Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 90.9%

Time: 22.1s

Alternatives: 21

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: 80.1% 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: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-256}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -5e-228)
     t_2
     (if (<= t_2 1e-256)
       (+ t (/ (- x t) (/ z (- y a))))
       (fma (- y z) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -5e-228) {
		tmp = t_2;
	} else if (t_2 <= 1e-256) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -5e-228)
		tmp = t_2;
	elseif (t_2 <= 1e-256)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-228], t$95$2, If[LessEqual[t$95$2, 1e-256], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999972e-228

   1. Initial program 88.4%

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

   if -4.99999999999999972e-228 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999977e-257

   1. Initial program 6.2%

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

   2. Taylor expanded in z around -inf 88.3%

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

      1. mul-1-neg 88.3%

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

      2. sub-neg 88.3%

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

      3. mul-1-neg 88.3%

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

      4. +-commutative 88.3%

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

      5. +-commutative 88.3%

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

      6. mul-1-neg 88.3%

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

      7. sub-neg 88.3%

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

      8. distribute-rgt-out-- 88.4%

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

      9. associate-/l* 97.6%

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

   4. Simplified 97.6%

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

   if 9.99999999999999977e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. fma-def 90.6%

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

   3. Simplified 90.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-228}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-256}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-228} \lor \neg \left(t_1 \leq 10^{-256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-228) (not (<= t_1 1e-256)))
     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 <= -5e-228) || !(t_1 <= 1e-256)) {
		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 <= (-5d-228)) .or. (.not. (t_1 <= 1d-256))) 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 <= -5e-228) || !(t_1 <= 1e-256)) {
		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 <= -5e-228) or not (t_1 <= 1e-256):
		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 <= -5e-228) || !(t_1 <= 1e-256))
		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 <= -5e-228) || ~((t_1 <= 1e-256)))
		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, -5e-228], N[Not[LessEqual[t$95$1, 1e-256]], $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)))) < -4.99999999999999972e-228 or 9.99999999999999977e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.6%

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

   if -4.99999999999999972e-228 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999977e-257

   1. Initial program 6.2%

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

   2. Taylor expanded in z around -inf 88.3%

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

      1. mul-1-neg 88.3%

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

      2. sub-neg 88.3%

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

      3. mul-1-neg 88.3%

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

      4. +-commutative 88.3%

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

      5. +-commutative 88.3%

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

      6. mul-1-neg 88.3%

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

      7. sub-neg 88.3%

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

      8. distribute-rgt-out-- 88.4%

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

      9. associate-/l* 97.6%

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

   4. Simplified 97.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-256}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= z -9.6e+109)
     t
     (if (<= z -2e+56)
       (/ (* t (- y)) z)
       (if (<= z -5.5e+39)
         t
         (if (<= z -3.65e-16)
           x
           (if (<= z -1.62e-96)
             t_1
             (if (<= z -1.5e-142)
               x
               (if (<= z 6.5e-300) t_1 (if (<= z 5.1e+81) x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -9.6e+109) {
		tmp = t;
	} else if (z <= -2e+56) {
		tmp = (t * -y) / z;
	} else if (z <= -5.5e+39) {
		tmp = t;
	} else if (z <= -3.65e-16) {
		tmp = x;
	} else if (z <= -1.62e-96) {
		tmp = t_1;
	} else if (z <= -1.5e-142) {
		tmp = x;
	} else if (z <= 6.5e-300) {
		tmp = t_1;
	} else if (z <= 5.1e+81) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (z <= (-9.6d+109)) then
        tmp = t
    else if (z <= (-2d+56)) then
        tmp = (t * -y) / z
    else if (z <= (-5.5d+39)) then
        tmp = t
    else if (z <= (-3.65d-16)) then
        tmp = x
    else if (z <= (-1.62d-96)) then
        tmp = t_1
    else if (z <= (-1.5d-142)) then
        tmp = x
    else if (z <= 6.5d-300) then
        tmp = t_1
    else if (z <= 5.1d+81) 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 t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -9.6e+109) {
		tmp = t;
	} else if (z <= -2e+56) {
		tmp = (t * -y) / z;
	} else if (z <= -5.5e+39) {
		tmp = t;
	} else if (z <= -3.65e-16) {
		tmp = x;
	} else if (z <= -1.62e-96) {
		tmp = t_1;
	} else if (z <= -1.5e-142) {
		tmp = x;
	} else if (z <= 6.5e-300) {
		tmp = t_1;
	} else if (z <= 5.1e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if z <= -9.6e+109:
		tmp = t
	elif z <= -2e+56:
		tmp = (t * -y) / z
	elif z <= -5.5e+39:
		tmp = t
	elif z <= -3.65e-16:
		tmp = x
	elif z <= -1.62e-96:
		tmp = t_1
	elif z <= -1.5e-142:
		tmp = x
	elif z <= 6.5e-300:
		tmp = t_1
	elif z <= 5.1e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (z <= -9.6e+109)
		tmp = t;
	elseif (z <= -2e+56)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (z <= -5.5e+39)
		tmp = t;
	elseif (z <= -3.65e-16)
		tmp = x;
	elseif (z <= -1.62e-96)
		tmp = t_1;
	elseif (z <= -1.5e-142)
		tmp = x;
	elseif (z <= 6.5e-300)
		tmp = t_1;
	elseif (z <= 5.1e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (z <= -9.6e+109)
		tmp = t;
	elseif (z <= -2e+56)
		tmp = (t * -y) / z;
	elseif (z <= -5.5e+39)
		tmp = t;
	elseif (z <= -3.65e-16)
		tmp = x;
	elseif (z <= -1.62e-96)
		tmp = t_1;
	elseif (z <= -1.5e-142)
		tmp = x;
	elseif (z <= 6.5e-300)
		tmp = t_1;
	elseif (z <= 5.1e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+109], t, If[LessEqual[z, -2e+56], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -5.5e+39], t, If[LessEqual[z, -3.65e-16], x, If[LessEqual[z, -1.62e-96], t$95$1, If[LessEqual[z, -1.5e-142], x, If[LessEqual[z, 6.5e-300], t$95$1, If[LessEqual[z, 5.1e+81], x, t]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.59999999999999949e109 or -2.00000000000000018e56 < z < -5.4999999999999997e39 or 5.1000000000000003e81 < z

