Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 94.7%

Time: 17.6s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-295} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -2e-295) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -2e-295) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -2e-295) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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)))) < -2.00000000000000012e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. remove-double-neg 88.3%

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

      3. unsub-neg 88.3%

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

      4. *-commutative 88.3%

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

      5. associate-*l/ 76.2%

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

      6. associate-/l* 93.5%

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

      7. fma-neg 93.5%

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

      8. remove-double-neg 93.5%

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

   3. Simplified 93.5%

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

   if -2.00000000000000012e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

   3. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.2%

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

      4. mul-1-neg 81.2%

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

      5. unsub-neg 81.2%

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

      6. div-sub 81.2%

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

      7. associate-/l* 83.9%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq -2 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-295} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-206}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -2e-295) (not (<= t_1 5e-206)))
     t_1
     (+ t (* x (/ (- y a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -2e-295) || !(t_1 <= 5e-206)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((t - x) / (z - a)))
    if ((t_1 <= (-2d-295)) .or. (.not. (t_1 <= 5d-206))) then
        tmp = t_1
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -2e-295) || !(t_1 <= 5e-206)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -2e-295) or not (t_1 <= 5e-206):
		tmp = t_1
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -2e-295) || !(t_1 <= 5e-206))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -2e-295) || ~((t_1 <= 5e-206)))
		tmp = t_1;
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-295], N[Not[LessEqual[t$95$1, 5e-206]], $MachinePrecision]], t$95$1, N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $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)))) < -2.00000000000000012e-295 or 5e-206 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.9%

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

   if -2.00000000000000012e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-206

   1. Initial program 4.2%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. associate--l+ 79.6%

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

      2. distribute-lft-out-- 79.6%

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

      3. div-sub 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. div-sub 79.6%

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

      7. associate-/l* 82.2%

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

      8. associate-/l* 94.8%

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

      9. distribute-rgt-out-- 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in t around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. associate-/l* 95.8%

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

   8. Simplified 95.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq -2 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq 5 \cdot 10^{-206}\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-206}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- t x) (- z a))))))
   (if (<= t_1 -2e-295)
     t_1
     (if (<= t_1 5e-206)
       (+ t (* x (/ (- y a) z)))
       (- x (/ (- y z) (/ (- a z) (- x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if (t_1 <= -2e-295) {
		tmp = t_1;
	} else if (t_1 <= 5e-206) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((t - x) / (z - a)))
    if (t_1 <= (-2d-295)) then
        tmp = t_1
    else if (t_1 <= 5d-206) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = x - ((y - z) / ((a - z) / (x - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if (t_1 <= -2e-295) {
		tmp = t_1;
	} else if (t_1 <= 5e-206) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((t - x) / (z - a)))
	tmp = 0
	if t_1 <= -2e-295:
		tmp = t_1
	elif t_1 <= 5e-206:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = x - ((y - z) / ((a - z) / (x - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if (t_1 <= -2e-295)
		tmp = t_1;
	elseif (t_1 <= 5e-206)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(x - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((t - x) / (z - a)));
	tmp = 0.0;
	if (t_1 <= -2e-295)
		tmp = t_1;
	elseif (t_1 <= 5e-206)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-295], t$95$1, If[LessEqual[t$95$1, 5e-206], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000012e-295

   1. Initial program 87.4%

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

   if -2.00000000000000012e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-206

   1. Initial program 4.2%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. associate--l+ 79.6%

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

      2. distribute-lft-out-- 79.6%

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

      3. div-sub 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. div-sub 79.6%

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

      7. associate-/l* 82.2%

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

      8. associate-/l* 94.8%

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

      9. distribute-rgt-out-- 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in t around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. associate-/l* 95.8%

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

   8. Simplified 95.8%

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

   if 5e-206 < (+.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. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 90.6%

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

      2. un-div-inv 92.2%

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

   4. Applied egg-rr 92.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq 5 \cdot 10^{-206}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.3 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-81}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -1.25e-56)
     x
     (if (<= a -9.3e-209)
       t_1
       (if (<= a -5.5e-257)
         t
         (if (<= a 2.35e-296)
           t_1
           (if (<= a 3.9e-81)
             t
             (if (<= a 1.65e+16) t_1 (if (<= a 7.6e+130) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -1.25e-56) {
		tmp = x;
	} else if (a <= -9.3e-209) {
		tmp = t_1;
	} else if (a <= -5.5e-257) {
		tmp = t;
	} else if (a <= 2.35e-296) {
		tmp = t_1;
	} else if (a <= 3.9e-81) {
		tmp = t;
	} else if (a <= 1.65e+16) {
		tmp = t_1;
	} else if (a <= 7.6e+130) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-1.25d-56)) then
        tmp = x
    else if (a <= (-9.3d-209)) then
        tmp = t_1
    else if (a <= (-5.5d-257)) then
        tmp = t
    else if (a <= 2.35d-296) then
        tmp = t_1
    else if (a <= 3.9d-81) then
        tmp = t
    else if (a <= 1.65d+16) then
        tmp = t_1
    else if (a <= 7.6d+130) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -1.25e-56) {
		tmp = x;
	} else if (a <= -9.3e-209) {
		tmp = t_1;
	} else if (a <= -5.5e-257) {
		tmp = t;
	} else if (a <= 2.35e-296) {
		tmp = t_1;
	} else if (a <= 3.9e-81) {
		tmp = t;
	} else if (a <= 1.65e+16) {
		tmp = t_1;
	} else if (a <= 7.6e+130) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -1.25e-56:
		tmp = x
	elif a <= -9.3e-209:
		tmp = t_1
	elif a <= -5.5e-257:
		tmp = t
	elif a <= 2.35e-296:
		tmp = t_1
	elif a <= 3.9e-81:
		tmp = t
	elif a <= 1.65e+16:
		tmp = t_1
	elif a <= 7.6e+130:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -1.25e-56)
		tmp = x;
	elseif (a <= -9.3e-209)
		tmp = t_1;
	elseif (a <= -5.5e-257)
		tmp = t;
	elseif (a <= 2.35e-296)
		tmp = t_1;
	elseif (a <= 3.9e-81)
		tmp = t;
	elseif (a <= 1.65e+16)
		tmp = t_1;
	elseif (a <= 7.6e+130)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -1.25e-56)
		tmp = x;
	elseif (a <= -9.3e-209)
		tmp = t_1;
	elseif (a <= -5.5e-257)
		tmp = t;
	elseif (a <= 2.35e-296)
		tmp = t_1;
	elseif (a <= 3.9e-81)
		tmp = t;
	elseif (a <= 1.65e+16)
		tmp = t_1;
	elseif (a <= 7.6e+130)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e-56], x, If[LessEqual[a, -9.3e-209], t$95$1, If[LessEqual[a, -5.5e-257], t, If[LessEqual[a, 2.35e-296], t$95$1, If[LessEqual[a, 3.9e-81], t, If[LessEqual[a, 1.65e+16], t$95$1, If[LessEqual[a, 7.6e+130], t, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.24999999999999999e-56 or 7.6000000000000004e130 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 48.3%

