
	} else if (z <= -1.95e-17) {
		tmp = t_1;
	} else if (z <= -6.6e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.4) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t - (y / (z / (t - x)))
    if (z <= (-7d+19)) then
        tmp = t_2
    else if (z <= (-1.95d-17)) then
        tmp = t_1
    else if (z <= (-6.6d-52)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.4d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t - (y / (z / (t - x)));
	double tmp;
	if (z <= -7e+19) {
		tmp = t_2;
	} else if (z <= -1.95e-17) {
		tmp = t_1;
	} else if (z <= -6.6e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.4) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t - (y / (z / (t - x)))
	tmp = 0
	if z <= -7e+19:
		tmp = t_2
	elif z <= -1.95e-17:
		tmp = t_1
	elif z <= -6.6e-52:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.4:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t - Float64(y / Float64(z / Float64(t - x))))
	tmp = 0.0
	if (z <= -7e+19)
		tmp = t_2;
	elseif (z <= -1.95e-17)
		tmp = t_1;
	elseif (z <= -6.6e-52)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.4)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t - (y / (z / (t - x)));
	tmp = 0.0;
	if (z <= -7e+19)
		tmp = t_2;
	elseif (z <= -1.95e-17)
		tmp = t_1;
	elseif (z <= -6.6e-52)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.4)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+19], t$95$2, If[LessEqual[z, -1.95e-17], t$95$1, If[LessEqual[z, -6.6e-52], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7e19 or 2.39999999999999991 < z

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. distribute-rgt-out-- 61.1%

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

      7. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around inf 57.0%

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

      1. associate-/l* 68.7%

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

   8. Simplified 68.7%

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

   if -7e19 < z < -1.94999999999999995e-17 or -6.5999999999999999e-52 < z < 2.39999999999999991

   1. Initial program 88.6%

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

   3. Taylor expanded in z around 0 76.5%

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

      1. expm1-log1p-u 57.2%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)\right)} \]

      2. expm1-udef 52.5%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)} - 1\right)} \]

      3. associate-/l* 52.4%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t - x}}}\right)} - 1\right) \]

   5. Applied egg-rr 52.4%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 54.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)\right)} \]

      2. expm1-log1p 73.5%

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

      3. associate-/r/ 78.0%

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

      4. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   if -1.94999999999999995e-17 < z < -6.5999999999999999e-52

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. div-inv 64.2%

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

      2. associate-*l* 87.9%

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

      3. un-div-inv 87.9%

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

   5. Applied egg-rr 87.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+19}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -28000000:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= z -28000000.0)
     (+ t (/ (- x t) (/ z y)))
     (if (<= z -1.95e-17)
       t_1
       (if (<= z -2.4e-52)
         (* t (/ (- y z) (- a z)))
         (if (<= z 0.1) t_1 (- t (/ y (/ z (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (z <= -28000000.0) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= -1.95e-17) {
		tmp = t_1;
	} else if (z <= -2.4e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 0.1) {
		tmp = t_1;
	} else {
		tmp = t - (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 + ((t - x) * (y / a))
    if (z <= (-28000000.0d0)) then
        tmp = t + ((x - t) / (z / y))
    else if (z <= (-1.95d-17)) then
        tmp = t_1
    else if (z <= (-2.4d-52)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 0.1d0) then
        tmp = t_1
    else
        tmp = t - (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 + ((t - x) * (y / a));
	double tmp;
	if (z <= -28000000.0) {
		tmp = t + ((x - t) / (z / y));
	} else if (z <= -1.95e-17) {
		tmp = t_1;
	} else if (z <= -2.4e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 0.1) {
		tmp = t_1;
	} else {
		tmp = t - (y / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if z <= -28000000.0:
		tmp = t + ((x - t) / (z / y))
	elif z <= -1.95e-17:
		tmp = t_1
	elif z <= -2.4e-52:
		tmp = t * ((y - z) / (a - z))
	elif z <= 0.1:
		tmp = t_1
	else:
		tmp = t - (y / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (z <= -28000000.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (z <= -1.95e-17)
		tmp = t_1;
	elseif (z <= -2.4e-52)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 0.1)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (z <= -28000000.0)
		tmp = t + ((x - t) / (z / y));
	elseif (z <= -1.95e-17)
		tmp = t_1;
	elseif (z <= -2.4e-52)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 0.1)
		tmp = t_1;
	else
		tmp = t - (y / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -28000000.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-17], t$95$1, If[LessEqual[z, -2.4e-52], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.1], t$95$1, N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e7

