Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 94.9%

Time: 20.2s

Alternatives: 15

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: 80.3% 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: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-304} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-304) (not (<= t_1 0.0)))
     (+ x (* (- t x) (* (- y z) (/ 1.0 (- a z)))))
     (+ 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-304) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	} 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-304)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) * (1.0d0 / (a - z))))
    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-304) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	} 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-304) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))))
	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-304) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) * Float64(1.0 / Float64(a - z)))));
	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-304) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	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-304], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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)))) < -1.99999999999999994e-304 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.0%

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

      1. add-cube-cbrt 88.0%

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

      2. pow3 88.1%

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

   4. Applied egg-rr 88.1%

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

      1. rem-cube-cbrt 89.0%

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

      2. *-commutative 89.0%

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

      3. div-inv 88.9%

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

      4. associate-*l* 93.7%

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

   6. Applied egg-rr 93.7%

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

   if -1.99999999999999994e-304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   3. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. distribute-lft-out-- 79.5%

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

      3. div-sub 79.5%

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

      4. mul-1-neg 79.5%

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

      5. unsub-neg 79.5%

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

      6. distribute-rgt-out-- 79.5%

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

      7. associate-/l* 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-304} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-259} \lor \neg \left(t_1 \leq 10^{-240}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-259) (not (<= t_1 1e-240)))
     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 <= -1e-259) || !(t_1 <= 1e-240)) {
		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 <= (-1d-259)) .or. (.not. (t_1 <= 1d-240))) 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 <= -1e-259) || !(t_1 <= 1e-240)) {
		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 <= -1e-259) or not (t_1 <= 1e-240):
		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 <= -1e-259) || !(t_1 <= 1e-240))
		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 <= -1e-259) || ~((t_1 <= 1e-240)))
		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, -1e-259], N[Not[LessEqual[t$95$1, 1e-240]], $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)))) < -1.0000000000000001e-259 or 9.9999999999999997e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.4%

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

   if -1.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999997e-241

   1. Initial program 8.7%

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

   3. Taylor expanded in z around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. distribute-lft-out-- 77.6%

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

      3. div-sub 77.6%

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

      4. mul-1-neg 77.6%

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

      5. unsub-neg 77.6%

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

      6. distribute-rgt-out-- 77.6%

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

      7. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-259} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-240}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-39}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (- t (/ (- t x) (/ z (- y a))))))
   (if (<= z -7.5e+135)
     t_2
     (if (<= z -1.3e+21)
       t_1
       (if (<= z -9.8e-39)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= z 2.05e+21) 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 - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -7.5e+135) {
		tmp = t_2;
	} else if (z <= -1.3e+21) {
		tmp = t_1;
	} else if (z <= -9.8e-39) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 2.05e+21) {
		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 - ((t - x) / (z / (y - a)))
    if (z <= (-7.5d+135)) then
        tmp = t_2
    else if (z <= (-1.3d+21)) then
        tmp = t_1
    else if (z <= (-9.8d-39)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 2.05d+21) 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 - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -7.5e+135) {
		tmp = t_2;
	} else if (z <= -1.3e+21) {
		tmp = t_1;
	} else if (z <= -9.8e-39) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 2.05e+21) {
		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 - ((t - x) / (z / (y - a)))
	tmp = 0
	if z <= -7.5e+135:
		tmp = t_2
	elif z <= -1.3e+21:
		tmp = t_1
	elif z <= -9.8e-39:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 2.05e+21:
		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(Float64(t - x) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -7.5e+135)
		tmp = t_2;
	elseif (z <= -1.3e+21)
		tmp = t_1;
	elseif (z <= -9.8e-39)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 2.05e+21)
		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 - ((t - x) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -7.5e+135)
		tmp = t_2;
	elseif (z <= -1.3e+21)
		tmp = t_1;
	elseif (z <= -9.8e-39)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 2.05e+21)
		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[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+135], t$95$2, If[LessEqual[z, -1.3e+21], t$95$1, If[LessEqual[z, -9.8e-39], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.49999999999999947e135 or 2.05e21 < z

   1. Initial program 59.6%

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

   3. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. distribute-rgt-out-- 66.7%

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

      7. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   if -7.49999999999999947e135 < z < -1.3e21 or -9.79999999999999947e-39 < z < 2.05e21