   1. Initial program 51.6%

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

   2. Taylor expanded in z around inf 58.8%

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

   if -9.59999999999999949e109 < z < -2.00000000000000018e56

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

      1. associate-/r/ 70.1%

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

   6. Applied egg-rr 70.1%

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

   7. Taylor expanded in y around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in a around 0 61.0%

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

       1. associate-*r/ 61.0%

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

       2. neg-mul-1 61.0%

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

       3. distribute-lft-neg-in 61.0%

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

       4. *-commutative 61.0%

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

   12. Simplified 61.0%

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

   if -5.4999999999999997e39 < z < -3.6500000000000001e-16 or -1.62000000000000001e-96 < z < -1.5000000000000001e-142 or 6.4999999999999997e-300 < z < 5.1000000000000003e81

   1. Initial program 87.5%

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

   2. Taylor expanded in a around inf 42.9%

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

   if -3.6500000000000001e-16 < z < -1.62000000000000001e-96 or -1.5000000000000001e-142 < z < 6.4999999999999997e-300

   1. Initial program 94.6%

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

   2. Taylor expanded in x around 0 52.4%

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

      1. associate-/l* 56.6%

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

   4. Simplified 56.6%

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

      1. associate-/r/ 58.6%

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

   6. Applied egg-rr 58.6%

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

   7. Taylor expanded in y around inf 46.1%

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

      1. *-commutative 46.1%

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

      2. associate-*r/ 52.4%

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

   9. Simplified 52.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.8e+40)
     t_2
     (if (<= z -1.15e-66)
       t_1
       (if (<= z -3.7e-91)
         (* y (/ (- t x) (- a z)))
         (if (<= z -1.42e-105)
           (+ x (/ (* (- y z) t) a))
           (if (<= z 7.2e+66) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.8e+40) {
		tmp = t_2;
	} else if (z <= -1.15e-66) {
		tmp = t_1;
	} else if (z <= -3.7e-91) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.42e-105) {
		tmp = x + (((y - z) * t) / a);
	} else if (z <= 7.2e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.8d+40)) then
        tmp = t_2
    else if (z <= (-1.15d-66)) then
        tmp = t_1
    else if (z <= (-3.7d-91)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= (-1.42d-105)) then
        tmp = x + (((y - z) * t) / a)
    else if (z <= 7.2d+66) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.8e+40) {
		tmp = t_2;
	} else if (z <= -1.15e-66) {
		tmp = t_1;
	} else if (z <= -3.7e-91) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.42e-105) {
		tmp = x + (((y - z) * t) / a);
	} else if (z <= 7.2e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.8e+40:
		tmp = t_2
	elif z <= -1.15e-66:
		tmp = t_1
	elif z <= -3.7e-91:
		tmp = y * ((t - x) / (a - z))
	elif z <= -1.42e-105:
		tmp = x + (((y - z) * t) / a)
	elif z <= 7.2e+66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.8e+40)
		tmp = t_2;
	elseif (z <= -1.15e-66)
		tmp = t_1;
	elseif (z <= -3.7e-91)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= -1.42e-105)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / a));
	elseif (z <= 7.2e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.8e+40)
		tmp = t_2;
	elseif (z <= -1.15e-66)
		tmp = t_1;
	elseif (z <= -3.7e-91)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= -1.42e-105)
		tmp = x + (((y - z) * t) / a);
	elseif (z <= 7.2e+66)
		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[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+40], t$95$2, If[LessEqual[z, -1.15e-66], t$95$1, If[LessEqual[z, -3.7e-91], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.42e-105], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+66], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8000000000000001e40 or 7.2e66 < z

   1. Initial program 56.1%

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

   2. Taylor expanded in x around 0 45.9%

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

      1. associate-/l* 67.6%

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

   4. Simplified 67.6%

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

      1. div-inv 67.6%

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

      2. *-commutative 67.6%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   if -2.8000000000000001e40 < z < -1.14999999999999996e-66 or -1.4199999999999999e-105 < z < 7.2e66

   1. Initial program 89.0%

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

   2. Taylor expanded in z around 0 72.9%

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

      1. associate-/l* 78.9%

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

   4. Simplified 78.9%

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

   if -1.14999999999999996e-66 < z < -3.7000000000000002e-91

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 87.7%

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

      1. div-sub 87.7%

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

   4. Simplified 87.7%

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

   if -3.7000000000000002e-91 < z < -1.4199999999999999e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.8%