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. distribute-lft-out-- 57.9%

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

      3. div-sub 57.9%

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

      4. mul-1-neg 57.9%

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

      5. unsub-neg 57.9%

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

      6. distribute-rgt-out-- 58.2%

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

      7. associate-/l* 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in y around inf 67.8%

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

   if -2.8e7 < z < -1.94999999999999995e-17 or -2.4000000000000002e-52 < z < 0.10000000000000001

   1. Initial program 88.6%

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

   3. Taylor expanded in z around 0 76.5%

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

      1. expm1-log1p-u 57.2%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)\right)} \]

      2. expm1-udef 52.5%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)} - 1\right)} \]

      3. associate-/l* 52.4%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t - x}}}\right)} - 1\right) \]

   5. Applied egg-rr 52.4%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 54.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)\right)} \]

      2. expm1-log1p 73.5%

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

      3. associate-/r/ 78.0%

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

      4. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   if -1.94999999999999995e-17 < z < -2.4000000000000002e-52

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. div-inv 64.2%

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

      2. associate-*l* 87.9%

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

      3. un-div-inv 87.9%

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

   5. Applied egg-rr 87.9%

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

   if 0.10000000000000001 < z

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. distribute-lft-out-- 64.9%

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

      3. div-sub 64.9%

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

      4. mul-1-neg 64.9%

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

      5. unsub-neg 64.9%

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

      6. distribute-rgt-out-- 64.9%

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

      7. associate-/l* 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around inf 61.3%

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

      1. associate-/l* 73.3%

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

   8. Simplified 73.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -28000000:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.1:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+185}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+185)
   t
   (if (<= z 5.6e-47)
     (+ x (/ (* y t) a))
     (if (<= z 3.8e+48)
       (* (- y a) (/ x z))
       (if (<= z 4.1e+89) (* x (+ (/ z a) 1.0)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+185) {
		tmp = t;
	} else if (z <= 5.6e-47) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.8e+48) {
		tmp = (y - a) * (x / z);
	} else if (z <= 4.1e+89) {
		tmp = x * ((z / a) + 1.0);
	} 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 <= (-3.2d+185)) then
        tmp = t
    else if (z <= 5.6d-47) then
        tmp = x + ((y * t) / a)
    else if (z <= 3.8d+48) then
        tmp = (y - a) * (x / z)
    else if (z <= 4.1d+89) then
        tmp = x * ((z / a) + 1.0d0)
    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 <= -3.2e+185) {
		tmp = t;
	} else if (z <= 5.6e-47) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.8e+48) {
		tmp = (y - a) * (x / z);
	} else if (z <= 4.1e+89) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+185:
		tmp = t
	elif z <= 5.6e-47:
		tmp = x + ((y * t) / a)
	elif z <= 3.8e+48:
		tmp = (y - a) * (x / z)
	elif z <= 4.1e+89:
		tmp = x * ((z / a) + 1.0)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+185)
		tmp = t;
	elseif (z <= 5.6e-47)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 3.8e+48)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= 4.1e+89)
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+185)
		tmp = t;
	elseif (z <= 5.6e-47)
		tmp = x + ((y * t) / a);
	elseif (z <= 3.8e+48)
		tmp = (y - a) * (x / z);
	elseif (z <= 4.1e+89)
		tmp = x * ((z / a) + 1.0);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+185], t, If[LessEqual[z, 5.6e-47], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+48], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+89], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.20000000000000006e185 or 4.09999999999999985e89 < z

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 54.5%

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

   if -3.20000000000000006e185 < z < 5.59999999999999986e-47

   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 57.9%

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

   4. Taylor expanded in t around inf 49.2%

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

      1. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   if 5.59999999999999986e-47 < z < 3.8e48

   1. Initial program 79.4%

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

   3. Taylor expanded in z around inf 54.6%

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

      1. associate--l+ 54.6%

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

      2. distribute-lft-out-- 54.6%

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

      3. div-sub 54.6%

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

      4. mul-1-neg 54.6%

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

      5. unsub-neg 54.6%

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

      6. distribute-rgt-out-- 59.9%

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

      7. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 40.2%

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

      1. associate-/l* 49.9%

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

      2. associate-/r/ 49.9%

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

   8. Simplified 49.9%

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

   if 3.8e48 < z < 4.09999999999999985e89

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. unsub-neg 32.3%

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

      3. associate-/l* 44.6%

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

      4. associate-/r/ 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in z around 0 46.6%

