Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 93.2%

Time: 15.8s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-274}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-274)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (- t (/ (* (- t x) (- y a)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

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-274) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	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-274)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	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[LessEqual[t$95$1, -2e-274], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999993e-274

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. remove-double-neg 87.5%

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

      3. unsub-neg 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-*l/ 86.2%

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

      6. associate-/l* 93.2%

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

      7. fma-neg 93.2%

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

      8. remove-double-neg 93.2%

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

   3. Simplified 93.2%

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

   if -1.99999999999999993e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. remove-double-neg 3.3%

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

      3. unsub-neg 3.3%

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

      4. *-commutative 3.3%

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

      5. associate-*l/ 6.7%

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

      6. associate-/l* 6.8%

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

      7. fma-neg 6.8%

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

      8. remove-double-neg 6.8%

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

   3. Simplified 6.8%

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

   5. Taylor expanded in z around inf 89.0%

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

      1. associate--l+ 89.0%

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

      2. associate-*r/ 89.0%

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

      3. associate-*r/ 89.0%

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

      4. mul-1-neg 89.0%

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

      5. div-sub 89.0%

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

      6. mul-1-neg 89.0%

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

      7. distribute-lft-out-- 89.0%

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

      8. associate-*r/ 89.0%

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

      9. mul-1-neg 89.0%

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

      10. unsub-neg 89.0%

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

      11. distribute-rgt-out-- 89.2%

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

   7. Simplified 89.2%

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

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

   1. Initial program 90.1%

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

   3. Taylor expanded in y around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. div-sub 76.0%

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

      3. mul-1-neg 76.0%

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

      4. associate-/l* 83.9%

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

      5. distribute-lft-neg-out 83.9%

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

      6. distribute-rgt-out 90.1%

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

      7. sub-neg 90.1%

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

      8. associate-/r/ 93.2%

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

   5. Simplified 93.2%

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

Alternative 2: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-274} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-274) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (- t (/ (* (- t x) (- y a)) z)))))

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-274) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-274)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-274) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	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-274) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	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-274) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	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-274) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999993e-274 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.8%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. div-sub 80.2%

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

      3. mul-1-neg 80.2%

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

      4. associate-/l* 85.7%

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

      5. distribute-lft-neg-out 85.7%

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

      6. distribute-rgt-out 88.8%

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

      7. sub-neg 88.8%

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

      8. associate-/r/ 92.6%

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

   5. Simplified 92.6%

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

   if -1.99999999999999993e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. remove-double-neg 3.3%

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

      3. unsub-neg 3.3%

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

      4. *-commutative 3.3%

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

      5. associate-*l/ 6.7%

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

      6. associate-/l* 6.8%

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

      7. fma-neg 6.8%

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

      8. remove-double-neg 6.8%

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

   3. Simplified 6.8%

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

   5. Taylor expanded in z around inf 89.0%

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

      1. associate--l+ 89.0%

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

      2. associate-*r/ 89.0%

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

      3. associate-*r/ 89.0%

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

      4. mul-1-neg 89.0%

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

      5. div-sub 89.0%

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

      6. mul-1-neg 89.0%

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

      7. distribute-lft-out-- 89.0%

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

      8. associate-*r/ 89.0%

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

      9. mul-1-neg 89.0%

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

      10. unsub-neg 89.0%

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

      11. distribute-rgt-out-- 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-274} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-274} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-274) (not (<= t_1 0.0)))
     t_1
     (- t (/ (* (- t x) (- y a)) z)))))

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-274) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-274)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-274) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	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-274) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	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-274) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	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-274) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999993e-274 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.8%

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

   if -1.99999999999999993e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. remove-double-neg 3.3%

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

      3. unsub-neg 3.3%

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

      4. *-commutative 3.3%

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

      5. associate-*l/ 6.7%

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

      6. associate-/l* 6.8%

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

      7. fma-neg 6.8%

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

      8. remove-double-neg 6.8%

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

   3. Simplified 6.8%

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

   5. Taylor expanded in z around inf 89.0%

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

      1. associate--l+ 89.0%

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

      2. associate-*r/ 89.0%

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

      3. associate-*r/ 89.0%

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

      4. mul-1-neg 89.0%

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

      5. div-sub 89.0%

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

      6. mul-1-neg 89.0%

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

      7. distribute-lft-out-- 89.0%

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

      8. associate-*r/ 89.0%

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

      9. mul-1-neg 89.0%

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

      10. unsub-neg 89.0%

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

      11. distribute-rgt-out-- 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-274} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7200:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-243}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+148}:\\ \;\;\;\;x - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -2.7e+52)
     t_1
     (if (<= z -7200.0)
       (/ (* x (- y a)) z)
       (if (<= z -6e-97)
         (+ x (/ t (/ a (- y z))))
         (if (<= z -8.2e-243)
           (+ x (/ (* y t) (- a z)))
           (if (<= z 1.6e-11)
             (+ x (/ y (/ a (- t x))))
             (if (<= z 8e+70)
               (+ x (/ t (/ z (- z y))))
               (if (<= z 3.5e+148) (- x (/ (* y (- t x)) z)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -2.7e+52) {
		tmp = t_1;
	} else if (z <= -7200.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -6e-97) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= -8.2e-243) {
		tmp = x + ((y * t) / (a - z));
	} else if (z <= 1.6e-11) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 8e+70) {
		tmp = x + (t / (z / (z - y)));
	} else if (z <= 3.5e+148) {
		tmp = x - ((y * (t - x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-2.7d+52)) then
        tmp = t_1
    else if (z <= (-7200.0d0)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-6d-97)) then
        tmp = x + (t / (a / (y - z)))
    else if (z <= (-8.2d-243)) then
        tmp = x + ((y * t) / (a - z))
    else if (z <= 1.6d-11) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 8d+70) then
        tmp = x + (t / (z / (z - y)))
    else if (z <= 3.5d+148) then
        tmp = x - ((y * (t - x)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -2.7e+52) {
		tmp = t_1;
	} else if (z <= -7200.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -6e-97) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= -8.2e-243) {
		tmp = x + ((y * t) / (a - z));
	} else if (z <= 1.6e-11) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 8e+70) {
		tmp = x + (t / (z / (z - y)));
	} else if (z <= 3.5e+148) {
		tmp = x - ((y * (t - x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -2.7e+52:
		tmp = t_1
	elif z <= -7200.0:
		tmp = (x * (y - a)) / z
	elif z <= -6e-97:
		tmp = x + (t / (a / (y - z)))
	elif z <= -8.2e-243:
		tmp = x + ((y * t) / (a - z))
	elif z <= 1.6e-11:
		tmp = x + (y / (a / (t - x)))
	elif z <= 8e+70:
		tmp = x + (t / (z / (z - y)))
	elif z <= 3.5e+148:
		tmp = x - ((y * (t - x)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.7e+52)
		tmp = t_1;
	elseif (z <= -7200.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -6e-97)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	elseif (z <= -8.2e-243)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (z <= 1.6e-11)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 8e+70)
		tmp = Float64(x + Float64(t / Float64(z / Float64(z - y))));
	elseif (z <= 3.5e+148)
		tmp = Float64(x - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.7e+52)
		tmp = t_1;
	elseif (z <= -7200.0)
		tmp = (x * (y - a)) / z;
	elseif (z <= -6e-97)
		tmp = x + (t / (a / (y - z)));
	elseif (z <= -8.2e-243)
		tmp = x + ((y * t) / (a - z));
	elseif (z <= 1.6e-11)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 8e+70)
		tmp = x + (t / (z / (z - y)));
	elseif (z <= 3.5e+148)
		tmp = x - ((y * (t - x)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+52], t$95$1, If[LessEqual[z, -7200.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -6e-97], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e-243], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-11], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+70], N[(x + N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+148], N[(x - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.7e52 or 3.4999999999999999e148 < z