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

   3. Taylor expanded in a around inf 81.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 5: 53.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := \frac{t}{\frac{z - a}{z}}\\ t_3 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z))))
        (t_2 (/ t (/ (- z a) z)))
        (t_3 (+ x (/ (* y t) a))))
   (if (<= z -1.4e+119)
     t_2
     (if (<= z -9.8e-98)
       t_1
       (if (<= z 4.7e-184)
         t_3
         (if (<= z 1.76e-159) t_1 (if (<= z 3.8e+64) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t / ((z - a) / z);
	double t_3 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.4e+119) {
		tmp = t_2;
	} else if (z <= -9.8e-98) {
		tmp = t_1;
	} else if (z <= 4.7e-184) {
		tmp = t_3;
	} else if (z <= 1.76e-159) {
		tmp = t_1;
	} else if (z <= 3.8e+64) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t / ((z - a) / z)
    t_3 = x + ((y * t) / a)
    if (z <= (-1.4d+119)) then
        tmp = t_2
    else if (z <= (-9.8d-98)) then
        tmp = t_1
    else if (z <= 4.7d-184) then
        tmp = t_3
    else if (z <= 1.76d-159) then
        tmp = t_1
    else if (z <= 3.8d+64) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t / ((z - a) / z);
	double t_3 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.4e+119) {
		tmp = t_2;
	} else if (z <= -9.8e-98) {
		tmp = t_1;
	} else if (z <= 4.7e-184) {
		tmp = t_3;
	} else if (z <= 1.76e-159) {
		tmp = t_1;
	} else if (z <= 3.8e+64) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t / ((z - a) / z)
	t_3 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.4e+119:
		tmp = t_2
	elif z <= -9.8e-98:
		tmp = t_1
	elif z <= 4.7e-184:
		tmp = t_3
	elif z <= 1.76e-159:
		tmp = t_1
	elif z <= 3.8e+64:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t / Float64(Float64(z - a) / z))
	t_3 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.4e+119)
		tmp = t_2;
	elseif (z <= -9.8e-98)
		tmp = t_1;
	elseif (z <= 4.7e-184)
		tmp = t_3;
	elseif (z <= 1.76e-159)
		tmp = t_1;
	elseif (z <= 3.8e+64)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t / ((z - a) / z);
	t_3 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.4e+119)
		tmp = t_2;
	elseif (z <= -9.8e-98)
		tmp = t_1;
	elseif (z <= 4.7e-184)
		tmp = t_3;
	elseif (z <= 1.76e-159)
		tmp = t_1;
	elseif (z <= 3.8e+64)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+119], t$95$2, If[LessEqual[z, -9.8e-98], t$95$1, If[LessEqual[z, 4.7e-184], t$95$3, If[LessEqual[z, 1.76e-159], t$95$1, If[LessEqual[z, 3.8e+64], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000007e119 or 3.8000000000000001e64 < z

   1. Initial program 51.6%

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

   2. Taylor expanded in x around 0 43.0%

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

      1. associate-/l* 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. neg-mul-1 65.8%

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

      3. neg-sub0 65.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(a - z\right)}}{z}} \]

      4. associate--r- 65.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - a\right) + z}}{z}} \]

      5. neg-sub0 65.8%

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

   7. Simplified 65.8%

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

   if -1.40000000000000007e119 < z < -9.80000000000000028e-98 or 4.70000000000000019e-184 < z < 1.76e-159

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 61.5%

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

      1. div-sub 61.5%

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

   4. Simplified 61.5%

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

   if -9.80000000000000028e-98 < z < 4.70000000000000019e-184 or 1.76e-159 < z < 3.8000000000000001e64

   1. Initial program 89.6%

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

   2. Taylor expanded in t around inf 73.4%

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

   3. Taylor expanded in z around 0 61.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+119}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 6: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.28e+150)
     t_1
     (if (<= z -1.65e-304)
       (- x (* (/ t (- a z)) (- z y)))
       (if (<= z 3.5e+80) (+ 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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.28e+150) {
		tmp = t_1;
	} else if (z <= -1.65e-304) {
		tmp = x - ((t / (a - z)) * (z - y));
	} else if (z <= 3.5e+80) {
		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 * ((y - z) / (a - z))
    if (z <= (-1.28d+150)) then
        tmp = t_1
    else if (z <= (-1.65d-304)) then
        tmp = x - ((t / (a - z)) * (z - y))
    else if (z <= 3.5d+80) 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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.28e+150) {
		tmp = t_1;
	} else if (z <= -1.65e-304) {
		tmp = x - ((t / (a - z)) * (z - y));
	} else if (z <= 3.5e+80) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.28e+150:
		tmp = t_1
	elif z <= -1.65e-304:
		tmp = x - ((t / (a - z)) * (z - y))
	elif z <= 3.5e+80:
		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(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.28e+150)
		tmp = t_1;
	elseif (z <= -1.65e-304)
		tmp = Float64(x - Float64(Float64(t / Float64(a - z)) * Float64(z - y)));
	elseif (z <= 3.5e+80)
		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 * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.28e+150)
		tmp = t_1;
	elseif (z <= -1.65e-304)
		tmp = x - ((t / (a - z)) * (z - y));
	elseif (z <= 3.5e+80)
		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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.28e+150], t$95$1, If[LessEqual[z, -1.65e-304], N[(x - N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+80], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2800000000000001e150 or 3.49999999999999994e80 < z

   1. Initial program 49.3%

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

   2. Taylor expanded in x around 0 43.2%

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

      1. associate-/l* 68.4%

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

   4. Simplified 68.4%

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

      1. div-inv 68.4%

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

      2. *-commutative 68.4%

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

      3. clear-num 68.4%

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

   6. Applied egg-rr 68.4%

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

   if -1.2800000000000001e150 < z < -1.65000000000000006e-304

   1. Initial program 89.0%

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

   2. Taylor expanded in t around inf 76.4%

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

   if -1.65000000000000006e-304 < z < 3.49999999999999994e80

   1. Initial program 88.9%

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

   2. Taylor expanded in a around inf 79.0%

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

      1. associate-/l* 83.3%

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

   4. Simplified 83.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 7: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -4.1e+76)
     t_1
     (if (<= z -1.65e-304)
       (- x (* (/ t (- a z)) (- z y)))
       (if (<= z 8.5e+42) (+ 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 <= -4.1e+76) {
		tmp = t_1;
	} else if (z <= -1.65e-304) {
		tmp = x - ((t / (a - z)) * (z - y));
	} else if (z <= 8.5e+42) {
		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 <= (-4.1d+76)) then
        tmp = t_1
    else if (z <= (-1.65d-304)) then
        tmp = x - ((t / (a - z)) * (z - y))
    else if (z <= 8.5d+42) 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 <= -4.1e+76) {
		tmp = t_1;
	} else if (z <= -1.65e-304) {
		tmp = x - ((t / (a - z)) * (z - y));
	} else if (z <= 8.5e+42) {
		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 <= -4.1e+76:
		tmp = t_1
	elif z <= -1.65e-304:
		tmp = x - ((t / (a - z)) * (z - y))
	elif z <= 8.5e+42:
		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 <= -4.1e+76)
		tmp = t_1;
	elseif (z <= -1.65e-304)
		tmp = Float64(x - Float64(Float64(t / Float64(a - z)) * Float64(z - y)));
	elseif (z <= 8.5e+42)
		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 <= -4.1e+76)
		tmp = t_1;
	elseif (z <= -1.65e-304)
		tmp = x - ((t / (a - z)) * (z - y));
	elseif (z <= 8.5e+42)
		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, -4.1e+76], t$95$1, If[LessEqual[z, -1.65e-304], N[(x - N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+42], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999998e76 or 8.5000000000000003e42 < z