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

   if -1.24999999999999999e-56 < a < -9.3e-209 or -5.50000000000000025e-257 < a < 2.35e-296 or 3.89999999999999985e-81 < a < 1.65e16

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf 82.0%

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

      1. associate--l+ 82.0%

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

      2. distribute-lft-out-- 82.0%

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

      3. div-sub 82.0%

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

      4. mul-1-neg 82.0%

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

      5. unsub-neg 82.0%

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

      6. div-sub 82.0%

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

      7. associate-/l* 82.0%

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

      8. associate-/l* 77.7%

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

      9. distribute-rgt-out-- 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in t around 0 50.5%

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

   7. Taylor expanded in y around inf 48.1%

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

      1. associate-/l* 48.9%

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

   9. Simplified 48.9%

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

   if -9.3e-209 < a < -5.50000000000000025e-257 or 2.35e-296 < a < 3.89999999999999985e-81 or 1.65e16 < a < 7.6000000000000004e130

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 47.7%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.3 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-81}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{z}\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-258}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) z)))
   (if (<= a -9.2e-57)
     x
     (if (<= a -1.22e-205)
       t_1
       (if (<= a -4.8e-258)
         t
         (if (<= a 1.85e-295)
           t_1
           (if (<= a 1.18e-95)
             t
             (if (<= a 1.3e+19) (* x (/ y z)) (if (<= a 7.6e+130) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / z;
	double tmp;
	if (a <= -9.2e-57) {
		tmp = x;
	} else if (a <= -1.22e-205) {
		tmp = t_1;
	} else if (a <= -4.8e-258) {
		tmp = t;
	} else if (a <= 1.85e-295) {
		tmp = t_1;
	} else if (a <= 1.18e-95) {
		tmp = t;
	} else if (a <= 1.3e+19) {
		tmp = x * (y / z);
	} else if (a <= 7.6e+130) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / z
    if (a <= (-9.2d-57)) then
        tmp = x
    else if (a <= (-1.22d-205)) then
        tmp = t_1
    else if (a <= (-4.8d-258)) then
        tmp = t
    else if (a <= 1.85d-295) then
        tmp = t_1
    else if (a <= 1.18d-95) then
        tmp = t
    else if (a <= 1.3d+19) then
        tmp = x * (y / z)
    else if (a <= 7.6d+130) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / z;
	double tmp;
	if (a <= -9.2e-57) {
		tmp = x;
	} else if (a <= -1.22e-205) {
		tmp = t_1;
	} else if (a <= -4.8e-258) {
		tmp = t;
	} else if (a <= 1.85e-295) {
		tmp = t_1;
	} else if (a <= 1.18e-95) {
		tmp = t;
	} else if (a <= 1.3e+19) {
		tmp = x * (y / z);
	} else if (a <= 7.6e+130) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / z
	tmp = 0
	if a <= -9.2e-57:
		tmp = x
	elif a <= -1.22e-205:
		tmp = t_1
	elif a <= -4.8e-258:
		tmp = t
	elif a <= 1.85e-295:
		tmp = t_1
	elif a <= 1.18e-95:
		tmp = t
	elif a <= 1.3e+19:
		tmp = x * (y / z)
	elif a <= 7.6e+130:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (a <= -9.2e-57)
		tmp = x;
	elseif (a <= -1.22e-205)
		tmp = t_1;
	elseif (a <= -4.8e-258)
		tmp = t;
	elseif (a <= 1.85e-295)
		tmp = t_1;
	elseif (a <= 1.18e-95)
		tmp = t;
	elseif (a <= 1.3e+19)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 7.6e+130)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / z;
	tmp = 0.0;
	if (a <= -9.2e-57)
		tmp = x;
	elseif (a <= -1.22e-205)
		tmp = t_1;
	elseif (a <= -4.8e-258)
		tmp = t;
	elseif (a <= 1.85e-295)
		tmp = t_1;
	elseif (a <= 1.18e-95)
		tmp = t;
	elseif (a <= 1.3e+19)
		tmp = x * (y / z);
	elseif (a <= 7.6e+130)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[a, -9.2e-57], x, If[LessEqual[a, -1.22e-205], t$95$1, If[LessEqual[a, -4.8e-258], t, If[LessEqual[a, 1.85e-295], t$95$1, If[LessEqual[a, 1.18e-95], t, If[LessEqual[a, 1.3e+19], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+130], t, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.2000000000000001e-57 or 7.6000000000000004e130 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 48.3%

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

   if -9.2000000000000001e-57 < a < -1.2200000000000001e-205 or -4.8000000000000003e-258 < a < 1.85e-295

   1. Initial program 68.9%

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

   3. Taylor expanded in z around inf 94.2%

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

      1. associate--l+ 94.2%

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

      2. distribute-lft-out-- 94.2%

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

      3. div-sub 94.1%

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

      4. mul-1-neg 94.1%

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

      5. unsub-neg 94.1%

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

      6. div-sub 94.2%

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

      7. associate-/l* 90.2%

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

      8. associate-/l* 83.8%

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

      9. distribute-rgt-out-- 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in t around 0 58.4%

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

   7. Taylor expanded in y around inf 54.5%

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

      1. *-commutative 54.5%

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

   9. Simplified 54.5%

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

   if -1.2200000000000001e-205 < a < -4.8000000000000003e-258 or 1.85e-295 < a < 1.17999999999999993e-95 or 1.3e19 < a < 7.6000000000000004e130

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 47.7%

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

   if 1.17999999999999993e-95 < a < 1.3e19

   1. Initial program 84.0%

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

   3. Taylor expanded in z around inf 58.2%

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

      1. associate--l+ 58.2%

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

      2. distribute-lft-out-- 58.2%

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

      3. div-sub 58.2%

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

      4. mul-1-neg 58.2%

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

      5. unsub-neg 58.2%

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

      6. div-sub 58.2%

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

      7. associate-/l* 65.9%

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

      8. associate-/l* 65.9%

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

      9. distribute-rgt-out-- 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in t around 0 35.1%