   1. Initial program 57.7%

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

      1. +-commutative 57.7%

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

      2. remove-double-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-*l/ 41.6%

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

      6. associate-/l* 67.2%

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

      7. fma-neg 67.2%

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

      8. remove-double-neg 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in a around 0 34.2%

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

      1. mul-1-neg 34.2%

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

      2. unsub-neg 34.2%

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

      3. associate-/l* 53.4%

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

      4. div-sub 53.4%

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

      5. sub-neg 53.4%

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

      6. *-inverses 53.4%

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

      7. metadata-eval 53.4%

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

   7. Simplified 53.4%

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

   8. Taylor expanded in t around inf 66.0%

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

   if -2.7e52 < z < -7200

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. remove-double-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*l/ 68.8%

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

      6. associate-/l* 68.1%

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

      7. fma-neg 68.1%

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

      8. remove-double-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-rgt-identity 68.8%

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

      3. associate-/l* 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. mul-1-neg 68.1%

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

      6. distribute-lft-in 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

      4. neg-mul-1 83.3%

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

      5. sub-neg 83.3%

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

   10. Simplified 83.3%

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

   if -7200 < z < -6.00000000000000048e-97

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 87.6%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

      1. clear-num 71.8%

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

      2. un-div-inv 72.0%

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

   8. Applied egg-rr 72.0%

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

   if -6.00000000000000048e-97 < z < -8.19999999999999962e-243

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 80.2%

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

   4. Taylor expanded in y around inf 77.1%

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

   if -8.19999999999999962e-243 < z < 1.59999999999999997e-11

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 75.8%

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

      1. clear-num 81.8%

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

      2. un-div-inv 83.1%

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

   7. Applied egg-rr 83.1%

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

   if 1.59999999999999997e-11 < z < 8.00000000000000058e70

   1. Initial program 90.7%

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

   3. Taylor expanded in y around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. div-sub 81.6%

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

      3. mul-1-neg 81.6%

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

      4. associate-/l* 90.7%

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

      5. distribute-lft-neg-out 90.7%

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

      6. distribute-rgt-out 90.7%

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

      7. sub-neg 90.7%

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

      8. associate-/r/ 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in t around inf 73.2%

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

   7. Taylor expanded in a around 0 58.8%

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

      1. neg-mul-1 58.8%

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

      2. distribute-neg-frac 58.8%

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

   9. Simplified 58.8%

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

   if 8.00000000000000058e70 < z < 3.4999999999999999e148

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. remove-double-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-*l/ 72.0%

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

      6. associate-/l* 87.7%

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

      7. fma-neg 87.6%

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

      8. remove-double-neg 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in a around 0 47.8%

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

      1. mul-1-neg 47.8%

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

      2. unsub-neg 47.8%

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

      3. associate-/l* 55.5%

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

      4. div-sub 55.5%

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

      5. sub-neg 55.5%

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

      6. *-inverses 55.5%

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

      7. metadata-eval 55.5%

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

   7. Simplified 55.5%

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

   8. Taylor expanded in y around inf 54.6%

      \[\leadsto x - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -7200:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-243}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+148}:\\ \;\;\;\;x - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -10500:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-242}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -7.5e+53)
     t_1
     (if (<= z -10500.0)
       (/ (* x (- y a)) z)
       (if (<= z -6.2e-95)
         (+ x (/ t (/ a (- y z))))
         (if (<= z -1.2e-242)
           (+ x (/ (* y t) (- a z)))
           (if (<= z 6e-11) (+ x (/ y (/ a (- t x)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -7.5e+53) {
		tmp = t_1;
	} else if (z <= -10500.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -6.2e-95) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= -1.2e-242) {
		tmp = x + ((y * t) / (a - z));
	} else if (z <= 6e-11) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-7.5d+53)) then
        tmp = t_1
    else if (z <= (-10500.0d0)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-6.2d-95)) then
        tmp = x + (t / (a / (y - z)))
    else if (z <= (-1.2d-242)) then
        tmp = x + ((y * t) / (a - z))
    else if (z <= 6d-11) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -7.5e+53) {
		tmp = t_1;
	} else if (z <= -10500.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -6.2e-95) {
		tmp = x + (t / (a / (y - z)));
	} else if (z <= -1.2e-242) {
		tmp = x + ((y * t) / (a - z));
	} else if (z <= 6e-11) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -7.5e+53:
		tmp = t_1
	elif z <= -10500.0:
		tmp = (x * (y - a)) / z
	elif z <= -6.2e-95:
		tmp = x + (t / (a / (y - z)))
	elif z <= -1.2e-242:
		tmp = x + ((y * t) / (a - z))
	elif z <= 6e-11:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -7.5e+53)
		tmp = t_1;
	elseif (z <= -10500.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -6.2e-95)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	elseif (z <= -1.2e-242)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (z <= 6e-11)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -7.5e+53)
		tmp = t_1;
	elseif (z <= -10500.0)
		tmp = (x * (y - a)) / z;
	elseif (z <= -6.2e-95)
		tmp = x + (t / (a / (y - z)));
	elseif (z <= -1.2e-242)
		tmp = x + ((y * t) / (a - z));
	elseif (z <= 6e-11)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+53], t$95$1, If[LessEqual[z, -10500.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -6.2e-95], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-242], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-11], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.4999999999999997e53 or 6e-11 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 54.8%