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

   7. Taylor expanded in x around inf 45.6%

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

      1. sub-neg 45.6%

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

      2. mul-1-neg 45.6%

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

      3. remove-double-neg 45.6%

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

   9. Simplified 45.6%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+185}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ t_2 := t + \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-160}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 0.48:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))) (t_2 (+ t (/ x (/ z y)))))
   (if (<= z -2.75e+48)
     t_2
     (if (<= z -4.1e-178)
       t_1
       (if (<= z 3.5e-160) (+ x (/ (* y t) a)) (if (<= z 0.48) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = t + (x / (z / y));
	double tmp;
	if (z <= -2.75e+48) {
		tmp = t_2;
	} else if (z <= -4.1e-178) {
		tmp = t_1;
	} else if (z <= 3.5e-160) {
		tmp = x + ((y * t) / a);
	} else if (z <= 0.48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    t_2 = t + (x / (z / y))
    if (z <= (-2.75d+48)) then
        tmp = t_2
    else if (z <= (-4.1d-178)) then
        tmp = t_1
    else if (z <= 3.5d-160) then
        tmp = x + ((y * t) / a)
    else if (z <= 0.48d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double t_2 = t + (x / (z / y));
	double tmp;
	if (z <= -2.75e+48) {
		tmp = t_2;
	} else if (z <= -4.1e-178) {
		tmp = t_1;
	} else if (z <= 3.5e-160) {
		tmp = x + ((y * t) / a);
	} else if (z <= 0.48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	t_2 = t + (x / (z / y))
	tmp = 0
	if z <= -2.75e+48:
		tmp = t_2
	elif z <= -4.1e-178:
		tmp = t_1
	elif z <= 3.5e-160:
		tmp = x + ((y * t) / a)
	elif z <= 0.48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	t_2 = Float64(t + Float64(x / Float64(z / y)))
	tmp = 0.0
	if (z <= -2.75e+48)
		tmp = t_2;
	elseif (z <= -4.1e-178)
		tmp = t_1;
	elseif (z <= 3.5e-160)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 0.48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	t_2 = t + (x / (z / y));
	tmp = 0.0;
	if (z <= -2.75e+48)
		tmp = t_2;
	elseif (z <= -4.1e-178)
		tmp = t_1;
	elseif (z <= 3.5e-160)
		tmp = x + ((y * t) / a);
	elseif (z <= 0.48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e+48], t$95$2, If[LessEqual[z, -4.1e-178], t$95$1, If[LessEqual[z, 3.5e-160], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7500000000000001e48 or 0.47999999999999998 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. distribute-lft-out-- 60.8%

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

      3. div-sub 60.8%

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

      4. mul-1-neg 60.8%

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

      5. unsub-neg 60.8%

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

      6. distribute-rgt-out-- 61.0%

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

      7. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around inf 69.8%

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

   7. Taylor expanded in t around 0 48.7%

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

      1. associate-/l* 57.8%

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

      2. neg-mul-1 57.8%

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

      3. distribute-neg-frac 57.8%

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

   9. Simplified 57.8%

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

   if -2.7500000000000001e48 < z < -4.0999999999999999e-178 or 3.5000000000000003e-160 < z < 0.47999999999999998

   1. Initial program 86.2%

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

      1. clear-num 86.1%

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

      2. associate-/r/ 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. associate-/l* 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. associate-/l* 59.2%

