Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 94.9%

Time: 25.5s

Alternatives: 19

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-296} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-296) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (- t (/ (- t x) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-296], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. remove-double-neg 90.5%

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

      3. unsub-neg 90.5%

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

      4. associate-*r/ 75.5%

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

      5. associate-/l* 90.8%

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

      6. associate-/r/ 93.6%

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

      7. fma-neg 93.6%

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

      8. remove-double-neg 93.6%

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

   3. Simplified 93.6%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

   2. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. distribute-lft-out-- 79.5%

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

      3. div-sub 79.4%

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

      4. mul-1-neg 79.4%

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

      5. unsub-neg 79.4%

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

      6. distribute-rgt-out-- 79.4%

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

      7. associate-/l* 96.3%

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

   4. Simplified 96.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-296} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-296) (not (<= t_1 0.0)))
     (+ x (/ 1.0 (/ (/ (- a z) (- y z)) (- t x))))
     (- t (/ (- t x) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-296)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + (1.0d0 / (((a - z) / (y - z)) / (t - x)))
    else
        tmp = t - ((t - x) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-296) or not (t_1 <= 0.0):
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)))
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(t - x))));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-296) || ~((t_1 <= 0.0)))
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)));
	else
		tmp = t - ((t - x) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-296], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-296 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

      1. associate-*r/ 75.5%

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

      2. clear-num 75.4%

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

      3. associate-/r* 93.6%

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

   3. Applied egg-rr 93.6%

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

   if -2e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

   2. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. distribute-lft-out-- 79.5%

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

      3. div-sub 79.4%

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

      4. mul-1-neg 79.4%

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

      5. unsub-neg 79.4%

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

      6. distribute-rgt-out-- 79.4%

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

      7. associate-/l* 96.3%

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

   4. Simplified 96.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-227} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-227) (not (<= t_1 0.0)))
     t_1
     (- t (/ (- t x) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-227) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-227)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - ((t - x) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-227) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-227) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-227) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-227) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((t - x) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-227], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999961e-227 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.6%

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

   if -4.99999999999999961e-227 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 7.2%

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

   2. Taylor expanded in z around inf 79.0%

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

      1. associate--l+ 79.0%

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

      2. distribute-lft-out-- 79.0%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. distribute-rgt-out-- 79.0%

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

      7. associate-/l* 93.8%

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

   4. Simplified 93.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-227} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-292}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.3e-12)
   x
   (if (<= a -3.2e-292)
     t
     (if (<= a 1.8e-155)
       (/ x (/ z y))
       (if (<= a 8.6e-51) t (if (<= a 1.8e+61) (* t (/ (- y z) a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.3e-12) {
		tmp = x;
	} else if (a <= -3.2e-292) {
		tmp = t;
	} else if (a <= 1.8e-155) {
		tmp = x / (z / y);
	} else if (a <= 8.6e-51) {
		tmp = t;
	} else if (a <= 1.8e+61) {
		tmp = t * ((y - z) / a);
	} 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 <= (-6.3d-12)) then
        tmp = x
    else if (a <= (-3.2d-292)) then
        tmp = t
    else if (a <= 1.8d-155) then
        tmp = x / (z / y)
    else if (a <= 8.6d-51) then
        tmp = t
    else if (a <= 1.8d+61) then
        tmp = t * ((y - z) / a)
    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 <= -6.3e-12) {
		tmp = x;
	} else if (a <= -3.2e-292) {
		tmp = t;
	} else if (a <= 1.8e-155) {
		tmp = x / (z / y);
	} else if (a <= 8.6e-51) {
		tmp = t;
	} else if (a <= 1.8e+61) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.3e-12:
		tmp = x
	elif a <= -3.2e-292:
		tmp = t
	elif a <= 1.8e-155:
		tmp = x / (z / y)
	elif a <= 8.6e-51:
		tmp = t
	elif a <= 1.8e+61:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.3e-12)
		tmp = x;
	elseif (a <= -3.2e-292)
		tmp = t;
	elseif (a <= 1.8e-155)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 8.6e-51)
		tmp = t;
	elseif (a <= 1.8e+61)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.3e-12)
		tmp = x;
	elseif (a <= -3.2e-292)
		tmp = t;
	elseif (a <= 1.8e-155)
		tmp = x / (z / y);
	elseif (a <= 8.6e-51)
		tmp = t;
	elseif (a <= 1.8e+61)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.3e-12], x, If[LessEqual[a, -3.2e-292], t, If[LessEqual[a, 1.8e-155], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e-51], t, If[LessEqual[a, 1.8e+61], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.3000000000000002e-12 or 1.80000000000000005e61 < a