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

      6. associate-/l* 75.4%

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

      7. fma-neg 75.4%

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

      8. remove-double-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 56.4%

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

      4. div-sub 56.4%

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

      5. sub-neg 56.4%

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

      6. *-inverses 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around inf 55.5%

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

   if -7.4999999999999997e53 < z < -10500

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. remove-double-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*l/ 68.8%

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

      6. associate-/l* 68.1%

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

      7. fma-neg 68.1%

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

      8. remove-double-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-rgt-identity 68.8%

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

      3. associate-/l* 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. mul-1-neg 68.1%

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

      6. distribute-lft-in 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

      4. neg-mul-1 83.3%

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

      5. sub-neg 83.3%

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

   10. Simplified 83.3%

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

   if -10500 < z < -6.19999999999999983e-95

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 87.6%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

      1. clear-num 71.8%

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

      2. un-div-inv 72.0%

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

   8. Applied egg-rr 72.0%

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

   if -6.19999999999999983e-95 < z < -1.2e-242

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 80.2%

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

   4. Taylor expanded in y around inf 77.1%

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

   if -1.2e-242 < z < 6e-11

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 75.8%

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

      1. clear-num 81.8%

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

      2. un-div-inv 83.1%

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

   7. Applied egg-rr 83.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -10500:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-242}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7700:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-152}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -1.95e+55)
     t_1
     (if (<= z -7700.0)
       (/ (* x (- y a)) z)
       (if (<= z -1.1e-152)
         (+ x (* (- y z) (/ t a)))
         (if (<= z 7.5e-9) (+ x (/ y (/ a (- t x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.95e+55) {
		tmp = t_1;
	} else if (z <= -7700.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -1.1e-152) {
		tmp = x + ((y - z) * (t / a));
	} else if (z <= 7.5e-9) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-1.95d+55)) then
        tmp = t_1
    else if (z <= (-7700.0d0)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-1.1d-152)) then
        tmp = x + ((y - z) * (t / a))
    else if (z <= 7.5d-9) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.95e+55) {
		tmp = t_1;
	} else if (z <= -7700.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -1.1e-152) {
		tmp = x + ((y - z) * (t / a));
	} else if (z <= 7.5e-9) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -1.95e+55:
		tmp = t_1
	elif z <= -7700.0:
		tmp = (x * (y - a)) / z
	elif z <= -1.1e-152:
		tmp = x + ((y - z) * (t / a))
	elif z <= 7.5e-9:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.95e+55)
		tmp = t_1;
	elseif (z <= -7700.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -1.1e-152)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	elseif (z <= 7.5e-9)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.95e+55)
		tmp = t_1;
	elseif (z <= -7700.0)
		tmp = (x * (y - a)) / z;
	elseif (z <= -1.1e-152)
		tmp = x + ((y - z) * (t / a));
	elseif (z <= 7.5e-9)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+55], t$95$1, If[LessEqual[z, -7700.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.1e-152], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-9], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.95000000000000014e55 or 7.49999999999999933e-9 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 54.8%

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

      6. associate-/l* 75.4%

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

      7. fma-neg 75.4%

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

      8. remove-double-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 56.4%

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

      4. div-sub 56.4%

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

      5. sub-neg 56.4%

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

      6. *-inverses 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around inf 55.5%

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

   if -1.95000000000000014e55 < z < -7700

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. remove-double-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*l/ 68.8%

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

      6. associate-/l* 68.1%

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

      7. fma-neg 68.1%

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

      8. remove-double-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-rgt-identity 68.8%

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

      3. associate-/l* 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. mul-1-neg 68.1%

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

      6. distribute-lft-in 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

      4. neg-mul-1 83.3%

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

      5. sub-neg 83.3%

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

   10. Simplified 83.3%

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

   if -7700 < z < -1.09999999999999992e-152

   1. Initial program 87.9%

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

   3. Taylor expanded in t around inf 82.7%

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

   4. Taylor expanded in a around inf 64.3%

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

   if -1.09999999999999992e-152 < z < 7.49999999999999933e-9

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

      1. clear-num 78.8%

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

      2. un-div-inv 79.9%

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

   7. Applied egg-rr 79.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -7700:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-152}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4200:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -3.1e+53)
     t_1
     (if (<= z -4200.0)
       (/ (* x (- y a)) z)
       (if (<= z -8.2e-151)
         (+ x (* (- y z) (/ t a)))
         (if (<= z 7.4e-10) (+ x (* y (/ (- t x) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -3.1e+53) {
		tmp = t_1;
	} else if (z <= -4200.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -8.2e-151) {
		tmp = x + ((y - z) * (t / a));
	} else if (z <= 7.4e-10) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-3.1d+53)) then
        tmp = t_1
    else if (z <= (-4200.0d0)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-8.2d-151)) then
        tmp = x + ((y - z) * (t / a))
    else if (z <= 7.4d-10) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -3.1e+53) {
		tmp = t_1;
	} else if (z <= -4200.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -8.2e-151) {
		tmp = x + ((y - z) * (t / a));
	} else if (z <= 7.4e-10) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -3.1e+53:
		tmp = t_1
	elif z <= -4200.0:
		tmp = (x * (y - a)) / z
	elif z <= -8.2e-151:
		tmp = x + ((y - z) * (t / a))
	elif z <= 7.4e-10:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.1e+53)
		tmp = t_1;
	elseif (z <= -4200.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -8.2e-151)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	elseif (z <= 7.4e-10)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.1e+53)
		tmp = t_1;
	elseif (z <= -4200.0)
		tmp = (x * (y - a)) / z;
	elseif (z <= -8.2e-151)
		tmp = x + ((y - z) * (t / a));
	elseif (z <= 7.4e-10)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+53], t$95$1, If[LessEqual[z, -4200.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8.2e-151], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-10], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.10000000000000019e53 or 7.4000000000000003e-10 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 54.8%