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

   10. Simplified 59.2%

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

   if -4.0999999999999999e-178 < z < 3.5000000000000003e-160

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 83.5%

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

   4. Taylor expanded in t around inf 69.1%

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

      1. *-commutative 69.1%

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

   6. Simplified 69.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-178}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-160}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 0.48:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.82e+71)
   (* t (/ y a))
   (if (<= y 5.8e-60)
     x
     (if (<= y 5.8e+86)
       t
       (if (<= y 4.5e+251) (* y (/ x z)) (* x (/ y (- a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.82e+71) {
		tmp = t * (y / a);
	} else if (y <= 5.8e-60) {
		tmp = x;
	} else if (y <= 5.8e+86) {
		tmp = t;
	} else if (y <= 4.5e+251) {
		tmp = y * (x / z);
	} else {
		tmp = x * (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 (y <= (-1.82d+71)) then
        tmp = t * (y / a)
    else if (y <= 5.8d-60) then
        tmp = x
    else if (y <= 5.8d+86) then
        tmp = t
    else if (y <= 4.5d+251) then
        tmp = y * (x / z)
    else
        tmp = x * (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 (y <= -1.82e+71) {
		tmp = t * (y / a);
	} else if (y <= 5.8e-60) {
		tmp = x;
	} else if (y <= 5.8e+86) {
		tmp = t;
	} else if (y <= 4.5e+251) {
		tmp = y * (x / z);
	} else {
		tmp = x * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.82e+71:
		tmp = t * (y / a)
	elif y <= 5.8e-60:
		tmp = x
	elif y <= 5.8e+86:
		tmp = t
	elif y <= 4.5e+251:
		tmp = y * (x / z)
	else:
		tmp = x * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.82e+71)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 5.8e-60)
		tmp = x;
	elseif (y <= 5.8e+86)
		tmp = t;
	elseif (y <= 4.5e+251)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.82e+71)
		tmp = t * (y / a);
	elseif (y <= 5.8e-60)
		tmp = x;
	elseif (y <= 5.8e+86)
		tmp = t;
	elseif (y <= 4.5e+251)
		tmp = y * (x / z);
	else
		tmp = x * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.82e+71], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-60], x, If[LessEqual[y, 5.8e+86], t, If[LessEqual[y, 4.5e+251], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.8200000000000001e71

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in z around 0 27.3%

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

      1. associate-/l* 34.6%

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

   6. Simplified 34.6%

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

      1. associate-/r/ 32.8%

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

   8. Applied egg-rr 32.8%

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

   9. Taylor expanded in t around 0 27.3%

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

       1. *-commutative 27.3%

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

       2. associate-*l/ 34.6%

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

   11. Simplified 34.6%

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

   if -1.8200000000000001e71 < y < 5.7999999999999999e-60

   1. Initial program 78.0%

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

   3. Taylor expanded in a around inf 43.4%

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

   if 5.7999999999999999e-60 < y < 5.79999999999999981e86

   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 53.8%

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

   if 5.79999999999999981e86 < y < 4.4999999999999998e251

   1. Initial program 84.7%

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

   3. Taylor expanded in z around inf 48.2%

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

      1. associate--l+ 48.2%

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

      2. distribute-lft-out-- 48.2%

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

      3. div-sub 51.4%

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

      4. mul-1-neg 51.4%

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

      5. unsub-neg 51.4%

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

      6. distribute-rgt-out-- 52.2%

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

      7. associate-/l* 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around inf 75.1%

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

   7. Taylor expanded in t around 0 33.6%

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

      1. associate-*l/ 47.8%

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

   9. Simplified 47.8%

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

   if 4.4999999999999998e251 < y

   1. Initial program 87.3%

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

      1. clear-num 87.2%

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

      2. associate-/r/ 87.4%

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

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in t around 0 41.1%

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

      1. mul-1-neg 41.1%

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

      2. unsub-neg 41.1%

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

      3. associate-/l* 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in y around inf 35.2%