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

   7. Taylor expanded in y around inf 35.5%

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

      1. associate-/l* 39.5%

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

   9. Simplified 39.5%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-258}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+15)
   t
   (if (<= z -2.1e-156)
     x
     (if (<= z -4e-201)
       (* t (/ y (- a z)))
       (if (<= z 7.5e-144)
         x
         (if (<= z 6.4e-77)
           (* t (/ (- y z) a))
           (if (<= z 1.36e+70) (/ (* x y) y) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+15) {
		tmp = t;
	} else if (z <= -2.1e-156) {
		tmp = x;
	} else if (z <= -4e-201) {
		tmp = t * (y / (a - z));
	} else if (z <= 7.5e-144) {
		tmp = x;
	} else if (z <= 6.4e-77) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.36e+70) {
		tmp = (x * y) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+15)) then
        tmp = t
    else if (z <= (-2.1d-156)) then
        tmp = x
    else if (z <= (-4d-201)) then
        tmp = t * (y / (a - z))
    else if (z <= 7.5d-144) then
        tmp = x
    else if (z <= 6.4d-77) then
        tmp = t * ((y - z) / a)
    else if (z <= 1.36d+70) then
        tmp = (x * y) / y
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+15) {
		tmp = t;
	} else if (z <= -2.1e-156) {
		tmp = x;
	} else if (z <= -4e-201) {
		tmp = t * (y / (a - z));
	} else if (z <= 7.5e-144) {
		tmp = x;
	} else if (z <= 6.4e-77) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.36e+70) {
		tmp = (x * y) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+15:
		tmp = t
	elif z <= -2.1e-156:
		tmp = x
	elif z <= -4e-201:
		tmp = t * (y / (a - z))
	elif z <= 7.5e-144:
		tmp = x
	elif z <= 6.4e-77:
		tmp = t * ((y - z) / a)
	elif z <= 1.36e+70:
		tmp = (x * y) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+15)
		tmp = t;
	elseif (z <= -2.1e-156)
		tmp = x;
	elseif (z <= -4e-201)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 7.5e-144)
		tmp = x;
	elseif (z <= 6.4e-77)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 1.36e+70)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+15)
		tmp = t;
	elseif (z <= -2.1e-156)
		tmp = x;
	elseif (z <= -4e-201)
		tmp = t * (y / (a - z));
	elseif (z <= 7.5e-144)
		tmp = x;
	elseif (z <= 6.4e-77)
		tmp = t * ((y - z) / a);
	elseif (z <= 1.36e+70)
		tmp = (x * y) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+15], t, If[LessEqual[z, -2.1e-156], x, If[LessEqual[z, -4e-201], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-144], x, If[LessEqual[z, 6.4e-77], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e+70], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2e15 or 1.35999999999999995e70 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 50.3%

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

   if -3.2e15 < z < -2.10000000000000012e-156 or -3.99999999999999978e-201 < z < 7.49999999999999963e-144

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf 43.3%

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

   if -2.10000000000000012e-156 < z < -3.99999999999999978e-201

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0 51.4%

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

   4. Taylor expanded in y around inf 40.0%

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

      1. associate-/l* 51.8%

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

   6. Simplified 51.8%

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

   if 7.49999999999999963e-144 < z < 6.39999999999999999e-77

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0 49.2%

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

   4. Taylor expanded in a around inf 42.3%

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

      1. associate-/l* 48.7%

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

   6. Simplified 48.7%

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

   if 6.39999999999999999e-77 < z < 1.35999999999999995e70

   1. Initial program 79.9%

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

   3. Taylor expanded in y around -inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in a around inf 25.8%

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

      1. associate-*r/ 25.8%

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

      2. mul-1-neg 25.8%

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

   8. Simplified 25.8%

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

      1. *-commutative 25.8%

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

      2. associate-*r/ 47.0%

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

      3. add-sqr-sqrt 13.1%

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

      4. sqrt-unprod 18.1%

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

      5. sqr-neg 18.1%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 6.0%

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

      8. add-sqr-sqrt 1.0%

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

      9. sqrt-unprod 23.2%

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

      10. sqr-neg 23.2%

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

      11. sqrt-unprod 30.0%

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

      12. add-sqr-sqrt 47.0%

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

   10. Applied egg-rr 47.0%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0021:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.0021)
   (* x (/ y z))
   (if (<= y -1.1e-218)
     x
     (if (<= y -4.9e-300)
       t
       (if (<= y 3.9e-203) x (if (<= y 9.5e+102) t (* t (/ y (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.0021) {
		tmp = x * (y / z);
	} else if (y <= -1.1e-218) {
		tmp = x;
	} else if (y <= -4.9e-300) {
		tmp = t;
	} else if (y <= 3.9e-203) {
		tmp = x;
	} else if (y <= 9.5e+102) {
		tmp = t;
	} else {
		tmp = t * (y / (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 (y <= (-0.0021d0)) then
        tmp = x * (y / z)
    else if (y <= (-1.1d-218)) then
        tmp = x
    else if (y <= (-4.9d-300)) then
        tmp = t
    else if (y <= 3.9d-203) then
        tmp = x
    else if (y <= 9.5d+102) then
        tmp = t
    else
        tmp = t * (y / (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 (y <= -0.0021) {
		tmp = x * (y / z);
	} else if (y <= -1.1e-218) {
		tmp = x;
	} else if (y <= -4.9e-300) {
		tmp = t;
	} else if (y <= 3.9e-203) {
		tmp = x;
	} else if (y <= 9.5e+102) {
		tmp = t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.0021:
		tmp = x * (y / z)
	elif y <= -1.1e-218:
		tmp = x
	elif y <= -4.9e-300:
		tmp = t
	elif y <= 3.9e-203:
		tmp = x
	elif y <= 9.5e+102:
		tmp = t
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.0021)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= -1.1e-218)
		tmp = x;
	elseif (y <= -4.9e-300)
		tmp = t;
	elseif (y <= 3.9e-203)
		tmp = x;
	elseif (y <= 9.5e+102)
		tmp = t;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.0021)
		tmp = x * (y / z);
	elseif (y <= -1.1e-218)
		tmp = x;
	elseif (y <= -4.9e-300)
		tmp = t;
	elseif (y <= 3.9e-203)
		tmp = x;
	elseif (y <= 9.5e+102)
		tmp = t;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.0021], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-218], x, If[LessEqual[y, -4.9e-300], t, If[LessEqual[y, 3.9e-203], x, If[LessEqual[y, 9.5e+102], t, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.00209999999999999987

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. distribute-lft-out-- 58.9%

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

      3. div-sub 59.1%

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

      4. mul-1-neg 59.1%

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

      5. unsub-neg 59.1%

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

      6. div-sub 58.9%

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

      7. associate-/l* 62.2%

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

      8. associate-/l* 62.2%

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

      9. distribute-rgt-out-- 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 40.7%

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

   7. Taylor expanded in y around inf 38.9%

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

      1. associate-/l* 44.2%

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

   9. Simplified 44.2%

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

   if -0.00209999999999999987 < y < -1.10000000000000003e-218 or -4.9e-300 < y < 3.8999999999999999e-203

   1. Initial program 74.6%

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

   3. Taylor expanded in a around inf 51.9%

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

   if -1.10000000000000003e-218 < y < -4.9e-300 or 3.8999999999999999e-203 < y < 9.4999999999999992e102

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 43.4%

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

   if 9.4999999999999992e102 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 33.3%