   1. Initial program 89.2%

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

   2. Taylor expanded in a around inf 48.1%

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

   if -6.3000000000000002e-12 < a < -3.2000000000000002e-292 or 1.79999999999999994e-155 < a < 8.5999999999999995e-51

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf 42.4%

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

   if -3.2000000000000002e-292 < a < 1.79999999999999994e-155

   1. Initial program 71.6%

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

   2. Taylor expanded in x around -inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in a around 0 43.1%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   if 8.5999999999999995e-51 < a < 1.80000000000000005e61

   1. Initial program 76.7%

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

   2. Taylor expanded in a around inf 66.7%

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

      1. associate-/l* 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in t around inf 40.0%

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

      1. div-sub 40.0%

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

   7. Simplified 40.0%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-292}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-293}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+57}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-12)
   x
   (if (<= a -3.4e-293)
     t
     (if (<= a 1.65e-156)
       (* x (/ y z))
       (if (<= a 1.6e-50)
         t
         (if (<= a 5.7e+57) (/ t (/ a y)) (if (<= a 2.5e+81) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-12) {
		tmp = x;
	} else if (a <= -3.4e-293) {
		tmp = t;
	} else if (a <= 1.65e-156) {
		tmp = x * (y / z);
	} else if (a <= 1.6e-50) {
		tmp = t;
	} else if (a <= 5.7e+57) {
		tmp = t / (a / y);
	} else if (a <= 2.5e+81) {
		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 <= (-8.5d-12)) then
        tmp = x
    else if (a <= (-3.4d-293)) then
        tmp = t
    else if (a <= 1.65d-156) then
        tmp = x * (y / z)
    else if (a <= 1.6d-50) then
        tmp = t
    else if (a <= 5.7d+57) then
        tmp = t / (a / y)
    else if (a <= 2.5d+81) 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 <= -8.5e-12) {
		tmp = x;
	} else if (a <= -3.4e-293) {
		tmp = t;
	} else if (a <= 1.65e-156) {
		tmp = x * (y / z);
	} else if (a <= 1.6e-50) {
		tmp = t;
	} else if (a <= 5.7e+57) {
		tmp = t / (a / y);
	} else if (a <= 2.5e+81) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-12:
		tmp = x
	elif a <= -3.4e-293:
		tmp = t
	elif a <= 1.65e-156:
		tmp = x * (y / z)
	elif a <= 1.6e-50:
		tmp = t
	elif a <= 5.7e+57:
		tmp = t / (a / y)
	elif a <= 2.5e+81:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-12)
		tmp = x;
	elseif (a <= -3.4e-293)
		tmp = t;
	elseif (a <= 1.65e-156)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.6e-50)
		tmp = t;
	elseif (a <= 5.7e+57)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 2.5e+81)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-12)
		tmp = x;
	elseif (a <= -3.4e-293)
		tmp = t;
	elseif (a <= 1.65e-156)
		tmp = x * (y / z);
	elseif (a <= 1.6e-50)
		tmp = t;
	elseif (a <= 5.7e+57)
		tmp = t / (a / y);
	elseif (a <= 2.5e+81)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-12], x, If[LessEqual[a, -3.4e-293], t, If[LessEqual[a, 1.65e-156], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-50], t, If[LessEqual[a, 5.7e+57], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+81], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.4999999999999997e-12 or 2.4999999999999999e81 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 49.2%

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

   if -8.4999999999999997e-12 < a < -3.4e-293 or 1.6499999999999999e-156 < a < 1.6e-50 or 5.6999999999999998e57 < a < 2.4999999999999999e81

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf 43.8%

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

   if -3.4e-293 < a < 1.6499999999999999e-156

   1. Initial program 71.6%

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

   2. Taylor expanded in x around -inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in a around 0 43.1%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