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

      1. associate-*r/ 35.2%

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

      2. associate-*r* 35.2%

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

      3. neg-mul-1 35.2%

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

   10. Simplified 35.2%

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

   11. Taylor expanded in a around inf 29.9%

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

       1. mul-1-neg 29.9%

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

       2. *-rgt-identity 29.9%

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

       3. associate-*r/ 29.9%

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

       4. distribute-rgt-neg-in 29.9%

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

       5. distribute-neg-frac 29.9%

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

       6. metadata-eval 29.9%

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

       7. metadata-eval 29.9%

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

       8. associate-/r* 29.9%

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

       9. neg-mul-1 29.9%

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

       10. associate-*l* 42.4%

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

       11. associate-*r/ 42.5%

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

       12. *-rgt-identity 42.5%

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

   13. Simplified 42.5%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9e+67)
   (* t (/ y a))
   (if (<= y 6e-60)
     x
     (if (<= y 8.8e+86)
       t
       (if (<= y 4.3e+251) (* y (/ x z)) (/ (- x) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+67) {
		tmp = t * (y / a);
	} else if (y <= 6e-60) {
		tmp = x;
	} else if (y <= 8.8e+86) {
		tmp = t;
	} else if (y <= 4.3e+251) {
		tmp = y * (x / z);
	} else {
		tmp = -x / (a / 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 (y <= (-9d+67)) then
        tmp = t * (y / a)
    else if (y <= 6d-60) then
        tmp = x
    else if (y <= 8.8d+86) then
        tmp = t
    else if (y <= 4.3d+251) then
        tmp = y * (x / z)
    else
        tmp = -x / (a / 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 (y <= -9e+67) {
		tmp = t * (y / a);
	} else if (y <= 6e-60) {
		tmp = x;
	} else if (y <= 8.8e+86) {
		tmp = t;
	} else if (y <= 4.3e+251) {
		tmp = y * (x / z);
	} else {
		tmp = -x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9e+67:
		tmp = t * (y / a)
	elif y <= 6e-60:
		tmp = x
	elif y <= 8.8e+86:
		tmp = t
	elif y <= 4.3e+251:
		tmp = y * (x / z)
	else:
		tmp = -x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9e+67)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 6e-60)
		tmp = x;
	elseif (y <= 8.8e+86)
		tmp = t;
	elseif (y <= 4.3e+251)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(-x) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9e+67)
		tmp = t * (y / a);
	elseif (y <= 6e-60)
		tmp = x;
	elseif (y <= 8.8e+86)
		tmp = t;
	elseif (y <= 4.3e+251)
		tmp = y * (x / z);
	else
		tmp = -x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9e+67], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-60], x, If[LessEqual[y, 8.8e+86], t, If[LessEqual[y, 4.3e+251], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.9999999999999997e67

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in z around 0 27.3%

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

      1. associate-/l* 34.6%

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

   6. Simplified 34.6%

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

      1. associate-/r/ 32.8%

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

   8. Applied egg-rr 32.8%

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

   9. Taylor expanded in t around 0 27.3%

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

       1. *-commutative 27.3%

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

       2. associate-*l/ 34.6%

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

   11. Simplified 34.6%

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

   if -8.9999999999999997e67 < y < 6.00000000000000038e-60

   1. Initial program 78.0%

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

   3. Taylor expanded in a around inf 43.4%

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

   if 6.00000000000000038e-60 < y < 8.80000000000000013e86

   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 53.8%

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

   if 8.80000000000000013e86 < y < 4.3e251

   1. Initial program 84.7%

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

   3. Taylor expanded in z around inf 48.2%

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

      1. associate--l+ 48.2%

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

      2. distribute-lft-out-- 48.2%

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

      3. div-sub 51.4%

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

      4. mul-1-neg 51.4%

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

      5. unsub-neg 51.4%

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

      6. distribute-rgt-out-- 52.2%

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

      7. associate-/l* 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around inf 75.1%

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

   7. Taylor expanded in t around 0 33.6%

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

      1. associate-*l/ 47.8%

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

   9. Simplified 47.8%

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

   if 4.3e251 < y

   1. Initial program 87.3%

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

      1. clear-num 87.2%

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

      2. associate-/r/ 87.4%

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

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in t around 0 41.1%

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

      1. mul-1-neg 41.1%

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

      2. unsub-neg 41.1%

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

      3. associate-/l* 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in y around inf 35.2%

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

      1. associate-*r/ 35.2%

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

      2. associate-*r* 35.2%

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

      3. neg-mul-1 35.2%

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

   10. Simplified 35.2%

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

   11. Taylor expanded in a around inf 29.9%

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

       1. mul-1-neg 29.9%

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

       2. associate-/l* 42.7%

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

       3. distribute-neg-frac 42.7%

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

   13. Simplified 42.7%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.016:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z y)))))
   (if (<= z -6.5e+100)
     t_1
     (if (<= z -6.8e-52)
       (* t (/ (- y z) (- a z)))
       (if (<= z 0.016) (+ x (* (- t x) (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double tmp;
	if (z <= -6.5e+100) {
		tmp = t_1;
	} else if (z <= -6.8e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 0.016) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / y))
    if (z <= (-6.5d+100)) then
        tmp = t_1
    else if (z <= (-6.8d-52)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 0.016d0) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double tmp;
	if (z <= -6.5e+100) {
		tmp = t_1;
	} else if (z <= -6.8e-52) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 0.016) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / y))
	tmp = 0
	if z <= -6.5e+100:
		tmp = t_1
	elif z <= -6.8e-52:
		tmp = t * ((y - z) / (a - z))
	elif z <= 0.016:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / y)))
	tmp = 0.0
	if (z <= -6.5e+100)
		tmp = t_1;
	elseif (z <= -6.8e-52)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 0.016)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / y));
	tmp = 0.0;
	if (z <= -6.5e+100)
		tmp = t_1;
	elseif (z <= -6.8e-52)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 0.016)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+100], t$95$1, If[LessEqual[z, -6.8e-52], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.016], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000001e100 or 0.016 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. distribute-lft-out-- 61.3%