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

   4. Taylor expanded in y around inf 32.9%

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

      1. associate-/l* 41.6%

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

   6. Simplified 41.6%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0021:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.14:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.14)
   (* x (/ (- y a) z))
   (if (<= y -1.1e-205)
     x
     (if (<= y -2.5e-299)
       t
       (if (<= y 2.45e-203) x (if (<= y 6.4e+105) t (* t (/ y (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.14) {
		tmp = x * ((y - a) / z);
	} else if (y <= -1.1e-205) {
		tmp = x;
	} else if (y <= -2.5e-299) {
		tmp = t;
	} else if (y <= 2.45e-203) {
		tmp = x;
	} else if (y <= 6.4e+105) {
		tmp = t;
	} else {
		tmp = t * (y / (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 (y <= (-0.14d0)) then
        tmp = x * ((y - a) / z)
    else if (y <= (-1.1d-205)) then
        tmp = x
    else if (y <= (-2.5d-299)) then
        tmp = t
    else if (y <= 2.45d-203) then
        tmp = x
    else if (y <= 6.4d+105) then
        tmp = t
    else
        tmp = t * (y / (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 (y <= -0.14) {
		tmp = x * ((y - a) / z);
	} else if (y <= -1.1e-205) {
		tmp = x;
	} else if (y <= -2.5e-299) {
		tmp = t;
	} else if (y <= 2.45e-203) {
		tmp = x;
	} else if (y <= 6.4e+105) {
		tmp = t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.14:
		tmp = x * ((y - a) / z)
	elif y <= -1.1e-205:
		tmp = x
	elif y <= -2.5e-299:
		tmp = t
	elif y <= 2.45e-203:
		tmp = x
	elif y <= 6.4e+105:
		tmp = t
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.14)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (y <= -1.1e-205)
		tmp = x;
	elseif (y <= -2.5e-299)
		tmp = t;
	elseif (y <= 2.45e-203)
		tmp = x;
	elseif (y <= 6.4e+105)
		tmp = t;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.14)
		tmp = x * ((y - a) / z);
	elseif (y <= -1.1e-205)
		tmp = x;
	elseif (y <= -2.5e-299)
		tmp = t;
	elseif (y <= 2.45e-203)
		tmp = x;
	elseif (y <= 6.4e+105)
		tmp = t;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.14], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-205], x, If[LessEqual[y, -2.5e-299], t, If[LessEqual[y, 2.45e-203], x, If[LessEqual[y, 6.4e+105], t, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.14000000000000001

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. distribute-lft-out-- 58.9%

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

      3. div-sub 59.1%

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

      4. mul-1-neg 59.1%

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

      5. unsub-neg 59.1%

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

      6. div-sub 58.9%

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

      7. associate-/l* 62.2%

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

      8. associate-/l* 62.2%

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

      9. distribute-rgt-out-- 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 40.7%

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

      1. associate-/l* 46.4%

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

   8. Simplified 46.4%

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

   if -0.14000000000000001 < y < -1.10000000000000005e-205 or -2.49999999999999978e-299 < y < 2.45e-203

   1. Initial program 74.6%

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

   3. Taylor expanded in a around inf 51.9%

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

   if -1.10000000000000005e-205 < y < -2.49999999999999978e-299 or 2.45e-203 < y < 6.4e105

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 43.4%

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

   if 6.4e105 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 33.3%

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

   4. Taylor expanded in y around inf 32.9%

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

      1. associate-/l* 41.6%

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

   6. Simplified 41.6%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.14:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.023:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.023)
   (* x (/ (- y a) z))
   (if (<= y -1.45e-207)
     x
     (if (<= y -1.92e-299)
       t
       (if (<= y 5.5e-203) x (if (<= y 2.8e+112) t (* y (/ (- t x) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.023) {
		tmp = x * ((y - a) / z);
	} else if (y <= -1.45e-207) {
		tmp = x;
	} else if (y <= -1.92e-299) {
		tmp = t;
	} else if (y <= 5.5e-203) {
		tmp = x;
	} else if (y <= 2.8e+112) {
		tmp = t;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-0.023d0)) then
        tmp = x * ((y - a) / z)
    else if (y <= (-1.45d-207)) then
        tmp = x
    else if (y <= (-1.92d-299)) then
        tmp = t
    else if (y <= 5.5d-203) then
        tmp = x
    else if (y <= 2.8d+112) then
        tmp = t
    else
        tmp = y * ((t - x) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.023) {
		tmp = x * ((y - a) / z);
	} else if (y <= -1.45e-207) {
		tmp = x;
	} else if (y <= -1.92e-299) {
		tmp = t;
	} else if (y <= 5.5e-203) {
		tmp = x;
	} else if (y <= 2.8e+112) {
		tmp = t;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.023:
		tmp = x * ((y - a) / z)
	elif y <= -1.45e-207:
		tmp = x
	elif y <= -1.92e-299:
		tmp = t
	elif y <= 5.5e-203:
		tmp = x
	elif y <= 2.8e+112:
		tmp = t
	else:
		tmp = y * ((t - x) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.023)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (y <= -1.45e-207)
		tmp = x;
	elseif (y <= -1.92e-299)
		tmp = t;
	elseif (y <= 5.5e-203)
		tmp = x;
	elseif (y <= 2.8e+112)
		tmp = t;
	else
		tmp = Float64(y * Float64(Float64(t - x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.023)
		tmp = x * ((y - a) / z);
	elseif (y <= -1.45e-207)
		tmp = x;
	elseif (y <= -1.92e-299)
		tmp = t;
	elseif (y <= 5.5e-203)
		tmp = x;
	elseif (y <= 2.8e+112)
		tmp = t;
	else
		tmp = y * ((t - x) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.023], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-207], x, If[LessEqual[y, -1.92e-299], t, If[LessEqual[y, 5.5e-203], x, If[LessEqual[y, 2.8e+112], t, N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.023

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. distribute-lft-out-- 58.9%

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

      3. div-sub 59.1%

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

      4. mul-1-neg 59.1%

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

      5. unsub-neg 59.1%

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

      6. div-sub 58.9%

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

      7. associate-/l* 62.2%

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

      8. associate-/l* 62.2%

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

      9. distribute-rgt-out-- 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 40.7%

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

      1. associate-/l* 46.4%

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

   8. Simplified 46.4%

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

   if -0.023 < y < -1.45000000000000006e-207 or -1.92e-299 < y < 5.5000000000000002e-203

   1. Initial program 74.6%

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

   3. Taylor expanded in a around inf 51.9%

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

   if -1.45000000000000006e-207 < y < -1.92e-299 or 5.5000000000000002e-203 < y < 2.8000000000000001e112

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 43.0%

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

   if 2.8000000000000001e112 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 46.1%

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

   4. Taylor expanded in y around inf 42.7%

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

      1. div-sub 45.6%

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

   6. Simplified 45.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.023:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -6.2e+16)
     t
     (if (<= z -8.5e-223)
       t_1
       (if (<= z 6.5e-258)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.05e+54)
           t_1
           (if (<= z 1.25e+181) (* y (/ (- x t) z)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.2e+16) {
		tmp = t;
	} else if (z <= -8.5e-223) {
		tmp = t_1;
	} else if (z <= 6.5e-258) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.05e+54) {
		tmp = t_1;
	} else if (z <= 1.25e+181) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-6.2d+16)) then
        tmp = t
    else if (z <= (-8.5d-223)) then
        tmp = t_1
    else if (z <= 6.5d-258) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.05d+54) then
        tmp = t_1
    else if (z <= 1.25d+181) then
        tmp = y * ((x - t) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.2e+16) {
		tmp = t;
	} else if (z <= -8.5e-223) {
		tmp = t_1;
	} else if (z <= 6.5e-258) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.05e+54) {
		tmp = t_1;
	} else if (z <= 1.25e+181) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -6.2e+16:
		tmp = t
	elif z <= -8.5e-223:
		tmp = t_1
	elif z <= 6.5e-258:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.05e+54:
		tmp = t_1
	elif z <= 1.25e+181:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -6.2e+16)
		tmp = t;
	elseif (z <= -8.5e-223)
		tmp = t_1;
	elseif (z <= 6.5e-258)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.05e+54)
		tmp = t_1;
	elseif (z <= 1.25e+181)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -6.2e+16)
		tmp = t;
	elseif (z <= -8.5e-223)
		tmp = t_1;
	elseif (z <= 6.5e-258)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.05e+54)
		tmp = t_1;
	elseif (z <= 1.25e+181)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+16], t, If[LessEqual[z, -8.5e-223], t$95$1, If[LessEqual[z, 6.5e-258], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+54], t$95$1, If[LessEqual[z, 1.25e+181], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2e16 or 1.2500000000000001e181 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in z around inf 55.4%