      1. div-inv 49.5%

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

      2. clear-num 49.5%

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

   9. Applied egg-rr 49.5%

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

   if 1.6e-50 < a < 5.6999999999999998e57

   1. Initial program 76.7%

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

      1. associate-*r/ 77.0%

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

      2. clear-num 76.9%

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

      3. associate-/r* 79.3%

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

   3. Applied egg-rr 79.3%

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

   4. Taylor expanded in x around 0 55.8%

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

      1. associate-/l* 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in z around 0 33.6%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-293}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+57}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-292}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.7e-15)
   x
   (if (<= a -2.95e-292)
     t
     (if (<= a 9.8e-157)
       (/ x (/ z y))
       (if (<= a 1.1e-50)
         t
         (if (<= a 6e+58) (/ t (/ a y)) (if (<= a 2.5e+81) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e-15) {
		tmp = x;
	} else if (a <= -2.95e-292) {
		tmp = t;
	} else if (a <= 9.8e-157) {
		tmp = x / (z / y);
	} else if (a <= 1.1e-50) {
		tmp = t;
	} else if (a <= 6e+58) {
		tmp = t / (a / y);
	} else if (a <= 2.5e+81) {
		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 <= (-4.7d-15)) then
        tmp = x
    else if (a <= (-2.95d-292)) then
        tmp = t
    else if (a <= 9.8d-157) then
        tmp = x / (z / y)
    else if (a <= 1.1d-50) then
        tmp = t
    else if (a <= 6d+58) then
        tmp = t / (a / y)
    else if (a <= 2.5d+81) 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 <= -4.7e-15) {
		tmp = x;
	} else if (a <= -2.95e-292) {
		tmp = t;
	} else if (a <= 9.8e-157) {
		tmp = x / (z / y);
	} else if (a <= 1.1e-50) {
		tmp = t;
	} else if (a <= 6e+58) {
		tmp = t / (a / y);
	} else if (a <= 2.5e+81) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.7e-15:
		tmp = x
	elif a <= -2.95e-292:
		tmp = t
	elif a <= 9.8e-157:
		tmp = x / (z / y)
	elif a <= 1.1e-50:
		tmp = t
	elif a <= 6e+58:
		tmp = t / (a / y)
	elif a <= 2.5e+81:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.7e-15)
		tmp = x;
	elseif (a <= -2.95e-292)
		tmp = t;
	elseif (a <= 9.8e-157)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 1.1e-50)
		tmp = t;
	elseif (a <= 6e+58)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 2.5e+81)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.7e-15)
		tmp = x;
	elseif (a <= -2.95e-292)
		tmp = t;
	elseif (a <= 9.8e-157)
		tmp = x / (z / y);
	elseif (a <= 1.1e-50)
		tmp = t;
	elseif (a <= 6e+58)
		tmp = t / (a / y);
	elseif (a <= 2.5e+81)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.7e-15], x, If[LessEqual[a, -2.95e-292], t, If[LessEqual[a, 9.8e-157], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-50], t, If[LessEqual[a, 6e+58], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+81], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.6999999999999999e-15 or 2.4999999999999999e81 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 49.2%

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

   if -4.6999999999999999e-15 < a < -2.95e-292 or 9.7999999999999995e-157 < a < 1.0999999999999999e-50 or 6.0000000000000005e58 < a < 2.4999999999999999e81

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf 43.8%

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

   if -2.95e-292 < a < 9.7999999999999995e-157

   1. Initial program 71.6%

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

   2. Taylor expanded in x around -inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in a around 0 43.1%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   if 1.0999999999999999e-50 < a < 6.0000000000000005e58

   1. Initial program 76.7%

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

      1. associate-*r/ 77.0%

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

      2. clear-num 76.9%

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

      3. associate-/r* 79.3%

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

   3. Applied egg-rr 79.3%

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

   4. Taylor expanded in x around 0 55.8%

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

      1. associate-/l* 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in z around 0 33.6%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-292}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 70.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+177} \lor \neg \left(y \leq 1.75 \cdot 10^{+115}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.6e+177) (not (<= y 1.75e+115)))
   (* y (/ (- t x) (- a z)))
   (+ x (* (- y z) (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.6e+177) || !(y <= 1.75e+115)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / (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 <= (-4.6d+177)) .or. (.not. (y <= 1.75d+115))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x + ((y - z) * (t / (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 <= -4.6e+177) || !(y <= 1.75e+115)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.6e+177) or not (y <= 1.75e+115):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x + ((y - z) * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.6e+177) || !(y <= 1.75e+115))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.6e+177) || ~((y <= 1.75e+115)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x + ((y - z) * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.6e+177], N[Not[LessEqual[y, 1.75e+115]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999998e177 or 1.75000000000000003e115 < y