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

      3. div-sub 61.3%

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

      4. mul-1-neg 61.3%

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

      5. unsub-neg 61.3%

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

      6. distribute-rgt-out-- 61.5%

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

      7. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around inf 72.1%

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

   7. Taylor expanded in t around 0 52.0%

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

      1. associate-/l* 62.7%

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

      2. neg-mul-1 62.7%

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

      3. distribute-neg-frac 62.7%

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

   9. Simplified 62.7%

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

   if -6.50000000000000001e100 < z < -6.80000000000000035e-52

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 48.7%

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

      1. div-inv 48.7%

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

      2. associate-*l* 60.9%

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

      3. un-div-inv 61.0%

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

   5. Applied egg-rr 61.0%

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

   if -6.80000000000000035e-52 < z < 0.016

   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 75.9%

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

      1. expm1-log1p-u 56.3%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)\right)} \]

      2. expm1-udef 52.1%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a}\right)} - 1\right)} \]

      3. associate-/l* 52.0%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t - x}}}\right)} - 1\right) \]

   5. Applied egg-rr 52.0%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 54.6%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t - x}}\right)\right)} \]

      2. expm1-log1p 73.5%

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

      3. associate-/r/ 77.5%

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

      4. *-commutative 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+100}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.016:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+183}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e+183)
   t
   (if (<= z -7e-184)
     x
     (if (<= z 2.7e-249) (* y (/ t a)) (if (<= z 3.8e+23) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e+183) {
		tmp = t;
	} else if (z <= -7e-184) {
		tmp = x;
	} else if (z <= 2.7e-249) {
		tmp = y * (t / a);
	} else if (z <= 3.8e+23) {
		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 <= (-7.8d+183)) then
        tmp = t
    else if (z <= (-7d-184)) then
        tmp = x
    else if (z <= 2.7d-249) then
        tmp = y * (t / a)
    else if (z <= 3.8d+23) 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 <= -7.8e+183) {
		tmp = t;
	} else if (z <= -7e-184) {
		tmp = x;
	} else if (z <= 2.7e-249) {
		tmp = y * (t / a);
	} else if (z <= 3.8e+23) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.8e+183:
		tmp = t
	elif z <= -7e-184:
		tmp = x
	elif z <= 2.7e-249:
		tmp = y * (t / a)
	elif z <= 3.8e+23:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e+183)
		tmp = t;
	elseif (z <= -7e-184)
		tmp = x;
	elseif (z <= 2.7e-249)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 3.8e+23)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.8e+183)
		tmp = t;
	elseif (z <= -7e-184)
		tmp = x;
	elseif (z <= 2.7e-249)
		tmp = y * (t / a);
	elseif (z <= 3.8e+23)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e+183], t, If[LessEqual[z, -7e-184], x, If[LessEqual[z, 2.7e-249], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+23], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.7999999999999998e183 or 3.79999999999999975e23 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 48.8%

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

   if -7.7999999999999998e183 < z < -6.99999999999999962e-184 or 2.7000000000000001e-249 < z < 3.79999999999999975e23