   1. Initial program 53.0%

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

   2. Taylor expanded in z around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. sub-neg 62.2%

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

      3. mul-1-neg 62.2%

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

      4. +-commutative 62.2%

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

      5. +-commutative 62.2%

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

      6. mul-1-neg 62.2%

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

      7. sub-neg 62.2%

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

      8. distribute-rgt-out-- 62.4%

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

      9. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

   if -4.0999999999999998e76 < z < -1.65000000000000006e-304

   1. Initial program 91.3%

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

   2. Taylor expanded in t around inf 79.2%

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

   if -1.65000000000000006e-304 < z < 8.5000000000000003e42

   1. Initial program 91.5%

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

   2. Taylor expanded in a around inf 82.0%

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

      1. associate-/l* 86.7%

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

   4. Simplified 86.7%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+76}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 8: 37.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+54}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+109)
   t
   (if (<= z -2.5e+54)
     (* (- y) (/ t z))
     (if (<= z -2.4e+37)
       t
       (if (<= z -9.5e-143)
         x
         (if (<= z 1.2e-305) (* y (/ t a)) (if (<= z 8.8e+80) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+109) {
		tmp = t;
	} else if (z <= -2.5e+54) {
		tmp = -y * (t / z);
	} else if (z <= -2.4e+37) {
		tmp = t;
	} else if (z <= -9.5e-143) {
		tmp = x;
	} else if (z <= 1.2e-305) {
		tmp = y * (t / a);
	} else if (z <= 8.8e+80) {
		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+109)) then
        tmp = t
    else if (z <= (-2.5d+54)) then
        tmp = -y * (t / z)
    else if (z <= (-2.4d+37)) then
        tmp = t
    else if (z <= (-9.5d-143)) then
        tmp = x
    else if (z <= 1.2d-305) then
        tmp = y * (t / a)
    else if (z <= 8.8d+80) 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+109) {
		tmp = t;
	} else if (z <= -2.5e+54) {
		tmp = -y * (t / z);
	} else if (z <= -2.4e+37) {
		tmp = t;
	} else if (z <= -9.5e-143) {
		tmp = x;
	} else if (z <= 1.2e-305) {
		tmp = y * (t / a);
	} else if (z <= 8.8e+80) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+109:
		tmp = t
	elif z <= -2.5e+54:
		tmp = -y * (t / z)
	elif z <= -2.4e+37:
		tmp = t
	elif z <= -9.5e-143:
		tmp = x
	elif z <= 1.2e-305:
		tmp = y * (t / a)
	elif z <= 8.8e+80:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+109)
		tmp = t;
	elseif (z <= -2.5e+54)
		tmp = Float64(Float64(-y) * Float64(t / z));
	elseif (z <= -2.4e+37)
		tmp = t;
	elseif (z <= -9.5e-143)
		tmp = x;
	elseif (z <= 1.2e-305)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 8.8e+80)
		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+109)
		tmp = t;
	elseif (z <= -2.5e+54)
		tmp = -y * (t / z);
	elseif (z <= -2.4e+37)
		tmp = t;
	elseif (z <= -9.5e-143)
		tmp = x;
	elseif (z <= 1.2e-305)
		tmp = y * (t / a);
	elseif (z <= 8.8e+80)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+109], t, If[LessEqual[z, -2.5e+54], N[((-y) * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e+37], t, If[LessEqual[z, -9.5e-143], x, If[LessEqual[z, 1.2e-305], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+80], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.49999999999999972e109 or -2.50000000000000003e54 < z < -2.4e37 or 8.80000000000000011e80 < z

   1. Initial program 51.6%

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

   2. Taylor expanded in z around inf 58.8%

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

   if -9.49999999999999972e109 < z < -2.50000000000000003e54

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

      1. associate-/r/ 70.1%

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

   6. Applied egg-rr 70.1%

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

   7. Taylor expanded in y around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in a around 0 60.8%

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

       1. associate-*r/ 60.8%

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

       2. neg-mul-1 60.8%

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

   12. Simplified 60.8%

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

   if -2.4e37 < z < -9.4999999999999993e-143 or 1.2000000000000001e-305 < z < 8.80000000000000011e80

   1. Initial program 88.2%

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

   2. Taylor expanded in a around inf 38.8%

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

   if -9.4999999999999993e-143 < z < 1.2000000000000001e-305

   1. Initial program 96.1%

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

   2. Taylor expanded in x around 0 49.5%

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

      1. associate-/l* 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in z around 0 56.4%