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 65.7%

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

      1. associate-/l* 75.2%

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

      2. associate-/r/ 76.7%

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

   5. Simplified 76.7%

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

   if -1.3e21 < z < -9.79999999999999947e-39

   1. Initial program 67.1%

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

      1. clear-num 67.1%

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

      2. associate-/r/ 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in z around inf 77.7%

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

      1. associate--l+ 77.7%

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

      2. associate-*r/ 77.7%

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

      3. associate-*r/ 77.7%

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

      4. div-sub 77.7%

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

      5. distribute-lft-out-- 77.7%

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

      6. associate-*r/ 77.7%

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

      7. mul-1-neg 77.7%

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

      8. unsub-neg 77.7%

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

      9. distribute-rgt-out-- 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+135}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+21}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-39}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+21}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -3 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (/ x (/ a y)))))
   (if (<= x -3e+188)
     t_2
     (if (<= x 2.85e+16)
       t_1
       (if (<= x 3.8e+96)
         (* y (/ (- t x) (- a z)))
         (if (<= x 9.5e+135) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (x <= -3e+188) {
		tmp = t_2;
	} else if (x <= 2.85e+16) {
		tmp = t_1;
	} else if (x <= 3.8e+96) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 9.5e+135) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (x / (a / y))
    if (x <= (-3d+188)) then
        tmp = t_2
    else if (x <= 2.85d+16) then
        tmp = t_1
    else if (x <= 3.8d+96) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 9.5d+135) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (x <= -3e+188) {
		tmp = t_2;
	} else if (x <= 2.85e+16) {
		tmp = t_1;
	} else if (x <= 3.8e+96) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 9.5e+135) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (x / (a / y))
	tmp = 0
	if x <= -3e+188:
		tmp = t_2
	elif x <= 2.85e+16:
		tmp = t_1
	elif x <= 3.8e+96:
		tmp = y * ((t - x) / (a - z))
	elif x <= 9.5e+135:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -3e+188)
		tmp = t_2;
	elseif (x <= 2.85e+16)
		tmp = t_1;
	elseif (x <= 3.8e+96)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 9.5e+135)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (x / (a / y));
	tmp = 0.0;
	if (x <= -3e+188)
		tmp = t_2;
	elseif (x <= 2.85e+16)
		tmp = t_1;
	elseif (x <= 3.8e+96)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 9.5e+135)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+188], t$95$2, If[LessEqual[x, 2.85e+16], t$95$1, If[LessEqual[x, 3.8e+96], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+135], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000001e188 or 9.50000000000000036e135 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in z around 0 48.6%

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

      1. associate-/l* 57.8%

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

      2. associate-/r/ 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. associate-/l* 61.7%

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

   8. Simplified 61.7%

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

   if -3.0000000000000001e188 < x < 2.85e16 or 3.8000000000000002e96 < x < 9.50000000000000036e135