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 37.6%

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

   if -6.99999999999999962e-184 < z < 2.7000000000000001e-249

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 44.6%

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

   4. Taylor expanded in z around 0 38.3%

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

      1. associate-/l* 44.8%

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

   6. Simplified 44.8%

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

      1. associate-/r/ 41.7%

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

   8. Applied egg-rr 41.7%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+183}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.3e+68)
   (* y (/ t a))
   (if (<= y 9.5e-57) x (if (<= y 5.8e+84) t (* y (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.3e+68) {
		tmp = y * (t / a);
	} else if (y <= 9.5e-57) {
		tmp = x;
	} else if (y <= 5.8e+84) {
		tmp = t;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.3d+68)) then
        tmp = y * (t / a)
    else if (y <= 9.5d-57) then
        tmp = x
    else if (y <= 5.8d+84) then
        tmp = t
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.3e+68) {
		tmp = y * (t / a);
	} else if (y <= 9.5e-57) {
		tmp = x;
	} else if (y <= 5.8e+84) {
		tmp = t;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.3e+68:
		tmp = y * (t / a)
	elif y <= 9.5e-57:
		tmp = x
	elif y <= 5.8e+84:
		tmp = t
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.3e+68)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 9.5e-57)
		tmp = x;
	elseif (y <= 5.8e+84)
		tmp = t;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.3e+68)
		tmp = y * (t / a);
	elseif (y <= 9.5e-57)
		tmp = x;
	elseif (y <= 5.8e+84)
		tmp = t;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.3e+68], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-57], x, If[LessEqual[y, 5.8e+84], t, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.30000000000000027e68

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in z around 0 27.3%

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

      1. associate-/l* 34.6%

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

   6. Simplified 34.6%

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

      1. associate-/r/ 32.8%

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

   8. Applied egg-rr 32.8%

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

   if -6.30000000000000027e68 < y < 9.5000000000000005e-57

   1. Initial program 78.0%

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

   3. Taylor expanded in a around inf 43.4%

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

   if 9.5000000000000005e-57 < y < 5.79999999999999977e84

   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 53.8%

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

   if 5.79999999999999977e84 < y

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 48.0%

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

      1. associate--l+ 48.0%

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

      2. distribute-lft-out-- 48.0%

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

      3. div-sub 50.2%

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

      4. mul-1-neg 50.2%

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

      5. unsub-neg 50.2%

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

      6. distribute-rgt-out-- 50.7%

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

      7. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around inf 70.3%

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

   7. Taylor expanded in t around 0 27.6%

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

      1. associate-*l/ 37.3%

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

   9. Simplified 37.3%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e+72)
   (* t (/ y a))
   (if (<= y 4.7e-55) x (if (<= y 6.5e+84) t (* y (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e+72) {
		tmp = t * (y / a);
	} else if (y <= 4.7e-55) {
		tmp = x;
	} else if (y <= 6.5e+84) {
		tmp = t;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1d+72)) then
        tmp = t * (y / a)
    else if (y <= 4.7d-55) then
        tmp = x
    else if (y <= 6.5d+84) then
        tmp = t
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e+72) {
		tmp = t * (y / a);
	} else if (y <= 4.7e-55) {
		tmp = x;
	} else if (y <= 6.5e+84) {
		tmp = t;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1e+72:
		tmp = t * (y / a)
	elif y <= 4.7e-55:
		tmp = x
	elif y <= 6.5e+84:
		tmp = t
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1e+72)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 4.7e-55)
		tmp = x;
	elseif (y <= 6.5e+84)
		tmp = t;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1e+72)
		tmp = t * (y / a);
	elseif (y <= 4.7e-55)
		tmp = x;
	elseif (y <= 6.5e+84)
		tmp = t;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1e+72], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-55], x, If[LessEqual[y, 6.5e+84], t, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.99999999999999944e71