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

      1. associate-/r/ 63.3%

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

   7. Applied egg-rr 63.3%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+54}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+109)
   t
   (if (<= z -2.7e+54)
     (/ (* t (- y)) z)
     (if (<= z -3.8e+36)
       t
       (if (<= z -3.1e-142)
         x
         (if (<= z 2e-306) (* y (/ t a)) (if (<= z 2.9e+81) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+109) {
		tmp = t;
	} else if (z <= -2.7e+54) {
		tmp = (t * -y) / z;
	} else if (z <= -3.8e+36) {
		tmp = t;
	} else if (z <= -3.1e-142) {
		tmp = x;
	} else if (z <= 2e-306) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+81) {
		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 <= (-9d+109)) then
        tmp = t
    else if (z <= (-2.7d+54)) then
        tmp = (t * -y) / z
    else if (z <= (-3.8d+36)) then
        tmp = t
    else if (z <= (-3.1d-142)) then
        tmp = x
    else if (z <= 2d-306) then
        tmp = y * (t / a)
    else if (z <= 2.9d+81) 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 <= -9e+109) {
		tmp = t;
	} else if (z <= -2.7e+54) {
		tmp = (t * -y) / z;
	} else if (z <= -3.8e+36) {
		tmp = t;
	} else if (z <= -3.1e-142) {
		tmp = x;
	} else if (z <= 2e-306) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+109:
		tmp = t
	elif z <= -2.7e+54:
		tmp = (t * -y) / z
	elif z <= -3.8e+36:
		tmp = t
	elif z <= -3.1e-142:
		tmp = x
	elif z <= 2e-306:
		tmp = y * (t / a)
	elif z <= 2.9e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+109)
		tmp = t;
	elseif (z <= -2.7e+54)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (z <= -3.8e+36)
		tmp = t;
	elseif (z <= -3.1e-142)
		tmp = x;
	elseif (z <= 2e-306)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.9e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+109)
		tmp = t;
	elseif (z <= -2.7e+54)
		tmp = (t * -y) / z;
	elseif (z <= -3.8e+36)
		tmp = t;
	elseif (z <= -3.1e-142)
		tmp = x;
	elseif (z <= 2e-306)
		tmp = y * (t / a);
	elseif (z <= 2.9e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+109], t, If[LessEqual[z, -2.7e+54], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -3.8e+36], t, If[LessEqual[z, -3.1e-142], x, If[LessEqual[z, 2e-306], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+81], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999992e109 or -2.70000000000000011e54 < z < -3.80000000000000025e36 or 2.9e81 < z

   1. Initial program 51.6%

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

   2. Taylor expanded in z around inf 58.8%

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

   if -8.9999999999999992e109 < z < -2.70000000000000011e54

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

      1. associate-/r/ 70.1%

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

   6. Applied egg-rr 70.1%

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

   7. Taylor expanded in y around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in a around 0 61.0%

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

       1. associate-*r/ 61.0%

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

       2. neg-mul-1 61.0%

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

       3. distribute-lft-neg-in 61.0%

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

       4. *-commutative 61.0%

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

   12. Simplified 61.0%

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

   if -3.80000000000000025e36 < z < -3.1e-142 or 2.00000000000000006e-306 < z < 2.9e81

   1. Initial program 88.2%

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

   2. Taylor expanded in a around inf 38.8%

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

   if -3.1e-142 < z < 2.00000000000000006e-306

   1. Initial program 96.1%

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

   2. Taylor expanded in x around 0 49.5%

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

      1. associate-/l* 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in z around 0 56.4%

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

      1. associate-/r/ 63.3%

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

   7. Applied egg-rr 63.3%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+111)
   t
   (if (<= z -1.1e+56)
     (/ (* t (- y)) z)
     (if (<= z -3.5e+36) t (if (<= z 1.8e+81) (+ x (/ (* y t) a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+111) {
		tmp = t;
	} else if (z <= -1.1e+56) {
		tmp = (t * -y) / z;
	} else if (z <= -3.5e+36) {
		tmp = t;
	} else if (z <= 1.8e+81) {
		tmp = x + ((y * t) / 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 <= (-4d+111)) then
        tmp = t
    else if (z <= (-1.1d+56)) then
        tmp = (t * -y) / z
    else if (z <= (-3.5d+36)) then
        tmp = t
    else if (z <= 1.8d+81) then
        tmp = x + ((y * t) / 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 <= -4e+111) {
		tmp = t;
	} else if (z <= -1.1e+56) {
		tmp = (t * -y) / z;
	} else if (z <= -3.5e+36) {
		tmp = t;
	} else if (z <= 1.8e+81) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+111:
		tmp = t
	elif z <= -1.1e+56:
		tmp = (t * -y) / z
	elif z <= -3.5e+36:
		tmp = t
	elif z <= 1.8e+81:
		tmp = x + ((y * t) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+111)
		tmp = t;
	elseif (z <= -1.1e+56)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (z <= -3.5e+36)
		tmp = t;
	elseif (z <= 1.8e+81)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+111)
		tmp = t;
	elseif (z <= -1.1e+56)
		tmp = (t * -y) / z;
	elseif (z <= -3.5e+36)
		tmp = t;
	elseif (z <= 1.8e+81)
		tmp = x + ((y * t) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+111], t, If[LessEqual[z, -1.1e+56], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -3.5e+36], t, If[LessEqual[z, 1.8e+81], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999983e111 or -1.10000000000000008e56 < z < -3.4999999999999998e36 or 1.80000000000000003e81 < z