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 82.6%

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

      1. div-sub 84.4%

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

   4. Simplified 84.4%

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

   if -4.5999999999999998e177 < y < 1.75000000000000003e115

   1. Initial program 79.0%

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

   2. Taylor expanded in t around inf 70.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+177} \lor \neg \left(y \leq 1.75 \cdot 10^{+115}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 8: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+64} \lor \neg \left(z \leq 4.1 \cdot 10^{+44}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+64) (not (<= z 4.1e+44)))
   (- t (/ (- t x) (/ z (- y a))))
   (+ x (/ (- t x) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+64) || !(z <= 4.1e+44)) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - 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 <= (-1.65d+64)) .or. (.not. (z <= 4.1d+44))) then
        tmp = t - ((t - x) / (z / (y - a)))
    else
        tmp = x + ((t - x) / (a / (y - 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 <= -1.65e+64) || !(z <= 4.1e+44)) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+64) or not (z <= 4.1e+44):
		tmp = t - ((t - x) / (z / (y - a)))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+64) || !(z <= 4.1e+44))
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e+64) || ~((z <= 4.1e+44)))
		tmp = t - ((t - x) / (z / (y - a)));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+64], N[Not[LessEqual[z, 4.1e+44]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999994e64 or 4.09999999999999965e44 < z

   1. Initial program 61.5%

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

   2. Taylor expanded in z around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. distribute-lft-out-- 63.3%

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

      3. div-sub 63.3%

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

      4. mul-1-neg 63.3%

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

      5. unsub-neg 63.3%

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

      6. distribute-rgt-out-- 63.5%

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

      7. associate-/l* 80.3%

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

   4. Simplified 80.3%

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

   if -1.64999999999999994e64 < z < 4.09999999999999965e44

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 71.1%

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

      1. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+64} \lor \neg \left(z \leq 4.1 \cdot 10^{+44}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 9: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+134)
   t
   (if (<= z 7e+47)
     (+ x (/ t (/ a y)))
     (if (<= z 1.6e+148) (/ x (/ z (- y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+134) {
		tmp = t;
	} else if (z <= 7e+47) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.6e+148) {
		tmp = x / (z / (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+134)) then
        tmp = t
    else if (z <= 7d+47) then
        tmp = x + (t / (a / y))
    else if (z <= 1.6d+148) then
        tmp = x / (z / (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+134) {
		tmp = t;
	} else if (z <= 7e+47) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.6e+148) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+134:
		tmp = t
	elif z <= 7e+47:
		tmp = x + (t / (a / y))
	elif z <= 1.6e+148:
		tmp = x / (z / (y - a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+134)
		tmp = t;
	elseif (z <= 7e+47)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.6e+148)
		tmp = Float64(x / Float64(z / 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+134)
		tmp = t;
	elseif (z <= 7e+47)
		tmp = x + (t / (a / y));
	elseif (z <= 1.6e+148)
		tmp = x / (z / (y - a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+134], t, If[LessEqual[z, 7e+47], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+148], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999984e134 or 1.6e148 < z

   1. Initial program 60.6%

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

   2. Taylor expanded in z around inf 69.3%

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

   if -1.99999999999999984e134 < z < 7.00000000000000031e47

   1. Initial program 90.4%

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

   2. Taylor expanded in z around 0 65.3%

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

   3. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 59.8%

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

   5. Simplified 59.8%

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

   if 7.00000000000000031e47 < z < 1.6e148

   1. Initial program 62.0%

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

   2. Taylor expanded in x around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. *-commutative 51.1%

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

      3. distribute-rgt-neg-in 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in z around -inf 35.7%