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

   if -6.2e16 < z < -8.5000000000000003e-223 or 6.5000000000000002e-258 < z < 1.04999999999999993e54

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 56.5%

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

   4. Taylor expanded in t around inf 51.5%

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

      1. associate-/l* 57.9%

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

   6. Simplified 57.9%

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

   if -8.5000000000000003e-223 < z < 6.5000000000000002e-258

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 93.5%

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

   4. Taylor expanded in x around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. mul-1-neg 76.3%

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

      3. sub-neg 76.3%

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

      4. metadata-eval 76.3%

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

   6. Simplified 76.3%

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

   if 1.04999999999999993e54 < z < 1.2500000000000001e181

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf 50.3%

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

      1. div-sub 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in a around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. associate-/l* 46.3%

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

      3. distribute-rgt-neg-in 46.3%

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

      4. distribute-neg-frac2 46.3%

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

   8. Simplified 46.3%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-223}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-35}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+53}:\\ \;\;\;\;x - \left(t - x\right) \cdot \left(y \cdot \frac{-1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-35)
   (+ t (* x (/ (- y a) z)))
   (if (<= z -2.75e-128)
     (* x (+ (/ (- y z) (- z a)) 1.0))
     (if (<= z -5.3e-182)
       (* t (/ (- y z) (- a z)))
       (if (<= z 7.5e+53)
         (- x (* (- t x) (* y (/ -1.0 a))))
         (- t (* y (/ (- t x) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-35) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= -2.75e-128) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= -5.3e-182) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.5e+53) {
		tmp = x - ((t - x) * (y * (-1.0 / a)));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d-35)) then
        tmp = t + (x * ((y - a) / z))
    else if (z <= (-2.75d-128)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (z <= (-5.3d-182)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 7.5d+53) then
        tmp = x - ((t - x) * (y * ((-1.0d0) / a)))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-35) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= -2.75e-128) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= -5.3e-182) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.5e+53) {
		tmp = x - ((t - x) * (y * (-1.0 / a)));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-35:
		tmp = t + (x * ((y - a) / z))
	elif z <= -2.75e-128:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif z <= -5.3e-182:
		tmp = t * ((y - z) / (a - z))
	elif z <= 7.5e+53:
		tmp = x - ((t - x) * (y * (-1.0 / a)))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-35)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (z <= -2.75e-128)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (z <= -5.3e-182)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 7.5e+53)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(y * Float64(-1.0 / a))));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e-35)
		tmp = t + (x * ((y - a) / z));
	elseif (z <= -2.75e-128)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (z <= -5.3e-182)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 7.5e+53)
		tmp = x - ((t - x) * (y * (-1.0 / a)));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-35], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.75e-128], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-182], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+53], N[(x - N[(N[(t - x), $MachinePrecision] * N[(y * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1499999999999999e-35

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. distribute-lft-out-- 63.9%

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

      3. div-sub 63.9%

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

      4. mul-1-neg 63.9%

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

      5. unsub-neg 63.9%

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

      6. div-sub 63.9%

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

      7. associate-/l* 68.4%

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

      8. associate-/l* 80.5%

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

      9. distribute-rgt-out-- 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   if -1.1499999999999999e-35 < z < -2.7500000000000002e-128

   1. Initial program 87.8%

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

   3. Taylor expanded in x around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   5. Simplified 71.0%

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

   if -2.7500000000000002e-128 < z < -5.30000000000000005e-182

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 54.6%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if -5.30000000000000005e-182 < z < 7.4999999999999997e53

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 73.9%

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

      1. div-inv 73.8%

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

      2. *-commutative 73.8%

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

   5. Applied egg-rr 73.8%

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

      1. associate-*l* 78.3%

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

   7. Simplified 78.3%

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

   if 7.4999999999999997e53 < z

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 73.2%

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

      1. associate--l+ 73.2%

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

      2. distribute-lft-out-- 73.2%

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

      3. div-sub 73.2%

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

      4. mul-1-neg 73.2%

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

      5. unsub-neg 73.2%

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

      6. div-sub 73.2%

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

      7. associate-/l* 79.9%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 76.4%

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

   8. Simplified 76.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-35}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+53}:\\ \;\;\;\;x - \left(t - x\right) \cdot \left(y \cdot \frac{-1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-37)
   (+ t (* x (/ (- y a) z)))
   (if (<= z -7.6e-128)
     (* x (+ (/ (- y z) (- z a)) 1.0))
     (if (<= z -5.3e-182)
       (* t (/ (- y z) (- a z)))
       (if (<= z 3.6e+52)
         (+ x (/ (* y (- t x)) a))
         (- t (* y (/ (- t x) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-37) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= -7.6e-128) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= -5.3e-182) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 3.6e+52) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d-37)) then
        tmp = t + (x * ((y - a) / z))
    else if (z <= (-7.6d-128)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (z <= (-5.3d-182)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 3.6d+52) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-37) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= -7.6e-128) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= -5.3e-182) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 3.6e+52) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-37:
		tmp = t + (x * ((y - a) / z))
	elif z <= -7.6e-128:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif z <= -5.3e-182:
		tmp = t * ((y - z) / (a - z))
	elif z <= 3.6e+52:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-37)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (z <= -7.6e-128)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (z <= -5.3e-182)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 3.6e+52)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e-37)
		tmp = t + (x * ((y - a) / z));
	elseif (z <= -7.6e-128)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (z <= -5.3e-182)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 3.6e+52)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-37], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-128], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-182], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+52], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.20000000000000002e-37

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. distribute-lft-out-- 63.9%

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

      3. div-sub 63.9%

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

      4. mul-1-neg 63.9%

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

      5. unsub-neg 63.9%

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

      6. div-sub 63.9%

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

      7. associate-/l* 68.4%

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

      8. associate-/l* 80.5%

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

      9. distribute-rgt-out-- 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   if -2.20000000000000002e-37 < z < -7.6000000000000005e-128

   1. Initial program 87.8%

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

   3. Taylor expanded in x around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   5. Simplified 71.0%

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

   if -7.6000000000000005e-128 < z < -5.30000000000000005e-182

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 54.6%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if -5.30000000000000005e-182 < z < 3.6e52