   1. Initial program 51.6%

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

   2. Taylor expanded in z around inf 58.8%

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

   if -3.99999999999999983e111 < z < -1.10000000000000008e56

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

      1. associate-/r/ 70.1%

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

   6. Applied egg-rr 70.1%

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

   7. Taylor expanded in y around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in a around 0 61.0%

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

       1. associate-*r/ 61.0%

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

       2. neg-mul-1 61.0%

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

       3. distribute-lft-neg-in 61.0%

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

       4. *-commutative 61.0%

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

   12. Simplified 61.0%

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

   if -3.4999999999999998e36 < z < 1.80000000000000003e81

   1. Initial program 89.6%

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

   2. Taylor expanded in t around inf 69.8%

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

   3. Taylor expanded in z around 0 54.9%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 56.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.0034:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= x -2.8e+161)
     t_1
     (if (<= x -0.0034)
       (+ x (/ (* y t) a))
       (if (<= x 2.05e+69) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -2.8e+161) {
		tmp = t_1;
	} else if (x <= -0.0034) {
		tmp = x + ((y * t) / a);
	} else if (x <= 2.05e+69) {
		tmp = t * ((y - z) / (a - 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 = y * ((t - x) / (a - z))
    if (x <= (-2.8d+161)) then
        tmp = t_1
    else if (x <= (-0.0034d0)) then
        tmp = x + ((y * t) / a)
    else if (x <= 2.05d+69) then
        tmp = t * ((y - z) / (a - 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 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -2.8e+161) {
		tmp = t_1;
	} else if (x <= -0.0034) {
		tmp = x + ((y * t) / a);
	} else if (x <= 2.05e+69) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if x <= -2.8e+161:
		tmp = t_1
	elif x <= -0.0034:
		tmp = x + ((y * t) / a)
	elif x <= 2.05e+69:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (x <= -2.8e+161)
		tmp = t_1;
	elseif (x <= -0.0034)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (x <= 2.05e+69)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (x <= -2.8e+161)
		tmp = t_1;
	elseif (x <= -0.0034)
		tmp = x + ((y * t) / a);
	elseif (x <= 2.05e+69)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+161], t$95$1, If[LessEqual[x, -0.0034], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+69], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.80000000000000021e161 or 2.05e69 < x

   1. Initial program 70.2%

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

   2. Taylor expanded in y around inf 57.1%

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

      1. div-sub 57.1%

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

   4. Simplified 57.1%

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

   if -2.80000000000000021e161 < x < -0.00339999999999999981

   1. Initial program 82.2%

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

   2. Taylor expanded in t around inf 75.7%

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

   3. Taylor expanded in z around 0 66.3%

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

   if -0.00339999999999999981 < x < 2.05e69

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 51.8%

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

      1. associate-/l* 65.8%

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

   4. Simplified 65.8%

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

      1. div-inv 65.8%

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

      2. *-commutative 65.8%

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

      3. clear-num 66.4%

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

   6. Applied egg-rr 66.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -0.0034:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 12: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 10^{+66}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -6.2e+148)
     t_1
     (if (<= z -1.65e-304)
       (- x (* (/ t (- a z)) (- z y)))
       (if (<= z 1e+66) (+ x (/ (- t x) (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.2e+148) {
		tmp = t_1;
	} else if (z <= -1.65e-304) {
		tmp = x - ((t / (a - z)) * (z - y));
	} else if (z <= 1e+66) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-6.2d+148)) then
        tmp = t_1
    else if (z <= (-1.65d-304)) then
        tmp = x - ((t / (a - z)) * (z - y))
    else if (z <= 1d+66) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.2e+148) {
		tmp = t_1;
	} else if (z <= -1.65e-304) {
		tmp = x - ((t / (a - z)) * (z - y));
	} else if (z <= 1e+66) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -6.2e+148:
		tmp = t_1
	elif z <= -1.65e-304:
		tmp = x - ((t / (a - z)) * (z - y))
	elif z <= 1e+66:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.2e+148)
		tmp = t_1;
	elseif (z <= -1.65e-304)
		tmp = Float64(x - Float64(Float64(t / Float64(a - z)) * Float64(z - y)));
	elseif (z <= 1e+66)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -6.2e+148)
		tmp = t_1;
	elseif (z <= -1.65e-304)
		tmp = x - ((t / (a - z)) * (z - y));
	elseif (z <= 1e+66)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+148], t$95$1, If[LessEqual[z, -1.65e-304], N[(x - N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+66], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.19999999999999951e148 or 9.99999999999999945e65 < z

   1. Initial program 51.0%

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

   2. Taylor expanded in x around 0 44.0%

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

      1. associate-/l* 68.3%

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

   4. Simplified 68.3%

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

      1. div-inv 68.3%

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

      2. *-commutative 68.3%

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

      3. clear-num 68.3%

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

   6. Applied egg-rr 68.3%

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

   if -6.19999999999999951e148 < z < -1.65000000000000006e-304

   1. Initial program 89.0%

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

   2. Taylor expanded in t around inf 76.4%

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

   if -1.65000000000000006e-304 < z < 9.99999999999999945e65

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 79.3%

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

      1. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around inf 80.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 10^{+66}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 13: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -600000000:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.45e+112)
   t
   (if (<= z -600000000.0)
     (* y (/ (- x t) z))
     (if (<= z 4.1e+81) (+ x (/ (* y t) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e+112) {
		tmp = t;
	} else if (z <= -600000000.0) {
		tmp = y * ((x - t) / z);
	} else if (z <= 4.1e+81) {
		tmp = x + ((y * t) / 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 <= (-2.45d+112)) then
        tmp = t
    else if (z <= (-600000000.0d0)) then
        tmp = y * ((x - t) / z)
    else if (z <= 4.1d+81) then
        tmp = x + ((y * t) / 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 <= -2.45e+112) {
		tmp = t;
	} else if (z <= -600000000.0) {
		tmp = y * ((x - t) / z);
	} else if (z <= 4.1e+81) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.45e+112:
		tmp = t
	elif z <= -600000000.0:
		tmp = y * ((x - t) / z)
	elif z <= 4.1e+81:
		tmp = x + ((y * t) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.45e+112)
		tmp = t;
	elseif (z <= -600000000.0)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= 4.1e+81)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.45e+112)
		tmp = t;
	elseif (z <= -600000000.0)
		tmp = y * ((x - t) / z);
	elseif (z <= 4.1e+81)
		tmp = x + ((y * t) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.45e+112], t, If[LessEqual[z, -600000000.0], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+81], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000002e112 or 4.10000000000000012e81 < z