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

      6. associate-/l* 75.4%

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

      7. fma-neg 75.4%

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

      8. remove-double-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 56.4%

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

      4. div-sub 56.4%

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

      5. sub-neg 56.4%

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

      6. *-inverses 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around inf 55.5%

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

   if -3.10000000000000019e53 < z < -4200

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. remove-double-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*l/ 68.8%

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

      6. associate-/l* 68.1%

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

      7. fma-neg 68.1%

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

      8. remove-double-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-rgt-identity 68.8%

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

      3. associate-/l* 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. mul-1-neg 68.1%

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

      6. distribute-lft-in 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

      4. neg-mul-1 83.3%

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

      5. sub-neg 83.3%

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

   10. Simplified 83.3%

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

   if -4200 < z < -8.2000000000000002e-151

   1. Initial program 87.9%

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

   3. Taylor expanded in t around inf 82.7%

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

   4. Taylor expanded in a around inf 64.3%

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

   if -8.2000000000000002e-151 < z < 7.4000000000000003e-10

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4200:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -11000:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -1.1e+52)
     t_1
     (if (<= z -11000.0)
       (/ (* x (- y a)) z)
       (if (<= z -7.5e-94)
         (+ x (* t (/ (- y z) a)))
         (if (<= z 8.5e-9) (+ x (* y (/ (- t x) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.1e+52) {
		tmp = t_1;
	} else if (z <= -11000.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -7.5e-94) {
		tmp = x + (t * ((y - z) / a));
	} else if (z <= 8.5e-9) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-1.1d+52)) then
        tmp = t_1
    else if (z <= (-11000.0d0)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-7.5d-94)) then
        tmp = x + (t * ((y - z) / a))
    else if (z <= 8.5d-9) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.1e+52) {
		tmp = t_1;
	} else if (z <= -11000.0) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -7.5e-94) {
		tmp = x + (t * ((y - z) / a));
	} else if (z <= 8.5e-9) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -1.1e+52:
		tmp = t_1
	elif z <= -11000.0:
		tmp = (x * (y - a)) / z
	elif z <= -7.5e-94:
		tmp = x + (t * ((y - z) / a))
	elif z <= 8.5e-9:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.1e+52)
		tmp = t_1;
	elseif (z <= -11000.0)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -7.5e-94)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif (z <= 8.5e-9)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.1e+52)
		tmp = t_1;
	elseif (z <= -11000.0)
		tmp = (x * (y - a)) / z;
	elseif (z <= -7.5e-94)
		tmp = x + (t * ((y - z) / a));
	elseif (z <= 8.5e-9)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+52], t$95$1, If[LessEqual[z, -11000.0], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -7.5e-94], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-9], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e52 or 8.5e-9 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 54.8%

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

      6. associate-/l* 75.4%

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

      7. fma-neg 75.4%

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

      8. remove-double-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 56.4%

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

      4. div-sub 56.4%

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

      5. sub-neg 56.4%

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

      6. *-inverses 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around inf 55.5%

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

   if -1.1e52 < z < -11000

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. remove-double-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*l/ 68.8%

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

      6. associate-/l* 68.1%

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

      7. fma-neg 68.1%

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

      8. remove-double-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-rgt-identity 68.8%

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

      3. associate-/l* 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. mul-1-neg 68.1%

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

      6. distribute-lft-in 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. associate-*r* 83.3%

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

      3. neg-mul-1 83.3%

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

      4. neg-mul-1 83.3%

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

      5. sub-neg 83.3%

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

   10. Simplified 83.3%

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

   if -11000 < z < -7.5000000000000003e-94

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 87.6%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   if -7.5000000000000003e-94 < z < 8.5e-9

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 70.0%

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

      1. associate-/l* 74.9%

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

   5. Simplified 74.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -11000:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= a -3.9e+58)
     t_2
     (if (<= a 1.35e-305)
       t_1
       (if (<= a 1.95e-177)
         (* x (/ (- y a) z))
         (if (<= a 1.05e-86) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -3.9e+58) {
		tmp = t_2;
	} else if (a <= 1.35e-305) {
		tmp = t_1;
	} else if (a <= 1.95e-177) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.05e-86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t * ((y - z) / a))
    if (a <= (-3.9d+58)) then
        tmp = t_2
    else if (a <= 1.35d-305) then
        tmp = t_1
    else if (a <= 1.95d-177) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.05d-86) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -3.9e+58) {
		tmp = t_2;
	} else if (a <= 1.35e-305) {
		tmp = t_1;
	} else if (a <= 1.95e-177) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.05e-86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -3.9e+58:
		tmp = t_2
	elif a <= 1.35e-305:
		tmp = t_1
	elif a <= 1.95e-177:
		tmp = x * ((y - a) / z)
	elif a <= 1.05e-86:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -3.9e+58)
		tmp = t_2;
	elseif (a <= 1.35e-305)
		tmp = t_1;
	elseif (a <= 1.95e-177)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.05e-86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -3.9e+58)
		tmp = t_2;
	elseif (a <= 1.35e-305)
		tmp = t_1;
	elseif (a <= 1.95e-177)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.05e-86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+58], t$95$2, If[LessEqual[a, 1.35e-305], t$95$1, If[LessEqual[a, 1.95e-177], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-86], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9000000000000001e58 or 1.05e-86 < a

   1. Initial program 85.6%

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

   3. Taylor expanded in t around inf 74.9%

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

   4. Taylor expanded in a around inf 59.4%

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

      1. associate-/l* 63.5%

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

   6. Simplified 63.5%

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

   if -3.9000000000000001e58 < a < 1.35e-305 or 1.95000000000000007e-177 < a < 1.05e-86

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. remove-double-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. *-commutative 76.4%