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 73.9%

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

   if 3.6e52 < z

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 73.2%

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

      1. associate--l+ 73.2%

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

      2. distribute-lft-out-- 73.2%

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

      3. div-sub 73.2%

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

      4. mul-1-neg 73.2%

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

      5. unsub-neg 73.2%

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

      6. div-sub 73.2%

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

      7. associate-/l* 79.9%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 76.4%

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

   8. Simplified 76.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+54} \lor \neg \left(x \leq 4.8 \cdot 10^{+136}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.6e+36)
     t_1
     (if (<= x 6.6e-116)
       (* t (/ (- y z) (- a z)))
       (if (or (<= x 1.8e+54) (not (<= x 4.8e+136)))
         t_1
         (* x (/ (- y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.6e+36) {
		tmp = t_1;
	} else if (x <= 6.6e-116) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 1.8e+54) || !(x <= 4.8e+136)) {
		tmp = t_1;
	} else {
		tmp = x * ((y - 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-1.6d+36)) then
        tmp = t_1
    else if (x <= 6.6d-116) then
        tmp = t * ((y - z) / (a - z))
    else if ((x <= 1.8d+54) .or. (.not. (x <= 4.8d+136))) then
        tmp = t_1
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.6e+36) {
		tmp = t_1;
	} else if (x <= 6.6e-116) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 1.8e+54) || !(x <= 4.8e+136)) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.6e+36:
		tmp = t_1
	elif x <= 6.6e-116:
		tmp = t * ((y - z) / (a - z))
	elif (x <= 1.8e+54) or not (x <= 4.8e+136):
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.6e+36)
		tmp = t_1;
	elseif (x <= 6.6e-116)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif ((x <= 1.8e+54) || !(x <= 4.8e+136))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -1.6e+36)
		tmp = t_1;
	elseif (x <= 6.6e-116)
		tmp = t * ((y - z) / (a - z));
	elseif ((x <= 1.8e+54) || ~((x <= 4.8e+136)))
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+36], t$95$1, If[LessEqual[x, 6.6e-116], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.8e+54], N[Not[LessEqual[x, 4.8e+136]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5999999999999999e36 or 6.60000000000000002e-116 < x < 1.8000000000000001e54 or 4.8000000000000001e136 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in z around 0 52.8%

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

   4. Taylor expanded in x around -inf 53.6%

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

      1. associate-*r* 53.6%

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

      2. mul-1-neg 53.6%

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

      3. sub-neg 53.6%

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

      4. metadata-eval 53.6%

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

   6. Simplified 53.6%

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

   if -1.5999999999999999e36 < x < 6.60000000000000002e-116

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0 54.2%

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

      1. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   if 1.8000000000000001e54 < x < 4.8000000000000001e136

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf 62.0%

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

      1. associate--l+ 62.0%

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

      2. distribute-lft-out-- 62.0%

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

      3. div-sub 62.0%

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

      4. mul-1-neg 62.0%

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

      5. unsub-neg 62.0%

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

      6. div-sub 62.0%

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

      7. associate-/l* 62.0%

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

      8. associate-/l* 67.0%

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

      9. distribute-rgt-out-- 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around 0 53.1%

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

      1. associate-/l* 58.0%

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

   8. Simplified 58.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+54} \lor \neg \left(x \leq 4.8 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -1.1e+19)
     t_2
     (if (<= z -1.15e-222)
       t_1
       (if (<= z 1.15e-257)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.1e+19) {
		tmp = t_2;
	} else if (z <= -1.15e-222) {
		tmp = t_1;
	} else if (z <= 1.15e-257) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-1.1d+19)) then
        tmp = t_2
    else if (z <= (-1.15d-222)) then
        tmp = t_1
    else if (z <= 1.15d-257) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.1e+19) {
		tmp = t_2;
	} else if (z <= -1.15e-222) {
		tmp = t_1;
	} else if (z <= 1.15e-257) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -1.1e+19:
		tmp = t_2
	elif z <= -1.15e-222:
		tmp = t_1
	elif z <= 1.15e-257:
		tmp = x * (1.0 - (y / a))
	elif z <= 1e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.1e+19)
		tmp = t_2;
	elseif (z <= -1.15e-222)
		tmp = t_1;
	elseif (z <= 1.15e-257)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.1e+19)
		tmp = t_2;
	elseif (z <= -1.15e-222)
		tmp = t_1;
	elseif (z <= 1.15e-257)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1e+69)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+19], t$95$2, If[LessEqual[z, -1.15e-222], t$95$1, If[LessEqual[z, 1.15e-257], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e19 or 1.0000000000000001e69 < z

   1. Initial program 63.1%

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

      1. clear-num 63.1%

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

      2. un-div-inv 63.3%

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

   4. Applied egg-rr 63.3%

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

   5. Taylor expanded in a around 0 49.5%

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

      1. associate-*r/ 49.5%

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

      2. neg-mul-1 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in x around 0 36.7%

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

      1. associate-/l* 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*l* 55.8%

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

      4. *-commutative 55.8%

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

      5. associate-*l* 55.8%

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

      6. div-sub 55.8%

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

      7. sub-neg 55.8%

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

      8. *-inverses 55.8%

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

      9. metadata-eval 55.8%

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

      10. +-commutative 55.8%

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

      11. neg-mul-1 55.8%

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

   10. Simplified 55.8%

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

   if -1.1e19 < z < -1.1500000000000001e-222 or 1.15e-257 < z < 1.0000000000000001e69

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 55.9%

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

   4. Taylor expanded in t around inf 51.1%

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

      1. associate-/l* 57.3%

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

   6. Simplified 57.3%

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

   if -1.1500000000000001e-222 < z < 1.15e-257

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 93.5%

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

   4. Taylor expanded in x around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. mul-1-neg 76.3%

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

      3. sub-neg 76.3%

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

      4. metadata-eval 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-222}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 10^{+69}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-57}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-302}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -2.8e-57)
     (+ x (* t (/ y a)))
     (if (<= a -6.6e-256)
       t_1
       (if (<= a 2.05e-302)
         (/ (* y (- x t)) z)
         (if (<= a 3.8e-56) t_1 (* x (- 1.0 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.8e-57) {
		tmp = x + (t * (y / a));
	} else if (a <= -6.6e-256) {
		tmp = t_1;
	} else if (a <= 2.05e-302) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 3.8e-56) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-2.8d-57)) then
        tmp = x + (t * (y / a))
    else if (a <= (-6.6d-256)) then
        tmp = t_1
    else if (a <= 2.05d-302) then
        tmp = (y * (x - t)) / z
    else if (a <= 3.8d-56) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.8e-57) {
		tmp = x + (t * (y / a));
	} else if (a <= -6.6e-256) {
		tmp = t_1;
	} else if (a <= 2.05e-302) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 3.8e-56) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -2.8e-57:
		tmp = x + (t * (y / a))
	elif a <= -6.6e-256:
		tmp = t_1
	elif a <= 2.05e-302:
		tmp = (y * (x - t)) / z
	elif a <= 3.8e-56:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -2.8e-57)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= -6.6e-256)
		tmp = t_1;
	elseif (a <= 2.05e-302)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 3.8e-56)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -2.8e-57)
		tmp = x + (t * (y / a));
	elseif (a <= -6.6e-256)
		tmp = t_1;
	elseif (a <= 2.05e-302)
		tmp = (y * (x - t)) / z;
	elseif (a <= 3.8e-56)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-57], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-256], t$95$1, If[LessEqual[a, 2.05e-302], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 3.8e-56], t$95$1, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7999999999999999e-57