   1. Initial program 51.0%

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

   2. Taylor expanded in z around inf 58.5%

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

   if -2.45000000000000002e112 < z < -6e8

   1. Initial program 81.8%

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

   2. Taylor expanded in z around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. sub-neg 62.0%

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

      3. mul-1-neg 62.0%

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

      4. +-commutative 62.0%

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

      5. +-commutative 62.0%

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

      6. mul-1-neg 62.0%

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

      7. sub-neg 62.0%

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

      8. distribute-rgt-out-- 62.0%

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

      9. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in y around -inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. associate-*r/ 53.1%

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

   7. Simplified 53.1%

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

   if -6e8 < z < 4.10000000000000012e81

   1. Initial program 90.3%

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

   2. Taylor expanded in t around inf 70.9%

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

   3. Taylor expanded in z around 0 56.4%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -600000000:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+184}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.1e+184)
   t
   (if (<= z -1e+38)
     (* (/ t z) (- z y))
     (if (<= z 4.2e+81) (+ x (/ (* y t) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+184) {
		tmp = t;
	} else if (z <= -1e+38) {
		tmp = (t / z) * (z - y);
	} else if (z <= 4.2e+81) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.1d+184)) then
        tmp = t
    else if (z <= (-1d+38)) then
        tmp = (t / z) * (z - y)
    else if (z <= 4.2d+81) then
        tmp = x + ((y * t) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+184) {
		tmp = t;
	} else if (z <= -1e+38) {
		tmp = (t / z) * (z - y);
	} else if (z <= 4.2e+81) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.1e+184:
		tmp = t
	elif z <= -1e+38:
		tmp = (t / z) * (z - y)
	elif z <= 4.2e+81:
		tmp = x + ((y * t) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.1e+184)
		tmp = t;
	elseif (z <= -1e+38)
		tmp = Float64(Float64(t / z) * Float64(z - y));
	elseif (z <= 4.2e+81)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.1e+184)
		tmp = t;
	elseif (z <= -1e+38)
		tmp = (t / z) * (z - y);
	elseif (z <= 4.2e+81)
		tmp = x + ((y * t) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.1e+184], t, If[LessEqual[z, -1e+38], N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+81], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999997e184 or 4.1999999999999997e81 < z

   1. Initial program 47.8%

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

   2. Taylor expanded in z around inf 61.4%

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

   if -4.0999999999999997e184 < z < -9.99999999999999977e37

   1. Initial program 77.4%

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

   2. Taylor expanded in x around 0 48.0%

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

      1. associate-/l* 62.2%

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

   4. Simplified 62.2%

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

      1. associate-/r/ 59.2%

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

   6. Applied egg-rr 59.2%

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

   7. Taylor expanded in a around 0 55.6%

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

      1. associate-*r/ 25.5%

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

      2. neg-mul-1 25.5%

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

   9. Simplified 55.6%

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

   if -9.99999999999999977e37 < z < 4.1999999999999997e81

   1. Initial program 89.6%

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

   2. Taylor expanded in t around inf 69.8%

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

   3. Taylor expanded in z around 0 54.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+184}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+39} \lor \neg \left(z \leq 9.2 \cdot 10^{+67}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+39) (not (<= z 9.2e+67)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+39) || !(z <= 9.2e+67)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (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) :: tmp
    if ((z <= (-1.9d+39)) .or. (.not. (z <= 9.2d+67))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+39) || !(z <= 9.2e+67)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+39) or not (z <= 9.2e+67):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+39) || !(z <= 9.2e+67))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+39) || ~((z <= 9.2e+67)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+39], N[Not[LessEqual[z, 9.2e+67]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e39 or 9.1999999999999994e67 < z

   1. Initial program 56.1%

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

   2. Taylor expanded in x around 0 45.9%

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

      1. associate-/l* 67.6%

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

   4. Simplified 67.6%

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

      1. div-inv 67.6%

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

      2. *-commutative 67.6%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   if -1.8999999999999999e39 < z < 9.1999999999999994e67

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 70.8%

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

      1. associate-/l* 76.3%

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

   4. Simplified 76.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+39} \lor \neg \left(z \leq 9.2 \cdot 10^{+67}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 16: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+38} \lor \neg \left(z \leq 8.2 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e+38) (not (<= z 8.2e+65)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+38) || !(z <= 8.2e+65)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - 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 ((z <= (-2.05d+38)) .or. (.not. (z <= 8.2d+65))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - 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 ((z <= -2.05e+38) || !(z <= 8.2e+65)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e+38) or not (z <= 8.2e+65):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e+38) || !(z <= 8.2e+65))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.05e+38) || ~((z <= 8.2e+65)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e+38], N[Not[LessEqual[z, 8.2e+65]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0500000000000002e38 or 8.2000000000000003e65 < z

   1. Initial program 56.1%

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

   2. Taylor expanded in x around 0 45.9%

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

      1. associate-/l* 67.6%

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

   4. Simplified 67.6%

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

      1. div-inv 67.6%

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

      2. *-commutative 67.6%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   if -2.0500000000000002e38 < z < 8.2000000000000003e65

   1. Initial program 89.9%

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

   2. Taylor expanded in a around inf 73.7%

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

      1. associate-/l* 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in y around inf 76.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+38} \lor \neg \left(z \leq 8.2 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 17: 53.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+36} \lor \neg \left(z \leq 1.5 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+36) (not (<= z 1.5e+81)))
   (/ t (/ (- z) (- y z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+36) || !(z <= 1.5e+81)) {
		tmp = t / (-z / (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 <= (-2.8d+36)) .or. (.not. (z <= 1.5d+81))) then
        tmp = t / (-z / (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 <= -2.8e+36) || !(z <= 1.5e+81)) {
		tmp = t / (-z / (y - z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+36) or not (z <= 1.5e+81):
		tmp = t / (-z / (y - z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+36) || !(z <= 1.5e+81))
		tmp = Float64(t / Float64(Float64(-z) / 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 <= -2.8e+36) || ~((z <= 1.5e+81)))
		tmp = t / (-z / (y - z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+36], N[Not[LessEqual[z, 1.5e+81]], $MachinePrecision]], N[(t / N[((-z) / 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 < -2.8000000000000001e36 or 1.49999999999999999e81 < z