   1. Initial program 80.6%

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

   3. Taylor expanded in x around 0 54.4%

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

      1. div-inv 54.4%

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

      2. associate-*l* 77.2%

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

      3. un-div-inv 77.3%

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

   5. Applied egg-rr 77.3%

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

   if 2.85e16 < x < 3.8000000000000002e96

   1. Initial program 78.7%

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

      1. clear-num 78.5%

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

      2. associate-/r/ 78.5%

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

   4. Applied egg-rr 78.5%

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

   5. Taylor expanded in y around inf 65.1%

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

      1. div-sub 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+188}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (/ x (/ a y)))))
   (if (<= x -2.6e+188)
     t_2
     (if (<= x 5.4e-39)
       t_1
       (if (<= x 2.5e+96)
         (* (- t x) (/ y (- a z)))
         (if (<= x 9.5e+135) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (x <= -2.6e+188) {
		tmp = t_2;
	} else if (x <= 5.4e-39) {
		tmp = t_1;
	} else if (x <= 2.5e+96) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 9.5e+135) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (x / (a / y))
    if (x <= (-2.6d+188)) then
        tmp = t_2
    else if (x <= 5.4d-39) then
        tmp = t_1
    else if (x <= 2.5d+96) then
        tmp = (t - x) * (y / (a - z))
    else if (x <= 9.5d+135) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x / (a / y));
	double tmp;
	if (x <= -2.6e+188) {
		tmp = t_2;
	} else if (x <= 5.4e-39) {
		tmp = t_1;
	} else if (x <= 2.5e+96) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 9.5e+135) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (x / (a / y))
	tmp = 0
	if x <= -2.6e+188:
		tmp = t_2
	elif x <= 5.4e-39:
		tmp = t_1
	elif x <= 2.5e+96:
		tmp = (t - x) * (y / (a - z))
	elif x <= 9.5e+135:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -2.6e+188)
		tmp = t_2;
	elseif (x <= 5.4e-39)
		tmp = t_1;
	elseif (x <= 2.5e+96)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (x <= 9.5e+135)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (x / (a / y));
	tmp = 0.0;
	if (x <= -2.6e+188)
		tmp = t_2;
	elseif (x <= 5.4e-39)
		tmp = t_1;
	elseif (x <= 2.5e+96)
		tmp = (t - x) * (y / (a - z));
	elseif (x <= 9.5e+135)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+188], t$95$2, If[LessEqual[x, 5.4e-39], t$95$1, If[LessEqual[x, 2.5e+96], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+135], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.59999999999999987e188 or 9.50000000000000036e135 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in z around 0 48.6%

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

      1. associate-/l* 57.8%

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

      2. associate-/r/ 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. associate-/l* 61.7%

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

   8. Simplified 61.7%

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

   if -2.59999999999999987e188 < x < 5.4000000000000001e-39 or 2.5000000000000002e96 < x < 9.50000000000000036e135

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. div-inv 55.1%

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

      2. associate-*l* 77.6%

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

      3. un-div-inv 77.7%

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

   5. Applied egg-rr 77.7%

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

   if 5.4000000000000001e-39 < x < 2.5000000000000002e96

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. div-sub 66.7%

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

      2. associate-*r/ 54.7%

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

      3. associate-/l* 66.8%

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

      4. associate-/r/ 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+188}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-39}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 162000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.2e+121)
     t_2
     (if (<= z -4.5e+20)
       t_1
       (if (<= z -5e-39)
         (* (- t x) (/ y (- a z)))
         (if (<= z 162000000000.0) 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) / (a - z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_2;
	} else if (z <= -4.5e+20) {
		tmp = t_1;
	} else if (z <= -5e-39) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 162000000000.0) {
		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) / (a - z))
    if (z <= (-2.2d+121)) then
        tmp = t_2
    else if (z <= (-4.5d+20)) then
        tmp = t_1
    else if (z <= (-5d-39)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 162000000000.0d0) 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) / (a - z));
	double tmp;
	if (z <= -2.2e+121) {
		tmp = t_2;
	} else if (z <= -4.5e+20) {
		tmp = t_1;
	} else if (z <= -5e-39) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 162000000000.0) {
		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) / (a - z))
	tmp = 0
	if z <= -2.2e+121:
		tmp = t_2
	elif z <= -4.5e+20:
		tmp = t_1
	elif z <= -5e-39:
		tmp = (t - x) * (y / (a - z))
	elif z <= 162000000000.0:
		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(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.2e+121)
		tmp = t_2;
	elseif (z <= -4.5e+20)
		tmp = t_1;
	elseif (z <= -5e-39)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 162000000000.0)
		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) / (a - z));
	tmp = 0.0;
	if (z <= -2.2e+121)
		tmp = t_2;
	elseif (z <= -4.5e+20)
		tmp = t_1;
	elseif (z <= -5e-39)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 162000000000.0)
		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[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+121], t$95$2, If[LessEqual[z, -4.5e+20], t$95$1, If[LessEqual[z, -5e-39], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 162000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000001e121 or 1.62e11 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in x around 0 41.7%

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

      1. div-inv 41.7%

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

      2. associate-*l* 74.6%

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

      3. un-div-inv 74.7%

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

   5. Applied egg-rr 74.7%

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

   if -2.20000000000000001e121 < z < -4.5e20 or -4.9999999999999998e-39 < z < 1.62e11