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0 61.4%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. associate-/l* 61.0%

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

   6. Simplified 61.0%

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

   if -2.7999999999999999e-57 < a < -6.6e-256 or 2.0499999999999999e-302 < a < 3.8000000000000002e-56

   1. Initial program 67.8%

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

      1. clear-num 67.7%

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

      2. un-div-inv 68.5%

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

   4. Applied egg-rr 68.5%

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

   5. Taylor expanded in a around 0 55.7%

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

      1. associate-*r/ 55.7%

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

      2. neg-mul-1 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in x around 0 48.5%

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

      1. associate-/l* 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-*l* 61.0%

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

      4. *-commutative 61.0%

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

      5. associate-*l* 61.0%

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

      6. div-sub 61.0%

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

      7. sub-neg 61.0%

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

      8. *-inverses 61.0%

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

      9. metadata-eval 61.0%

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

      10. +-commutative 61.0%

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

      11. neg-mul-1 61.0%

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

   10. Simplified 61.0%

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

   if -6.6e-256 < a < 2.0499999999999999e-302

   1. Initial program 77.0%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. distribute-lft-out-- 99.8%

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

      3. div-sub 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. div-sub 99.8%

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

      7. associate-/l* 94.3%

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

      8. associate-/l* 88.4%

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

      9. distribute-rgt-out-- 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in y around -inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. associate-*r* 73.8%

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

      3. *-commutative 73.8%

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

      4. associate-*r* 73.8%

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

      5. mul-1-neg 73.8%

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

   8. Simplified 73.8%

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

   if 3.8000000000000002e-56 < a

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 53.4%

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

   4. Taylor expanded in x around -inf 53.0%

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

      1. associate-*r* 53.0%

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

      2. mul-1-neg 53.0%

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

      3. sub-neg 53.0%

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

      4. metadata-eval 53.0%

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

   6. Simplified 53.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-57}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-302}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-200}:\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -2.8e+23)
     t_1
     (if (<= z -2.85e-200)
       (- x (/ (- y z) (/ (- z a) t)))
       (if (<= z 3.6e+52) (- x (* (- t x) (/ (- z y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -2.8e+23) {
		tmp = t_1;
	} else if (z <= -2.85e-200) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else if (z <= 3.6e+52) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) / z) * (a - y))
    if (z <= (-2.8d+23)) then
        tmp = t_1
    else if (z <= (-2.85d-200)) then
        tmp = x - ((y - z) / ((z - a) / t))
    else if (z <= 3.6d+52) then
        tmp = x - ((t - x) * ((z - y) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -2.8e+23) {
		tmp = t_1;
	} else if (z <= -2.85e-200) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else if (z <= 3.6e+52) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -2.8e+23:
		tmp = t_1
	elif z <= -2.85e-200:
		tmp = x - ((y - z) / ((z - a) / t))
	elif z <= 3.6e+52:
		tmp = x - ((t - x) * ((z - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -2.8e+23)
		tmp = t_1;
	elseif (z <= -2.85e-200)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(z - a) / t)));
	elseif (z <= 3.6e+52)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -2.8e+23)
		tmp = t_1;
	elseif (z <= -2.85e-200)
		tmp = x - ((y - z) / ((z - a) / t));
	elseif (z <= 3.6e+52)
		tmp = x - ((t - x) * ((z - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+23], t$95$1, If[LessEqual[z, -2.85e-200], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+52], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e23 or 3.6e52 < z

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. distribute-lft-out-- 68.8%

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

      3. div-sub 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. div-sub 68.8%

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

      7. associate-/l* 74.7%

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

      8. associate-/l* 83.2%

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

      9. distribute-rgt-out-- 83.2%

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

   5. Simplified 83.2%

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

   if -2.8e23 < z < -2.84999999999999975e-200

   1. Initial program 86.7%

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

      1. clear-num 86.5%

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

      2. un-div-inv 88.8%

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

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in t around inf 72.1%

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

   if -2.84999999999999975e-200 < z < 3.6e52

   1. Initial program 88.8%

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

   3. Taylor expanded in a around inf 77.3%

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

      1. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+23}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-200}:\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+53}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+20)
   t
   (if (<= z 2.15e+53)
     (+ x (* t (/ y a)))
     (if (<= z 1.25e+181) (* y (/ (- x t) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+20) {
		tmp = t;
	} else if (z <= 2.15e+53) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.25e+181) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+20)) then
        tmp = t
    else if (z <= 2.15d+53) then
        tmp = x + (t * (y / a))
    else if (z <= 1.25d+181) then
        tmp = y * ((x - t) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+20) {
		tmp = t;
	} else if (z <= 2.15e+53) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.25e+181) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+20:
		tmp = t
	elif z <= 2.15e+53:
		tmp = x + (t * (y / a))
	elif z <= 1.25e+181:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+20)
		tmp = t;
	elseif (z <= 2.15e+53)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.25e+181)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+20)
		tmp = t;
	elseif (z <= 2.15e+53)
		tmp = x + (t * (y / a));
	elseif (z <= 1.25e+181)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+20], t, If[LessEqual[z, 2.15e+53], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+181], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e20 or 1.2500000000000001e181 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in z around inf 55.4%

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

   if -4.8e20 < z < 2.1499999999999999e53

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 65.3%

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

   4. Taylor expanded in t around inf 53.7%

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

      1. associate-/l* 58.4%

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

   6. Simplified 58.4%

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

   if 2.1499999999999999e53 < z < 1.2500000000000001e181

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf 50.3%

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

      1. div-sub 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in a around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. associate-/l* 46.3%

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

      3. distribute-rgt-neg-in 46.3%

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

      4. distribute-neg-frac2 46.3%

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

   8. Simplified 46.3%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+53}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-57} \lor \neg \left(a \leq 6.2 \cdot 10^{-47}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e-57) (not (<= a 6.2e-47)))
   (- x (/ (- y z) (/ (- z a) t)))
   (- t (* y (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-57) || !(a <= 6.2e-47)) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.3d-57)) .or. (.not. (a <= 6.2d-47))) then
        tmp = x - ((y - z) / ((z - a) / t))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-57) || !(a <= 6.2e-47)) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e-57) or not (a <= 6.2e-47):
		tmp = x - ((y - z) / ((z - a) / t))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e-57) || !(a <= 6.2e-47))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(z - a) / t)));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.3e-57) || ~((a <= 6.2e-47)))
		tmp = x - ((y - z) / ((z - a) / t));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e-57], N[Not[LessEqual[a, 6.2e-47]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2999999999999998e-57 or 6.1999999999999996e-47 < a