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in z around 0 27.3%

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

      1. associate-/l* 34.6%

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

   6. Simplified 34.6%

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

      1. associate-/r/ 32.8%

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

   8. Applied egg-rr 32.8%

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

   9. Taylor expanded in t around 0 27.3%

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

       1. *-commutative 27.3%

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

       2. associate-*l/ 34.6%

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

   11. Simplified 34.6%

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

   if -9.99999999999999944e71 < y < 4.7e-55

   1. Initial program 78.0%

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

   3. Taylor expanded in a around inf 43.4%

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

   if 4.7e-55 < y < 6.50000000000000027e84

   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 53.8%

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

   if 6.50000000000000027e84 < y

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 48.0%

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

      1. associate--l+ 48.0%

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

      2. distribute-lft-out-- 48.0%

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

      3. div-sub 50.2%

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

      4. mul-1-neg 50.2%

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

      5. unsub-neg 50.2%

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

      6. distribute-rgt-out-- 50.7%

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

      7. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around inf 70.3%

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

   7. Taylor expanded in t around 0 27.6%

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

      1. associate-*l/ 37.3%

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

   9. Simplified 37.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-52} \lor \neg \left(z \leq 3.7\right):\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.6e-52) (not (<= z 3.7)))
   (- t (* t (/ y z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e-52) || !(z <= 3.7)) {
		tmp = t - (t * (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.6d-52)) .or. (.not. (z <= 3.7d0))) then
        tmp = t - (t * (y / z))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e-52) || !(z <= 3.7)) {
		tmp = t - (t * (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.6e-52) or not (z <= 3.7):
		tmp = t - (t * (y / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.6e-52) || !(z <= 3.7))
		tmp = Float64(t - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.6e-52) || ~((z <= 3.7)))
		tmp = t - (t * (y / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.6e-52], N[Not[LessEqual[z, 3.7]], $MachinePrecision]], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999989e-52 or 3.7000000000000002 < z

   1. Initial program 75.6%

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

   3. Taylor expanded in z around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. distribute-lft-out-- 58.8%

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

      3. div-sub 58.8%

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

      4. mul-1-neg 58.8%

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

      5. unsub-neg 58.8%

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

      6. distribute-rgt-out-- 59.0%

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

      7. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in y around inf 66.4%

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

   7. Taylor expanded in t around inf 45.1%

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

      1. associate-*r/ 49.8%

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

   9. Simplified 49.8%

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

   if -5.59999999999999989e-52 < z < 3.7000000000000002

   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 76.1%

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

   4. Taylor expanded in t around inf 60.6%

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

      1. *-commutative 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-52} \lor \neg \left(z \leq 3.7\right):\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+103}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.08e+46)
   x
   (if (<= a 3.2e+103) (* (- y a) (/ x z)) (* x (+ (/ z a) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e+46) {
		tmp = x;
	} else if (a <= 3.2e+103) {
		tmp = (y - a) * (x / z);
	} else {
		tmp = x * ((z / a) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.08d+46)) then
        tmp = x
    else if (a <= 3.2d+103) then
        tmp = (y - a) * (x / z)
    else
        tmp = x * ((z / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e+46) {
		tmp = x;
	} else if (a <= 3.2e+103) {
		tmp = (y - a) * (x / z);
	} else {
		tmp = x * ((z / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.08e+46:
		tmp = x
	elif a <= 3.2e+103:
		tmp = (y - a) * (x / z)
	else:
		tmp = x * ((z / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.08e+46)
		tmp = x;
	elseif (a <= 3.2e+103)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.08e+46)
		tmp = x;
	elseif (a <= 3.2e+103)
		tmp = (y - a) * (x / z);
	else
		tmp = x * ((z / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.08e+46], x, If[LessEqual[a, 3.2e+103], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.07999999999999994e46

   1. Initial program 86.7%

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

   3. Taylor expanded in a around inf 55.0%

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

   if -1.07999999999999994e46 < a < 3.19999999999999993e103

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. distribute-lft-out-- 62.3%

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

      3. div-sub 64.3%

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

      4. mul-1-neg 64.3%

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

      5. unsub-neg 64.3%

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

      6. distribute-rgt-out-- 65.0%

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

      7. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 26.7%

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

      1. associate-/l* 33.0%

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

      2. associate-/r/ 32.4%

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

   8. Simplified 32.4%

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

   if 3.19999999999999993e103 < a

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

      3. associate-/l* 72.7%

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

      4. associate-/r/ 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in z around 0 57.3%

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

   7. Taylor expanded in x around inf 54.4%

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

      1. sub-neg 54.4%

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

      2. mul-1-neg 54.4%

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

      3. remove-double-neg 54.4%

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

   9. Simplified 54.4%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+103}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+187}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+187) t (if (<= z 1.4e+23) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+187) {
		tmp = t;
	} else if (z <= 1.4e+23) {
		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 <= (-1.3d+187)) then
        tmp = t
    else if (z <= 1.4d+23) 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 <= -1.3e+187) {
		tmp = t;
	} else if (z <= 1.4e+23) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+187:
		tmp = t
	elif z <= 1.4e+23:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+187)
		tmp = t;
	elseif (z <= 1.4e+23)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+187)
		tmp = t;
	elseif (z <= 1.4e+23)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+187], t, If[LessEqual[z, 1.4e+23], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e187 or 1.4e23 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 48.8%

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

   if -1.2999999999999999e187 < z < 1.4e23

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf 35.7%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+187}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 25.8% 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 81.6%

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

3. Taylor expanded in z around inf 21.8%

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

4. Final simplification 21.8%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(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)))))