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 66.3%

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

      1. associate-/l* 75.6%

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

      2. associate-/r/ 77.1%

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

   5. Simplified 77.1%

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

   if -4.5e20 < z < -4.9999999999999998e-39

   1. Initial program 67.1%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

      2. associate-*r/ 69.9%

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

      3. associate-/l* 75.5%

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

      4. associate-/r/ 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-39}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 162000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-146}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -1.3e+163)
     t_1
     (if (<= a -3.4e-62)
       (* t (/ (- y z) (- a z)))
       (if (<= a 1.85e-146)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= a 1.3e-12) (/ t (/ (- a z) (- y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.3e+163) {
		tmp = t_1;
	} else if (a <= -3.4e-62) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.85e-146) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 1.3e-12) {
		tmp = t / ((a - z) / (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 = x + ((t - x) * (y / a))
    if (a <= (-1.3d+163)) then
        tmp = t_1
    else if (a <= (-3.4d-62)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.85d-146) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (a <= 1.3d-12) then
        tmp = t / ((a - z) / (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 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.3e+163) {
		tmp = t_1;
	} else if (a <= -3.4e-62) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.85e-146) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 1.3e-12) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -1.3e+163:
		tmp = t_1
	elif a <= -3.4e-62:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.85e-146:
		tmp = t + (((t - x) * (a - y)) / z)
	elif a <= 1.3e-12:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	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 (a <= -1.3e+163)
		tmp = t_1;
	elseif (a <= -3.4e-62)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.85e-146)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (a <= 1.3e-12)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	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 (a <= -1.3e+163)
		tmp = t_1;
	elseif (a <= -3.4e-62)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.85e-146)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (a <= 1.3e-12)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	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[a, -1.3e+163], t$95$1, If[LessEqual[a, -3.4e-62], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-146], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-12], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3000000000000001e163 or 1.29999999999999991e-12 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 56.5%

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

      1. associate-/l* 73.1%

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

      2. associate-/r/ 74.1%

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

   5. Simplified 74.1%

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

   if -1.3000000000000001e163 < a < -3.39999999999999988e-62

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 47.7%

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

      1. div-inv 47.7%

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

      2. associate-*l* 75.5%

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

      3. un-div-inv 75.6%

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

   5. Applied egg-rr 75.6%

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

   if -3.39999999999999988e-62 < a < 1.84999999999999993e-146

   1. Initial program 64.3%

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

      1. clear-num 64.2%

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

      2. associate-/r/ 64.4%

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

   4. Applied egg-rr 64.4%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. associate--l+ 82.4%

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

      2. associate-*r/ 82.4%

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

      3. associate-*r/ 82.4%

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

      4. div-sub 83.6%

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

      5. distribute-lft-out-- 83.6%

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

      6. associate-*r/ 83.6%

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

      7. mul-1-neg 83.6%

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

      8. unsub-neg 83.6%

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

      9. distribute-rgt-out-- 83.6%

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

   7. Simplified 83.6%

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

   if 1.84999999999999993e-146 < a < 1.29999999999999991e-12

   1. Initial program 67.4%

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

   3. Taylor expanded in x around 0 50.8%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+163}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-146}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+113)
   t
   (if (<= z -3.1e+19) x (if (<= z 1.3e+31) (* t (/ y (- a z))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+113) {
		tmp = t;
	} else if (z <= -3.1e+19) {
		tmp = x;
	} else if (z <= 1.3e+31) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+113)) then
        tmp = t
    else if (z <= (-3.1d+19)) then
        tmp = x
    else if (z <= 1.3d+31) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+113) {
		tmp = t;
	} else if (z <= -3.1e+19) {
		tmp = x;
	} else if (z <= 1.3e+31) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+113:
		tmp = t
	elif z <= -3.1e+19:
		tmp = x
	elif z <= 1.3e+31:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+113)
		tmp = t;
	elseif (z <= -3.1e+19)
		tmp = x;
	elseif (z <= 1.3e+31)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+113)
		tmp = t;
	elseif (z <= -3.1e+19)
		tmp = x;
	elseif (z <= 1.3e+31)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+113], t, If[LessEqual[z, -3.1e+19], x, If[LessEqual[z, 1.3e+31], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e113 or 1.3e31 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 58.6%

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

   if -1.0499999999999999e113 < z < -3.1e19

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 41.3%

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

   if -3.1e19 < z < 1.3e31

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 50.5%

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

      1. associate-/l* 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y around inf 42.5%