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

      5. associate-*l/ 72.8%

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

      6. associate-/l* 81.9%

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

      7. fma-neg 81.9%

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

      8. remove-double-neg 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in a around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. associate-/l* 62.1%

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

      4. div-sub 62.1%

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

      5. sub-neg 62.1%

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

      6. *-inverses 62.1%

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

      7. metadata-eval 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in t around inf 61.1%

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

   if 1.35e-305 < a < 1.95000000000000007e-177

   1. Initial program 62.5%

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

      1. +-commutative 62.5%

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

      2. remove-double-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. associate-*l/ 66.5%

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

      6. associate-/l* 74.4%

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

      7. fma-neg 74.4%

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

      8. remove-double-neg 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in t around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. *-rgt-identity 40.9%

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

      3. associate-/l* 48.3%

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

      4. distribute-rgt-neg-in 48.3%

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

      5. mul-1-neg 48.3%

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

      6. distribute-lft-in 48.2%

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

      7. mul-1-neg 48.2%

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

      8. unsub-neg 48.2%

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

   7. Simplified 48.2%

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

   8. Taylor expanded in z around inf 74.0%

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

      1. neg-mul-1 74.0%

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

      2. sub-neg 74.0%

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

      3. mul-1-neg 74.0%

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

   10. Simplified 74.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{if}\;z \leq -7200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-154}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* (- t x) (- y a)) z))))
   (if (<= z -7200.0)
     t_1
     (if (<= z -3.9e-154)
       (+ x (* (- y z) (/ t (- a z))))
       (if (<= z 6.6e-9) (+ x (/ (- t x) (/ (- a z) y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) * (y - a)) / z);
	double tmp;
	if (z <= -7200.0) {
		tmp = t_1;
	} else if (z <= -3.9e-154) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 6.6e-9) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (((t - x) * (y - a)) / z)
    if (z <= (-7200.0d0)) then
        tmp = t_1
    else if (z <= (-3.9d-154)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 6.6d-9) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) * (y - a)) / z);
	double tmp;
	if (z <= -7200.0) {
		tmp = t_1;
	} else if (z <= -3.9e-154) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 6.6e-9) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (((t - x) * (y - a)) / z)
	tmp = 0
	if z <= -7200.0:
		tmp = t_1
	elif z <= -3.9e-154:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 6.6e-9:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z))
	tmp = 0.0
	if (z <= -7200.0)
		tmp = t_1;
	elseif (z <= -3.9e-154)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 6.6e-9)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (((t - x) * (y - a)) / z);
	tmp = 0.0;
	if (z <= -7200.0)
		tmp = t_1;
	elseif (z <= -3.9e-154)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 6.6e-9)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7200.0], t$95$1, If[LessEqual[z, -3.9e-154], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-9], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7200 or 6.60000000000000037e-9 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 55.4%

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

      6. associate-/l* 75.1%

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

      7. fma-neg 75.0%

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

      8. remove-double-neg 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. mul-1-neg 75.8%

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

      5. div-sub 75.8%

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

      6. mul-1-neg 75.8%

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

      7. distribute-lft-out-- 75.8%

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

      8. associate-*r/ 75.8%

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

      9. mul-1-neg 75.8%

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

      10. unsub-neg 75.8%

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

      11. distribute-rgt-out-- 75.9%

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

   7. Simplified 75.9%

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

   if -7200 < z < -3.90000000000000032e-154

   1. Initial program 87.9%

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

   3. Taylor expanded in t around inf 82.7%

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

   if -3.90000000000000032e-154 < z < 6.60000000000000037e-9

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 93.6%

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

      1. +-commutative 93.6%

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

      2. div-sub 93.7%

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

      3. mul-1-neg 93.7%

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

      4. associate-/l* 87.2%

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

      5. distribute-lft-neg-out 87.2%

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

      6. distribute-rgt-out 93.8%

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

      7. sub-neg 93.8%

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

      8. associate-/r/ 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in y around inf 89.3%

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

Alternative 11: 55.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -1.02e+55)
     t_1
     (if (<= z -3.8e-13)
       (/ (* x (- y a)) z)
       (if (<= z 1.85e-13) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.02e+55) {
		tmp = t_1;
	} else if (z <= -3.8e-13) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 1.85e-13) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-1.02d+55)) then
        tmp = t_1
    else if (z <= (-3.8d-13)) then
        tmp = (x * (y - a)) / z
    else if (z <= 1.85d-13) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -1.02e+55) {
		tmp = t_1;
	} else if (z <= -3.8e-13) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 1.85e-13) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -1.02e+55:
		tmp = t_1
	elif z <= -3.8e-13:
		tmp = (x * (y - a)) / z
	elif z <= 1.85e-13:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.02e+55)
		tmp = t_1;
	elseif (z <= -3.8e-13)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= 1.85e-13)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.02e+55)
		tmp = t_1;
	elseif (z <= -3.8e-13)
		tmp = (x * (y - a)) / z;
	elseif (z <= 1.85e-13)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+55], t$95$1, If[LessEqual[z, -3.8e-13], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.85e-13], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02000000000000002e55 or 1.84999999999999994e-13 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 54.8%

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

      6. associate-/l* 75.4%

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

      7. fma-neg 75.4%

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

      8. remove-double-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 56.4%

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

      4. div-sub 56.4%

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

      5. sub-neg 56.4%

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

      6. *-inverses 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around inf 55.5%

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

   if -1.02000000000000002e55 < z < -3.8e-13

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. remove-double-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*l/ 79.0%

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

      6. associate-/l* 78.5%

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

      7. fma-neg 78.5%

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

      8. remove-double-neg 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-rgt-identity 68.2%

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

      3. associate-/l* 67.5%

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

      4. distribute-rgt-neg-in 67.5%

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

      5. mul-1-neg 67.5%

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

      6. distribute-lft-in 67.5%

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

      7. mul-1-neg 67.5%

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

      8. unsub-neg 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in z around inf 67.8%

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

      1. associate-*r/ 67.8%

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

      2. associate-*r* 67.8%

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

      3. neg-mul-1 67.8%

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

      4. neg-mul-1 67.8%

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

      5. sub-neg 67.8%

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

   10. Simplified 67.8%

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

   if -3.8e-13 < z < 1.84999999999999994e-13

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. div-sub 91.9%

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

      3. mul-1-neg 91.9%

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

      4. associate-/l* 86.3%

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

      5. distribute-lft-neg-out 86.3%

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

      6. distribute-rgt-out 91.9%

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

      7. sub-neg 91.9%

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

      8. associate-/r/ 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around inf 76.3%