   1. Initial program 55.3%

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

   2. Taylor expanded in x around 0 45.7%

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

      1. associate-/l* 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in a around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-neg-frac 60.8%

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

   7. Simplified 60.8%

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

   if -2.8000000000000001e36 < z < 1.49999999999999999e81

   1. Initial program 89.6%

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

   2. Taylor expanded in t around inf 69.8%

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

   3. Taylor expanded in z around 0 54.9%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+36} \lor \neg \left(z \leq 1.5 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 18: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.25e+37)
   t
   (if (<= z -2.3e-135)
     x
     (if (<= z 2.15e-303) (* y (/ t a)) (if (<= z 3.45e+81) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e+37) {
		tmp = t;
	} else if (z <= -2.3e-135) {
		tmp = x;
	} else if (z <= 2.15e-303) {
		tmp = y * (t / a);
	} else if (z <= 3.45e+81) {
		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 <= (-2.25d+37)) then
        tmp = t
    else if (z <= (-2.3d-135)) then
        tmp = x
    else if (z <= 2.15d-303) then
        tmp = y * (t / a)
    else if (z <= 3.45d+81) 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 <= -2.25e+37) {
		tmp = t;
	} else if (z <= -2.3e-135) {
		tmp = x;
	} else if (z <= 2.15e-303) {
		tmp = y * (t / a);
	} else if (z <= 3.45e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.25e+37:
		tmp = t
	elif z <= -2.3e-135:
		tmp = x
	elif z <= 2.15e-303:
		tmp = y * (t / a)
	elif z <= 3.45e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.25e+37)
		tmp = t;
	elseif (z <= -2.3e-135)
		tmp = x;
	elseif (z <= 2.15e-303)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 3.45e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.25e+37)
		tmp = t;
	elseif (z <= -2.3e-135)
		tmp = x;
	elseif (z <= 2.15e-303)
		tmp = y * (t / a);
	elseif (z <= 3.45e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.25e+37], t, If[LessEqual[z, -2.3e-135], x, If[LessEqual[z, 2.15e-303], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.45e+81], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.24999999999999981e37 or 3.4499999999999998e81 < z

   1. Initial program 55.3%

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

   2. Taylor expanded in z around inf 54.3%

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

   if -2.24999999999999981e37 < z < -2.2999999999999999e-135 or 2.14999999999999991e-303 < z < 3.4499999999999998e81

   1. Initial program 88.2%

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

   2. Taylor expanded in a around inf 38.8%

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

   if -2.2999999999999999e-135 < z < 2.14999999999999991e-303

   1. Initial program 96.1%

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

   2. Taylor expanded in x around 0 49.5%

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

      1. associate-/l* 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in z around 0 56.4%

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

      1. associate-/r/ 63.3%

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

   7. Applied egg-rr 63.3%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 53.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e+38)
   (/ t (/ (- z) (- y z)))
   (if (<= z 1.45e+68) (+ x (/ (* y t) a)) (/ t (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+38) {
		tmp = t / (-z / (y - z));
	} else if (z <= 1.45e+68) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t / ((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 (z <= (-3.15d+38)) then
        tmp = t / (-z / (y - z))
    else if (z <= 1.45d+68) then
        tmp = x + ((y * t) / a)
    else
        tmp = t / ((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 (z <= -3.15e+38) {
		tmp = t / (-z / (y - z));
	} else if (z <= 1.45e+68) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t / ((z - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e+38:
		tmp = t / (-z / (y - z))
	elif z <= 1.45e+68:
		tmp = x + ((y * t) / a)
	else:
		tmp = t / ((z - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e+38)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (z <= 1.45e+68)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(t / Float64(Float64(z - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.15e+38)
		tmp = t / (-z / (y - z));
	elseif (z <= 1.45e+68)
		tmp = x + ((y * t) / a);
	else
		tmp = t / ((z - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e+38], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+68], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.15000000000000001e38

   1. Initial program 62.8%

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

   2. Taylor expanded in x around 0 47.2%

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

      1. associate-/l* 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in a around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-neg-frac 66.6%

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

   7. Simplified 66.6%

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

   if -3.15000000000000001e38 < z < 1.45000000000000006e68

   1. Initial program 89.9%

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

   2. Taylor expanded in t around inf 69.6%

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

   3. Taylor expanded in z around 0 55.6%

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

   if 1.45000000000000006e68 < z

   1. Initial program 50.3%

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

   2. Taylor expanded in x around 0 44.8%

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

      1. associate-/l* 63.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in y around 0 62.2%

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

      1. associate-*r/ 62.2%

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

      2. neg-mul-1 62.2%

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

      3. neg-sub0 62.2%

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(a - z\right)}}{z}} \]

      4. associate--r- 62.2%

         \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - a\right) + z}}{z}} \]

      5. neg-sub0 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 20: 38.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+39) t (if (<= z 3.5e+81) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+39) {
		tmp = t;
	} else if (z <= 3.5e+81) {
		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 <= (-6.6d+39)) then
        tmp = t
    else if (z <= 3.5d+81) 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 <= -6.6e+39) {
		tmp = t;
	} else if (z <= 3.5e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+39:
		tmp = t
	elif z <= 3.5e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+39)
		tmp = t;
	elseif (z <= 3.5e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+39)
		tmp = t;
	elseif (z <= 3.5e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+39], t, If[LessEqual[z, 3.5e+81], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.60000000000000042e39 or 3.5e81 < z

   1. Initial program 55.3%

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

   2. Taylor expanded in z around inf 54.3%

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

   if -6.60000000000000042e39 < z < 3.5e81

   1. Initial program 89.6%

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

   2. Taylor expanded in a around inf 37.5%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 25.4% 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 75.9%

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

2. Taylor expanded in z around inf 26.8%

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

3. Final simplification 26.8%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023301 
(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)))))