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

      1. associate-*r/ 47.2%

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

   8. Simplified 47.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+188} \lor \neg \left(x \leq 1.1 \cdot 10^{+136}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.45e+188) (not (<= x 1.1e+136)))
   (- x (/ x (/ a y)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.45e+188) || !(x <= 1.1e+136)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t * ((y - z) / (a - 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 ((x <= (-2.45d+188)) .or. (.not. (x <= 1.1d+136))) then
        tmp = x - (x / (a / y))
    else
        tmp = t * ((y - z) / (a - 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 ((x <= -2.45e+188) || !(x <= 1.1e+136)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.45e+188) or not (x <= 1.1e+136):
		tmp = x - (x / (a / y))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.45e+188) || !(x <= 1.1e+136))
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.45e+188) || ~((x <= 1.1e+136)))
		tmp = x - (x / (a / y));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.45e+188], N[Not[LessEqual[x, 1.1e+136]], $MachinePrecision]], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e188 or 1.1e136 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in z around 0 48.6%

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

      1. associate-/l* 57.8%

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

      2. associate-/r/ 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in t around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. associate-/l* 61.7%

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

   8. Simplified 61.7%

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

   if -2.45e188 < x < 1.1e136

   1. Initial program 80.4%

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

   3. Taylor expanded in x around 0 52.1%

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

      1. div-inv 52.1%

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

      2. associate-*l* 73.8%

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

      3. un-div-inv 73.9%

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

   5. Applied egg-rr 73.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+188} \lor \neg \left(x \leq 1.1 \cdot 10^{+136}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+135}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+135)
   (- t (/ t (/ z y)))
   (if (<= z 1.6e+31) (+ x (* t (/ y a))) (/ (- t) (+ (/ a z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+135) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.6e+31) {
		tmp = x + (t * (y / a));
	} else {
		tmp = -t / ((a / z) + -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 (z <= (-4.8d+135)) then
        tmp = t - (t / (z / y))
    else if (z <= 1.6d+31) then
        tmp = x + (t * (y / a))
    else
        tmp = -t / ((a / z) + (-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 (z <= -4.8e+135) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.6e+31) {
		tmp = x + (t * (y / a));
	} else {
		tmp = -t / ((a / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+135:
		tmp = t - (t / (z / y))
	elif z <= 1.6e+31:
		tmp = x + (t * (y / a))
	else:
		tmp = -t / ((a / z) + -1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+135)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (z <= 1.6e+31)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+135)
		tmp = t - (t / (z / y));
	elseif (z <= 1.6e+31)
		tmp = x + (t * (y / a));
	else
		tmp = -t / ((a / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+135], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+31], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999995e135

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0 34.9%

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

      1. associate-/l* 79.4%

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

      2. associate-/r/ 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in a around 0 32.2%

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

      1. associate-*r/ 32.2%

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

      2. *-commutative 32.2%

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

      3. neg-mul-1 32.2%

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

      4. distribute-rgt-neg-in 32.2%

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

   8. Simplified 32.2%

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

   9. Taylor expanded in y around 0 59.1%

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

       1. mul-1-neg 59.1%

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

       2. unsub-neg 59.1%

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

       3. associate-/l* 76.6%

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

   11. Simplified 76.6%

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

   if -4.79999999999999995e135 < z < 1.6e31

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 61.8%

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

      1. associate-/l* 71.1%

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

      2. associate-/r/ 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around inf 55.2%

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

      1. associate-*r/ 61.4%

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

   8. Simplified 61.4%

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

   if 1.6e31 < z

   1. Initial program 52.2%

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

   3. Taylor expanded in x around 0 42.3%

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

   4. Taylor expanded in y around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. associate-/l* 62.1%

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

      3. div-sub 62.1%

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

      4. sub-neg 62.1%

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

      5. *-inverses 62.1%

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

      6. metadata-eval 62.1%

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

   6. Simplified 62.1%

      \[\leadsto \color{blue}{-\frac{t}{\frac{a}{z} + -1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+135}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+113)
   t
   (if (<= z -9.8e-154) x (if (<= z 1.65e+31) (/ t (/ a y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+113) {
		tmp = t;
	} else if (z <= -9.8e-154) {
		tmp = x;
	} else if (z <= 1.65e+31) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+113)) then
        tmp = t
    else if (z <= (-9.8d-154)) then
        tmp = x
    else if (z <= 1.65d+31) then
        tmp = t / (a / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+113) {
		tmp = t;
	} else if (z <= -9.8e-154) {
		tmp = x;
	} else if (z <= 1.65e+31) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+113:
		tmp = t
	elif z <= -9.8e-154:
		tmp = x
	elif z <= 1.65e+31:
		tmp = t / (a / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+113)
		tmp = t;
	elseif (z <= -9.8e-154)
		tmp = x;
	elseif (z <= 1.65e+31)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+113)
		tmp = t;
	elseif (z <= -9.8e-154)
		tmp = x;
	elseif (z <= 1.65e+31)
		tmp = t / (a / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+113], t, If[LessEqual[z, -9.8e-154], x, If[LessEqual[z, 1.65e+31], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000005e113 or 1.64999999999999996e31 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 58.6%