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

      1. associate-/l* 47.9%

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

   7. Simplified 47.9%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+133)
   (/ t (/ (- z) (- y z)))
   (if (<= z 3.5e+47)
     (+ x (/ t (/ a y)))
     (if (<= z 1.8e+152) (/ x (/ z (- y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = t / (-z / (y - z));
	} else if (z <= 3.5e+47) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.8e+152) {
		tmp = x / (z / (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 <= (-3.8d+133)) then
        tmp = t / (-z / (y - z))
    else if (z <= 3.5d+47) then
        tmp = x + (t / (a / y))
    else if (z <= 1.8d+152) then
        tmp = x / (z / (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 <= -3.8e+133) {
		tmp = t / (-z / (y - z));
	} else if (z <= 3.5e+47) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.8e+152) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+133:
		tmp = t / (-z / (y - z))
	elif z <= 3.5e+47:
		tmp = x + (t / (a / y))
	elif z <= 1.8e+152:
		tmp = x / (z / (y - a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+133)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (z <= 3.5e+47)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.8e+152)
		tmp = Float64(x / Float64(z / 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 <= -3.8e+133)
		tmp = t / (-z / (y - z));
	elseif (z <= 3.5e+47)
		tmp = x + (t / (a / y));
	elseif (z <= 1.8e+152)
		tmp = x / (z / (y - a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+133], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+47], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+152], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8000000000000002e133

   1. Initial program 55.1%

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

      1. associate-*r/ 36.5%

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

      2. clear-num 36.6%

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

      3. associate-/r* 59.9%

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

   3. Applied egg-rr 59.9%

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

   4. Taylor expanded in x around 0 44.4%

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

      1. associate-/l* 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in a around 0 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-neg-frac 67.1%

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

   9. Simplified 67.1%

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

   if -3.8000000000000002e133 < z < 3.50000000000000015e47

   1. Initial program 90.4%

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

   2. Taylor expanded in z around 0 65.3%

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

   3. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 59.8%

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

   5. Simplified 59.8%

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

   if 3.50000000000000015e47 < z < 1.7999999999999999e152

   1. Initial program 62.0%

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

   2. Taylor expanded in x around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. *-commutative 51.1%

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

      3. distribute-rgt-neg-in 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in z around -inf 35.7%

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

      1. associate-/l* 47.9%

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

   7. Simplified 47.9%

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

   if 1.7999999999999999e152 < z

   1. Initial program 68.3%

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

   2. Taylor expanded in z around inf 80.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+104} \lor \neg \left(z \leq 2.35 \cdot 10^{-33}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.6e+104) (not (<= z 2.35e-33)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.6e+104) || !(z <= 2.35e-33)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.6d+104)) .or. (.not. (z <= 2.35d-33))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.6e+104) || !(z <= 2.35e-33)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.6e+104) or not (z <= 2.35e-33):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.6e+104) || !(z <= 2.35e-33))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.6e+104) || ~((z <= 2.35e-33)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.6e+104], N[Not[LessEqual[z, 2.35e-33]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6e104 or 2.3500000000000001e-33 < z

   1. Initial program 65.4%

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

   2. Taylor expanded in x around 0 41.7%

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

      1. associate-*r/ 60.2%

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

   4. Simplified 60.2%

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

   if -9.6e104 < z < 2.3500000000000001e-33

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+104} \lor \neg \left(z \leq 2.35 \cdot 10^{-33}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(-\frac{y}{a - z}\right)\\ \mathbf{elif}\;x \leq 1300000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.4e+44)
   (* x (- (/ y (- a z))))
   (if (<= x 1300000000.0) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e+44) {
		tmp = x * -(y / (a - z));
	} else if (x <= 1300000000.0) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.4d+44)) then
        tmp = x * -(y / (a - z))
    else if (x <= 1300000000.0d0) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e+44) {
		tmp = x * -(y / (a - z));
	} else if (x <= 1300000000.0) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.4e+44:
		tmp = x * -(y / (a - z))
	elif x <= 1300000000.0:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.4e+44)
		tmp = Float64(x * Float64(-Float64(y / Float64(a - z))));
	elseif (x <= 1300000000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.4e+44)
		tmp = x * -(y / (a - z));
	elseif (x <= 1300000000.0)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.4e+44], N[(x * (-N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1300000000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.40000000000000013e44

   1. Initial program 69.8%

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

   2. Taylor expanded in x around -inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. *-commutative 81.6%

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

      3. distribute-rgt-neg-in 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in y around inf 56.4%

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

   if -2.40000000000000013e44 < x < 1.3e9

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 56.4%

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

      1. associate-*r/ 69.7%

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

   4. Simplified 69.7%

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

   if 1.3e9 < x

   1. Initial program 81.0%

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

   2. Taylor expanded in x around -inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in z around 0 60.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(-\frac{y}{a - z}\right)\\ \mathbf{elif}\;x \leq 1300000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 13: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.4e+104)
   (* t (/ (- y z) (- a z)))
   (if (<= z 2.4e-42) (+ x (/ y (/ a (- t x)))) (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.4e+104) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.4e-42) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - 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 <= (-8.4d+104)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.4d-42) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t / ((a - z) / (y - 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 <= -8.4e+104) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.4e-42) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.4e+104:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.4e-42:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.4e+104)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.4e-42)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.4e+104)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.4e-42)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.4e+104], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-42], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.3999999999999994e104