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

   7. Taylor expanded in z around 0 56.8%

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

      1. associate-/l* 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -9e+52)
     t_1
     (if (<= z -7.8e-13)
       (* x (/ (- y a) z))
       (if (<= z 5.8e-9) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -9e+52) {
		tmp = t_1;
	} else if (z <= -7.8e-13) {
		tmp = x * ((y - a) / z);
	} else if (z <= 5.8e-9) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-9d+52)) then
        tmp = t_1
    else if (z <= (-7.8d-13)) then
        tmp = x * ((y - a) / z)
    else if (z <= 5.8d-9) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -9e+52) {
		tmp = t_1;
	} else if (z <= -7.8e-13) {
		tmp = x * ((y - a) / z);
	} else if (z <= 5.8e-9) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -9e+52:
		tmp = t_1
	elif z <= -7.8e-13:
		tmp = x * ((y - a) / z)
	elif z <= 5.8e-9:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -9e+52)
		tmp = t_1;
	elseif (z <= -7.8e-13)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 5.8e-9)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -9e+52)
		tmp = t_1;
	elseif (z <= -7.8e-13)
		tmp = x * ((y - a) / z);
	elseif (z <= 5.8e-9)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+52], t$95$1, If[LessEqual[z, -7.8e-13], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-9], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999999e52 or 5.79999999999999982e-9 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. remove-double-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l/ 54.8%

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

      6. associate-/l* 75.4%

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

      7. fma-neg 75.4%

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

      8. remove-double-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 56.4%

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

      4. div-sub 56.4%

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

      5. sub-neg 56.4%

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

      6. *-inverses 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around inf 55.5%

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

   if -8.9999999999999999e52 < z < -7.80000000000000009e-13

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. remove-double-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*l/ 79.0%

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

      6. associate-/l* 78.5%

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

      7. fma-neg 78.5%

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

      8. remove-double-neg 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-rgt-identity 68.2%

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

      3. associate-/l* 67.5%

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

      4. distribute-rgt-neg-in 67.5%

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

      5. mul-1-neg 67.5%

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

      6. distribute-lft-in 67.5%

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

      7. mul-1-neg 67.5%

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

      8. unsub-neg 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in z around inf 67.5%

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

      1. neg-mul-1 67.5%

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

      2. sub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

   10. Simplified 67.5%

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

   if -7.80000000000000009e-13 < z < 5.79999999999999982e-9

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. div-sub 91.9%

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

      3. mul-1-neg 91.9%

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

      4. associate-/l* 86.3%

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

      5. distribute-lft-neg-out 86.3%

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

      6. distribute-rgt-out 91.9%

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

      7. sub-neg 91.9%

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

      8. associate-/r/ 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around inf 76.3%

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

   7. Taylor expanded in z around 0 56.8%

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

      1. associate-/l* 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+62} \lor \neg \left(y \leq 1.4 \cdot 10^{+71}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.2e+62) (not (<= y 1.4e+71)))
   (+ x (/ (- t x) (/ (- a z) y)))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.2e+62) || !(y <= 1.4e+71)) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.2d+62)) .or. (.not. (y <= 1.4d+71))) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.2e+62) || !(y <= 1.4e+71)) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.2e+62) or not (y <= 1.4e+71):
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.2e+62) || !(y <= 1.4e+71))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.2e+62) || ~((y <= 1.4e+71)))
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.2e+62], N[Not[LessEqual[y, 1.4e+71]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999984e62 or 1.40000000000000001e71 < y

   1. Initial program 86.2%

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

   3. Taylor expanded in y around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. div-sub 79.6%

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

      3. mul-1-neg 79.6%

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

      4. associate-/l* 79.5%

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

      5. distribute-lft-neg-out 79.5%

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

      6. distribute-rgt-out 86.2%

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

      7. sub-neg 86.2%

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

      8. associate-/r/ 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in y around inf 84.1%

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

   if -3.19999999999999984e62 < y < 1.40000000000000001e71

   1. Initial program 76.4%

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

   3. Taylor expanded in t around inf 68.1%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+62} \lor \neg \left(y \leq 1.4 \cdot 10^{+71}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-208} \lor \neg \left(t \leq 2 \cdot 10^{-132}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e-208) (not (<= t 2e-132)))
   (+ x (* t (/ (- y z) (- a z))))
   (* x (+ (/ (- y z) (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e-208) || !(t <= 2e-132)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.8d-208)) .or. (.not. (t <= 2d-132))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e-208) || !(t <= 2e-132)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.8e-208) or not (t <= 2e-132):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e-208) || !(t <= 2e-132))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.8e-208) || ~((t <= 2e-132)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x * (((y - z) / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e-208], N[Not[LessEqual[t, 2e-132]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.80000000000000011e-208 or 2e-132 < t

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf 67.2%

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

      1. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -3.80000000000000011e-208 < t < 2e-132

   1. Initial program 65.6%

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

      1. +-commutative 65.6%

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

      2. remove-double-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

      5. associate-*l/ 64.9%

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

      6. associate-/l* 67.9%

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

      7. fma-neg 67.9%

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

      8. remove-double-neg 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-rgt-identity 57.9%

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

      3. associate-/l* 62.1%

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

      4. distribute-rgt-neg-in 62.1%

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

      5. mul-1-neg 62.1%

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

      6. distribute-lft-in 62.1%

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

      7. mul-1-neg 62.1%

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

      8. unsub-neg 62.1%

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

   7. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-208} \lor \neg \left(t \leq 2 \cdot 10^{-132}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+234}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -20000.0) t (if (<= z 5e-128) x (if (<= z 2.7e+234) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -20000.0) {
		tmp = t;
	} else if (z <= 5e-128) {
		tmp = x;
	} else if (z <= 2.7e+234) {
		tmp = x + t;
	} 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 <= (-20000.0d0)) then
        tmp = t
    else if (z <= 5d-128) then
        tmp = x
    else if (z <= 2.7d+234) then
        tmp = x + t
    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 <= -20000.0) {
		tmp = t;
	} else if (z <= 5e-128) {
		tmp = x;
	} else if (z <= 2.7e+234) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -20000.0:
		tmp = t
	elif z <= 5e-128:
		tmp = x
	elif z <= 2.7e+234:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -20000.0)
		tmp = t;
	elseif (z <= 5e-128)
		tmp = x;
	elseif (z <= 2.7e+234)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -20000.0)
		tmp = t;
	elseif (z <= 5e-128)
		tmp = x;
	elseif (z <= 2.7e+234)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -20000.0], t, If[LessEqual[z, 5e-128], x, If[LessEqual[z, 2.7e+234], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e4 or 2.7000000000000002e234 < z