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

   if -1.10000000000000005e113 < z < -9.79999999999999993e-154

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf 32.7%

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

   if -9.79999999999999993e-154 < z < 1.64999999999999996e31

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 52.9%

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

   4. Taylor expanded in y around inf 46.3%

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

   5. Taylor expanded in a around inf 40.9%

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

      1. associate-/l* 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+135} \lor \neg \left(z \leq 2.05 \cdot 10^{+20}\right):\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.1e+135) (not (<= z 2.05e+20)))
   (- t (/ t (/ z y)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.1e+135) || !(z <= 2.05e+20)) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.1d+135)) .or. (.not. (z <= 2.05d+20))) then
        tmp = t - (t / (z / y))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.1e+135) || !(z <= 2.05e+20)) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.1e+135) or not (z <= 2.05e+20):
		tmp = t - (t / (z / y))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.1e+135) || !(z <= 2.05e+20))
		tmp = Float64(t - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.1e+135) || ~((z <= 2.05e+20)))
		tmp = t - (t / (z / y));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.1e+135], N[Not[LessEqual[z, 2.05e+20]], $MachinePrecision]], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e135 or 2.05e20 < z

   1. Initial program 59.6%

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

   3. Taylor expanded in x around 0 40.2%

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

      1. associate-/l* 74.2%

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

      2. associate-/r/ 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in a around 0 34.2%

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

      1. associate-*r/ 34.2%

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

      2. *-commutative 34.2%

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

      3. neg-mul-1 34.2%

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

      4. distribute-rgt-neg-in 34.2%

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

   8. Simplified 34.2%

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

   9. Taylor expanded in y around 0 57.5%

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

       1. mul-1-neg 57.5%

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

       2. unsub-neg 57.5%

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

       3. associate-/l* 65.6%

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

   11. Simplified 65.6%

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

   if -4.1e135 < z < 2.05e20

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 62.2%

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

      1. associate-/l* 71.5%

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

      2. associate-/r/ 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in t around inf 55.5%

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

      1. associate-*r/ 61.8%

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

   8. Simplified 61.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+135} \lor \neg \left(z \leq 2.05 \cdot 10^{+20}\right):\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+139}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+139) t (if (<= z 3e+31) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+139) {
		tmp = t;
	} else if (z <= 3e+31) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.2d+139)) then
        tmp = t
    else if (z <= 3d+31) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+139) {
		tmp = t;
	} else if (z <= 3e+31) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+139:
		tmp = t
	elif z <= 3e+31:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+139)
		tmp = t;
	elseif (z <= 3e+31)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+139)
		tmp = t;
	elseif (z <= 3e+31)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+139], t, If[LessEqual[z, 3e+31], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e139 or 2.99999999999999989e31 < z

   1. Initial program 59.2%

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

   3. Taylor expanded in z around inf 60.3%

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

   if -9.2e139 < z < 2.99999999999999989e31

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 61.8%

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

      1. associate-/l* 71.1%

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

      2. associate-/r/ 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around inf 55.2%

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

      1. associate-*r/ 61.4%

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

   8. Simplified 61.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+139}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+112) t (if (<= z 1.4e+19) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+112) {
		tmp = t;
	} else if (z <= 1.4e+19) {
		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 <= (-9.5d+112)) then
        tmp = t
    else if (z <= 1.4d+19) 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 <= -9.5e+112) {
		tmp = t;
	} else if (z <= 1.4e+19) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+112:
		tmp = t
	elif z <= 1.4e+19:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+112)
		tmp = t;
	elseif (z <= 1.4e+19)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+112)
		tmp = t;
	elseif (z <= 1.4e+19)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+112], t, If[LessEqual[z, 1.4e+19], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000008e112 or 1.4e19 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 57.6%

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

   if -9.5000000000000008e112 < z < 1.4e19

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf 28.7%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.3% 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 78.0%

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

3. Taylor expanded in z around inf 28.4%

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

4. Final simplification 28.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(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)))))