   1. Initial program 81.7%

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

      1. clear-num 81.2%

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

      2. un-div-inv 82.0%

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

   4. Applied egg-rr 82.0%

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

   5. Taylor expanded in t around inf 73.0%

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

   if -3.2999999999999998e-57 < a < 6.1999999999999996e-47

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. associate--l+ 85.6%

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

      2. distribute-lft-out-- 85.6%

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

      3. div-sub 85.6%

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

      4. mul-1-neg 85.6%

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

      5. unsub-neg 85.6%

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

      6. div-sub 85.6%

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

      7. associate-/l* 82.3%

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

      8. associate-/l* 78.9%

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

      9. distribute-rgt-out-- 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in y around inf 79.3%

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

      1. associate-/l* 78.5%

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

   8. Simplified 78.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-57} \lor \neg \left(a \leq 6.2 \cdot 10^{-47}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e-16)
   (+ t (* x (/ (- y a) z)))
   (if (<= z 4.8e+52)
     (- x (* (- t x) (/ (- z y) a)))
     (- t (* y (/ (- t x) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e-16) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= 4.8e+52) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.7d-16)) then
        tmp = t + (x * ((y - a) / z))
    else if (z <= 4.8d+52) then
        tmp = x - ((t - x) * ((z - y) / a))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e-16) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= 4.8e+52) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.7e-16:
		tmp = t + (x * ((y - a) / z))
	elif z <= 4.8e+52:
		tmp = x - ((t - x) * ((z - y) / a))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e-16)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (z <= 4.8e+52)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.7e-16)
		tmp = t + (x * ((y - a) / z));
	elseif (z <= 4.8e+52)
		tmp = x - ((t - x) * ((z - y) / a));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e-16], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+52], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e-16

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. distribute-lft-out-- 64.9%

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

      3. div-sub 64.9%

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

      4. mul-1-neg 64.9%

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

      5. unsub-neg 64.9%

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

      6. div-sub 64.9%

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

      7. associate-/l* 69.5%

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

      8. associate-/l* 81.8%

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

      9. distribute-rgt-out-- 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in t around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. associate-/l* 75.7%

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

   8. Simplified 75.7%

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

   if -3.7e-16 < z < 4.8e52

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 70.4%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   if 4.8e52 < z

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 73.2%

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

      1. associate--l+ 73.2%

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

      2. distribute-lft-out-- 73.2%

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

      3. div-sub 73.2%

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

      4. mul-1-neg 73.2%

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

      5. unsub-neg 73.2%

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

      6. div-sub 73.2%

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

      7. associate-/l* 79.9%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 76.4%

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

   8. Simplified 76.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-64} \lor \neg \left(z \leq 2.4 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e-64) (not (<= z 2.4e+69)))
   (* t (/ (- y z) (- a z)))
   (- x (* y (/ (- x t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e-64) || !(z <= 2.4e+69)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.5d-64)) .or. (.not. (z <= 2.4d+69))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - (y * ((x - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e-64) || !(z <= 2.4e+69)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e-64) or not (z <= 2.4e+69):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - (y * ((x - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e-64) || !(z <= 2.4e+69))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e-64) || ~((z <= 2.4e+69)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - (y * ((x - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e-64], N[Not[LessEqual[z, 2.4e+69]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e-64 or 2.4000000000000002e69 < z

   1. Initial program 66.1%

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

   3. Taylor expanded in x around 0 39.2%

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

      1. associate-/l* 59.9%

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

   5. Simplified 59.9%

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

   if -1.5e-64 < z < 2.4000000000000002e69

   1. Initial program 86.0%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. associate-/l* 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-64} \lor \neg \left(z \leq 2.4 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-57} \lor \neg \left(a \leq 1.2 \cdot 10^{+59}\right):\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.3e-57) (not (<= a 1.2e+59)))
   (- x (* y (/ (- x t) a)))
   (- t (* y (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.3e-57) || !(a <= 1.2e+59)) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.3d-57)) .or. (.not. (a <= 1.2d+59))) then
        tmp = x - (y * ((x - t) / a))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.3e-57) || !(a <= 1.2e+59)) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.3e-57) or not (a <= 1.2e+59):
		tmp = x - (y * ((x - t) / a))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.3e-57) || !(a <= 1.2e+59))
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.3e-57) || ~((a <= 1.2e+59)))
		tmp = x - (y * ((x - t) / a));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.3e-57], N[Not[LessEqual[a, 1.2e+59]], $MachinePrecision]], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.30000000000000022e-57 or 1.2000000000000001e59 < a

   1. Initial program 81.9%

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

   3. Taylor expanded in z around 0 59.2%

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

      1. associate-/l* 64.4%

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

   5. Simplified 64.4%

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

   if -4.30000000000000022e-57 < a < 1.2000000000000001e59

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 79.9%

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

      1. associate--l+ 79.9%

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

      2. distribute-lft-out-- 79.9%

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

      3. div-sub 79.9%

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

      4. mul-1-neg 79.9%

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

      5. unsub-neg 79.9%

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

      6. div-sub 79.9%

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

      7. associate-/l* 78.5%

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

      8. associate-/l* 76.2%

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

      9. distribute-rgt-out-- 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in y around inf 74.6%

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

      1. associate-/l* 75.2%

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

   8. Simplified 75.2%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-57} \lor \neg \left(a \leq 1.2 \cdot 10^{+59}\right):\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+21) t (if (<= z 4.8e+69) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+21) {
		tmp = t;
	} else if (z <= 4.8e+69) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+21)) then
        tmp = t
    else if (z <= 4.8d+69) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+21) {
		tmp = t;
	} else if (z <= 4.8e+69) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+21:
		tmp = t
	elif z <= 4.8e+69:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+21)
		tmp = t;
	elseif (z <= 4.8e+69)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+21)
		tmp = t;
	elseif (z <= 4.8e+69)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+21], t, If[LessEqual[z, 4.8e+69], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2e21 or 4.8000000000000003e69 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 50.3%

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

   if -2e21 < z < 4.8000000000000003e69

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 64.7%

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

   4. Taylor expanded in t around inf 53.3%

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

      1. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+131}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-56) x (if (<= a 2.2e+131) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-56) {
		tmp = x;
	} else if (a <= 2.2e+131) {
		tmp = t;
	} else {
		tmp = 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 (a <= (-1.2d-56)) then
        tmp = x
    else if (a <= 2.2d+131) then
        tmp = t
    else
        tmp = 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 (a <= -1.2e-56) {
		tmp = x;
	} else if (a <= 2.2e+131) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-56:
		tmp = x
	elif a <= 2.2e+131:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-56)
		tmp = x;
	elseif (a <= 2.2e+131)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-56)
		tmp = x;
	elseif (a <= 2.2e+131)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-56], x, If[LessEqual[a, 2.2e+131], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2e-56 or 2.1999999999999999e131 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 48.3%

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

   if -1.2e-56 < a < 2.1999999999999999e131

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf 35.6%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+131}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.9% 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 76.3%

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

3. Taylor expanded in z around inf 25.7%

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

4. Final simplification 25.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(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)))))