   1. Initial program 52.8%

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

   3. Taylor expanded in y around 0 41.1%

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

      1. +-commutative 41.1%

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

      2. div-sub 41.1%

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

      3. mul-1-neg 41.1%

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

      4. associate-/l* 52.8%

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

      5. distribute-lft-neg-out 52.8%

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

      6. distribute-rgt-out 52.8%

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

      7. sub-neg 52.8%

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

      8. associate-/r/ 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in z around inf 54.9%

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

   if -2e4 < z < 5.0000000000000001e-128

   1. Initial program 91.4%

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

      1. +-commutative 91.4%

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

      2. remove-double-neg 91.4%

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

      3. unsub-neg 91.4%

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

      4. *-commutative 91.4%

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

      5. associate-*l/ 89.4%

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

      6. associate-/l* 92.7%

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

      7. fma-neg 92.7%

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

      8. remove-double-neg 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around inf 40.4%

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

   if 5.0000000000000001e-128 < z < 2.7000000000000002e234

   1. Initial program 87.0%

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

   3. Taylor expanded in t around inf 67.1%

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

   4. Taylor expanded in z around inf 43.7%

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

Alternative 16: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+36} \lor \neg \left(z \leq 2.1 \cdot 10^{-10}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+36) (not (<= z 2.1e-10)))
   (* t (- 1.0 (/ y z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+36) || !(z <= 2.1e-10)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+36)) .or. (.not. (z <= 2.1d-10))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+36) || !(z <= 2.1e-10)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+36) or not (z <= 2.1e-10):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+36) || !(z <= 2.1e-10))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+36) || ~((z <= 2.1e-10)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+36], N[Not[LessEqual[z, 2.1e-10]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000034e36 or 2.1e-10 < z

   1. Initial program 66.3%

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

      1. +-commutative 66.3%

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

      2. remove-double-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-*l/ 54.3%

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

      6. associate-/l* 74.5%

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

      7. fma-neg 74.4%

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

      8. remove-double-neg 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in a around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. unsub-neg 41.2%

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

      3. associate-/l* 55.1%

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

      4. div-sub 55.1%

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

      5. sub-neg 55.1%

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

      6. *-inverses 55.1%

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

      7. metadata-eval 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in t around inf 54.3%

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

   if -8.00000000000000034e36 < z < 2.1e-10

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. div-sub 92.2%

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

      3. mul-1-neg 92.2%

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

      4. associate-/l* 86.9%

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

      5. distribute-lft-neg-out 86.9%

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

      6. distribute-rgt-out 92.2%

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

      7. sub-neg 92.2%

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

      8. associate-/r/ 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in t around inf 74.4%

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

   7. Taylor expanded in z around 0 55.2%

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

      1. associate-/l* 58.0%

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

   9. Simplified 58.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+36} \lor \neg \left(z \leq 2.1 \cdot 10^{-10}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+38} \lor \neg \left(z \leq 3.5 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+38) (not (<= z 3.5e-20)))
   (* t (- 1.0 (/ y z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+38) || !(z <= 3.5e-20)) {
		tmp = t * (1.0 - (y / 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 ((z <= (-1.7d+38)) .or. (.not. (z <= 3.5d-20))) then
        tmp = t * (1.0d0 - (y / 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 ((z <= -1.7e+38) || !(z <= 3.5e-20)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+38) or not (z <= 3.5e-20):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+38) || !(z <= 3.5e-20))
		tmp = Float64(t * Float64(1.0 - Float64(y / 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 ((z <= -1.7e+38) || ~((z <= 3.5e-20)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+38], N[Not[LessEqual[z, 3.5e-20]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999998e38 or 3.50000000000000003e-20 < z

   1. Initial program 66.3%

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

      1. +-commutative 66.3%

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

      2. remove-double-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-*l/ 54.3%

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

      6. associate-/l* 74.5%

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

      7. fma-neg 74.4%

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

      8. remove-double-neg 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in a around 0 41.3%

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

      1. mul-1-neg 41.3%

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

      2. unsub-neg 41.3%

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

      3. associate-/l* 55.2%

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

      4. div-sub 55.2%

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

      5. sub-neg 55.2%

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

      6. *-inverses 55.2%

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

      7. metadata-eval 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around inf 54.4%

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

   if -1.69999999999999998e38 < z < 3.50000000000000003e-20

   1. Initial program 92.2%

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

      1. +-commutative 92.2%

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

      2. remove-double-neg 92.2%

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

      3. unsub-neg 92.2%

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

      4. *-commutative 92.2%

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

      5. associate-*l/ 89.1%

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

      6. associate-/l* 93.0%

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

      7. fma-neg 93.0%

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

      8. remove-double-neg 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. *-rgt-identity 55.7%

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

      3. associate-/l* 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. mul-1-neg 61.9%

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

      6. distribute-lft-in 61.9%

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

      7. mul-1-neg 61.9%

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

      8. unsub-neg 61.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   8. Taylor expanded in z around 0 55.5%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+38} \lor \neg \left(z \leq 3.5 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 170000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+64) x (if (<= a 170000000.0) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+64) {
		tmp = x;
	} else if (a <= 170000000.0) {
		tmp = t * (1.0 - (y / z));
	} 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 <= (-2d+64)) then
        tmp = x
    else if (a <= 170000000.0d0) then
        tmp = t * (1.0d0 - (y / z))
    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 <= -2e+64) {
		tmp = x;
	} else if (a <= 170000000.0) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+64:
		tmp = x
	elif a <= 170000000.0:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+64)
		tmp = x;
	elseif (a <= 170000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e+64)
		tmp = x;
	elseif (a <= 170000000.0)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+64], x, If[LessEqual[a, 170000000.0], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000004e64 or 1.7e8 < a