   1. Initial program 58.4%

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

   2. Taylor expanded in x around 0 39.5%

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

      1. associate-*r/ 64.1%

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

   4. Simplified 64.1%

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

   if -8.3999999999999994e104 < z < 2.40000000000000003e-42

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 78.0%

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

   4. Simplified 78.0%

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

   if 2.40000000000000003e-42 < z

   1. Initial program 69.4%

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

      1. associate-*r/ 53.2%

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

      2. clear-num 53.1%

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

      3. associate-/r* 76.3%

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

   3. Applied egg-rr 76.3%

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

   4. Taylor expanded in x around 0 43.0%

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

      1. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 14: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-15)
   x
   (if (<= a -6.6e-295)
     t
     (if (<= a 5e-155) (* x (/ y z)) (if (<= a 3.3e+80) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-15) {
		tmp = x;
	} else if (a <= -6.6e-295) {
		tmp = t;
	} else if (a <= 5e-155) {
		tmp = x * (y / z);
	} else if (a <= 3.3e+80) {
		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 <= (-4.5d-15)) then
        tmp = x
    else if (a <= (-6.6d-295)) then
        tmp = t
    else if (a <= 5d-155) then
        tmp = x * (y / z)
    else if (a <= 3.3d+80) 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 <= -4.5e-15) {
		tmp = x;
	} else if (a <= -6.6e-295) {
		tmp = t;
	} else if (a <= 5e-155) {
		tmp = x * (y / z);
	} else if (a <= 3.3e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-15:
		tmp = x
	elif a <= -6.6e-295:
		tmp = t
	elif a <= 5e-155:
		tmp = x * (y / z)
	elif a <= 3.3e+80:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-15)
		tmp = x;
	elseif (a <= -6.6e-295)
		tmp = t;
	elseif (a <= 5e-155)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.3e+80)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e-15)
		tmp = x;
	elseif (a <= -6.6e-295)
		tmp = t;
	elseif (a <= 5e-155)
		tmp = x * (y / z);
	elseif (a <= 3.3e+80)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-15], x, If[LessEqual[a, -6.6e-295], t, If[LessEqual[a, 5e-155], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+80], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4999999999999998e-15 or 3.29999999999999991e80 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 49.2%

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

   if -4.4999999999999998e-15 < a < -6.5999999999999997e-295 or 4.9999999999999999e-155 < a < 3.29999999999999991e80

   1. Initial program 77.0%

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

   2. Taylor expanded in z around inf 35.9%

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

   if -6.5999999999999997e-295 < a < 4.9999999999999999e-155

   1. Initial program 71.6%

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

   2. Taylor expanded in x around -inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in a around 0 43.1%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

      1. div-inv 49.5%

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

      2. clear-num 49.5%

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

   9. Applied egg-rr 49.5%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 40.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+54) t (if (<= z 1.6e-59) (* y (/ (- t x) a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+54) {
		tmp = t;
	} else if (z <= 1.6e-59) {
		tmp = y * ((t - x) / 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 <= (-6.5d+54)) then
        tmp = t
    else if (z <= 1.6d-59) then
        tmp = y * ((t - x) / 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 <= -6.5e+54) {
		tmp = t;
	} else if (z <= 1.6e-59) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+54:
		tmp = t
	elif z <= 1.6e-59:
		tmp = y * ((t - x) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+54)
		tmp = t;
	elseif (z <= 1.6e-59)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+54)
		tmp = t;
	elseif (z <= 1.6e-59)
		tmp = y * ((t - x) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+54], t, If[LessEqual[z, 1.6e-59], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e54 or 1.6e-59 < z

   1. Initial program 65.8%

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

   2. Taylor expanded in z around inf 46.4%

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

   if -6.5e54 < z < 1.6e-59

   1. Initial program 93.7%

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

   2. Taylor expanded in a around inf 73.9%

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

      1. associate-/l* 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in y around inf 45.8%