   1. Initial program 88.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 88.0%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 88.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 88.0%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 72.8%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 88.6%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 88.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 88.6%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{x} \]

   if -2.00000000000000004e64 < a < 1.7e8

   1. Initial program 74.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 74.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 74.0%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 74.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 74.0%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 72.1%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 80.9%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 80.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 80.9%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 50.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 50.8%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)} \]

      2. unsub-neg 50.8%

         \[\leadsto \color{blue}{x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* 60.2%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 60.2%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg 60.2%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{z}{z}\right)\right)} \]

      6. *-inverses 60.2%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 60.2%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

   7. Simplified 60.2%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \left(\frac{y}{z} + -1\right)} \]

   8. Taylor expanded in t around inf 53.1%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 39.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+60} \lor \neg \left(y \leq 7.5 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.5e+60) (not (<= y 7.5e+55))) (* x (/ y z)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e+60) || !(y <= 7.5e+55)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.5d+60)) .or. (.not. (y <= 7.5d+55))) then
        tmp = x * (y / z)
    else
        tmp = x + 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 ((y <= -1.5e+60) || !(y <= 7.5e+55)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.5e+60) or not (y <= 7.5e+55):
		tmp = x * (y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.5e+60) || !(y <= 7.5e+55))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.5e+60) || ~((y <= 7.5e+55)))
		tmp = x * (y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.5e+60], N[Not[LessEqual[y, 7.5e+55]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e60 or 7.50000000000000014e55 < y

   1. Initial program 85.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 85.6%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 85.6%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 85.6%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 85.6%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 76.1%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 90.4%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 90.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 90.4%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 45.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot \left(y - z\right)}{a - z}\right)} \]

      2. *-rgt-identity 45.7%

         \[\leadsto \color{blue}{x \cdot 1} + \left(-\frac{x \cdot \left(y - z\right)}{a - z}\right) \]

      3. associate-/l* 54.9%

         \[\leadsto x \cdot 1 + \left(-\color{blue}{x \cdot \frac{y - z}{a - z}}\right) \]

      4. distribute-rgt-neg-in 54.9%

         \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(-\frac{y - z}{a - z}\right)} \]

      5. mul-1-neg 54.9%

         \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left(-1 \cdot \frac{y - z}{a - z}\right)} \]

      6. distribute-lft-in 54.9%

         \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      7. mul-1-neg 54.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      8. unsub-neg 54.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   7. Simplified 54.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   8. Taylor expanded in a around 0 42.3%

      \[\leadsto x \cdot \color{blue}{\frac{y}{z}} \]

   if -1.4999999999999999e60 < y < 7.50000000000000014e55

   1. Initial program 76.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.0%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

   4. Taylor expanded in z around inf 50.9%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+60} \lor \neg \left(y \leq 7.5 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20500:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -20500.0) t (if (<= z 5e-28) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -20500.0) {
		tmp = t;
	} else if (z <= 5e-28) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-20500.0d0)) then
        tmp = t
    else if (z <= 5d-28) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -20500.0) {
		tmp = t;
	} else if (z <= 5e-28) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -20500.0:
		tmp = t
	elif z <= 5e-28:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -20500.0)
		tmp = t;
	elseif (z <= 5e-28)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -20500.0)
		tmp = t;
	elseif (z <= 5e-28)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -20500.0], t, If[LessEqual[z, 5e-28], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -20500 or 5.0000000000000002e-28 < z

   1. Initial program 67.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 52.9%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. div-sub 52.9%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

      3. mul-1-neg 52.9%

         \[\leadsto x + \left(y \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. associate-/l* 67.6%

         \[\leadsto x + \left(y \cdot \frac{t - x}{a - z} + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right)\right) \]

      5. distribute-lft-neg-out 67.6%

         \[\leadsto x + \left(y \cdot \frac{t - x}{a - z} + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}}\right) \]

      6. distribute-rgt-out 67.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y + \left(-z\right)\right)} \]

      7. sub-neg 67.6%

         \[\leadsto x + \frac{t - x}{a - z} \cdot \color{blue}{\left(y - z\right)} \]

      8. associate-/r/ 74.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   5. Simplified 74.6%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   6. Taylor expanded in z around inf 45.9%

      \[\leadsto \color{blue}{t} \]

   if -20500 < z < 5.0000000000000002e-28

   1. Initial program 92.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 92.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      2. remove-double-neg 92.0%

         \[\leadsto \left(y - z\right) \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\left(-x\right)\right)} \]

      3. unsub-neg 92.0%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} - \left(-x\right)} \]

      4. *-commutative 92.0%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} - \left(-x\right) \]

      5. associate-*l/ 89.4%

         \[\leadsto \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} - \left(-x\right) \]

      6. associate-/l* 93.0%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} - \left(-x\right) \]

      7. fma-neg 93.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, -\left(-x\right)\right)} \]

      8. remove-double-neg 93.0%

         \[\leadsto \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, \color{blue}{x}\right) \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 40.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 24.6% 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 79.8%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 72.4%

   \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
4. Step-by-step derivation

   1. +-commutative 72.4%

      \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

   2. div-sub 72.5%

      \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}\right) \]

   3. mul-1-neg 72.5%

      \[\leadsto x + \left(y \cdot \frac{t - x}{a - z} + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

   4. associate-/l* 77.0%

      \[\leadsto x + \left(y \cdot \frac{t - x}{a - z} + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right)\right) \]

   5. distribute-lft-neg-out 77.0%

      \[\leadsto x + \left(y \cdot \frac{t - x}{a - z} + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}}\right) \]

   6. distribute-rgt-out 79.8%

      \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y + \left(-z\right)\right)} \]

   7. sub-neg 79.8%

      \[\leadsto x + \frac{t - x}{a - z} \cdot \color{blue}{\left(y - z\right)} \]

   8. associate-/r/ 83.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

5. Simplified 83.5%

   \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

6. Taylor expanded in z around inf 27.3%

   \[\leadsto \color{blue}{t} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024145 
(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)))))