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

      1. div-sub 49.5%

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

   7. Simplified 49.5%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+135}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+135) t (if (<= z 4.7e+50) (+ x (/ t (/ a y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+135) {
		tmp = t;
	} else if (z <= 4.7e+50) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+135)) then
        tmp = t
    else if (z <= 4.7d+50) then
        tmp = x + (t / (a / y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+135) {
		tmp = t;
	} else if (z <= 4.7e+50) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+135:
		tmp = t
	elif z <= 4.7e+50:
		tmp = x + (t / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+135)
		tmp = t;
	elseif (z <= 4.7e+50)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+135)
		tmp = t;
	elseif (z <= 4.7e+50)
		tmp = x + (t / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+135], t, If[LessEqual[z, 4.7e+50], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000007e135 or 4.69999999999999974e50 < z

   1. Initial program 60.6%

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

   2. Taylor expanded in z around inf 56.6%

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

   if -1.25000000000000007e135 < z < 4.69999999999999974e50

   1. Initial program 90.5%

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

   2. Taylor expanded in z around 0 65.5%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. associate-/l* 59.6%

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

   5. Simplified 59.6%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+135}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 54.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+133)
   (/ t (/ (- z) (- y z)))
   (if (<= z 1.15e+50) (+ x (/ t (/ a y))) (/ t (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+133) {
		tmp = t / (-z / (y - z));
	} else if (z <= 1.15e+50) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t / ((z - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+133)) then
        tmp = t / (-z / (y - z))
    else if (z <= 1.15d+50) then
        tmp = x + (t / (a / y))
    else
        tmp = t / ((z - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+133) {
		tmp = t / (-z / (y - z));
	} else if (z <= 1.15e+50) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t / ((z - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+133:
		tmp = t / (-z / (y - z))
	elif z <= 1.15e+50:
		tmp = x + (t / (a / y))
	else:
		tmp = t / ((z - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+133)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (z <= 1.15e+50)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(t / Float64(Float64(z - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+133)
		tmp = t / (-z / (y - z));
	elseif (z <= 1.15e+50)
		tmp = x + (t / (a / y));
	else
		tmp = t / ((z - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+133], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+50], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999985e133

   1. Initial program 55.1%

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

      1. associate-*r/ 36.5%

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

      2. clear-num 36.6%

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

      3. associate-/r* 59.9%

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

   3. Applied egg-rr 59.9%

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

   4. Taylor expanded in x around 0 44.4%

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

      1. associate-/l* 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in a around 0 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-neg-frac 67.1%

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

   9. Simplified 67.1%

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

   if -4.49999999999999985e133 < z < 1.14999999999999998e50

   1. Initial program 90.5%

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

   2. Taylor expanded in z around 0 65.5%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. associate-/l* 59.6%

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

   5. Simplified 59.6%

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

   if 1.14999999999999998e50 < z

   1. Initial program 64.3%

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

      1. associate-*r/ 40.4%

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

      2. clear-num 40.3%

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

      3. associate-/r* 71.7%

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

   3. Applied egg-rr 71.7%

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

   4. Taylor expanded in x around 0 42.5%

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

      1. associate-/l* 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in y around 0 61.1%

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

      1. associate-*r/ 61.1%

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

      2. sub-neg 61.1%

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

      3. mul-1-neg 61.1%

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

      4. distribute-lft-in 61.1%

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

      5. mul-1-neg 61.1%

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

      6. neg-mul-1 61.1%

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

      7. mul-1-neg 61.1%

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

      8. remove-double-neg 61.1%

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

   9. Simplified 61.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 18: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e-16) x (if (<= a 1.7e+87) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e-16) {
		tmp = x;
	} else if (a <= 1.7e+87) {
		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 <= (-4.6d-16)) then
        tmp = x
    else if (a <= 1.7d+87) 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 <= -4.6e-16) {
		tmp = x;
	} else if (a <= 1.7e+87) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e-16:
		tmp = x
	elif a <= 1.7e+87:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e-16)
		tmp = x;
	elseif (a <= 1.7e+87)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.6e-16)
		tmp = x;
	elseif (a <= 1.7e+87)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e-16], x, If[LessEqual[a, 1.7e+87], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5999999999999998e-16 or 1.7000000000000001e87 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 49.2%

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

   if -4.5999999999999998e-16 < a < 1.7000000000000001e87

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf 35.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 24.9% 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 81.0%

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

2. Taylor expanded in z around inf 25.4%

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

3. Final simplification 25.4%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023279 
(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)))))