Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.2% → 88.5%

Time: 18.7s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.2% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 5.4 \cdot 10^{+81}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \left(\left(a - y\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e+82) (not (<= z 5.4e+81)))
   (- t (* (- t x) (* (- a y) (/ -1.0 z))))
   (+ x (/ (- t x) (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+82) || !(z <= 5.4e+81)) {
		tmp = t - ((t - x) * ((a - y) * (-1.0 / z)));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.15d+82)) .or. (.not. (z <= 5.4d+81))) then
        tmp = t - ((t - x) * ((a - y) * ((-1.0d0) / z)))
    else
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+82) || !(z <= 5.4e+81)) {
		tmp = t - ((t - x) * ((a - y) * (-1.0 / z)));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e+82) or not (z <= 5.4e+81):
		tmp = t - ((t - x) * ((a - y) * (-1.0 / z)))
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e+82) || !(z <= 5.4e+81))
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(a - y) * Float64(-1.0 / z))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e+82) || ~((z <= 5.4e+81)))
		tmp = t - ((t - x) * ((a - y) * (-1.0 / z)));
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e+82], N[Not[LessEqual[z, 5.4e+81]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $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 2 regimes

2. if z < -2.15000000000000007e82 or 5.3999999999999999e81 < z

   1. Initial program 26.2%

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

      1. +-commutative 26.2%

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

      2. *-commutative 26.2%

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

      3. associate-/l* 59.7%

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

      4. fma-define 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. associate-*r/ 60.6%

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

      3. associate-*r/ 60.6%

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

      4. mul-1-neg 60.6%

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

      5. div-sub 60.6%

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

      6. mul-1-neg 60.6%

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

      7. distribute-lft-out-- 60.6%

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

      8. associate-*r/ 60.6%

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

      9. mul-1-neg 60.6%

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

      10. unsub-neg 60.6%

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

      11. distribute-rgt-out-- 63.3%

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

   7. Simplified 63.3%

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

      1. div-inv 63.2%

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

   9. Applied egg-rr 63.2%

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

       1. associate-*l* 84.7%

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

   11. Simplified 84.7%

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

   if -2.15000000000000007e82 < z < 5.3999999999999999e81

   1. Initial program 84.8%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. associate-/l* 88.7%

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

      3. distribute-lft-neg-out 88.7%

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

      4. +-commutative 88.7%

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

      5. div-sub 88.7%

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

      6. distribute-rgt-out 91.2%

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

      7. sub-neg 91.2%

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

      8. associate-/r/ 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 5.4 \cdot 10^{+81}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \left(\left(a - y\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-297} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t x) (- y z)) (- a z)))))
   (if (or (<= t_1 -5e-297) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-297) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((t - x) * (y - z)) / (a - z))
    if ((t_1 <= (-5d-297)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-297) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - x) * (y - z)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-297) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-297) || !(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(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - x) * (y - z)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -5e-297) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-297], 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[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5e-297 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.0%

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

      1. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in y around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-/l* 84.5%

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

      3. distribute-lft-neg-out 84.5%

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

      4. +-commutative 84.5%

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

      5. div-sub 84.5%

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

      6. distribute-rgt-out 86.3%

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

      7. sub-neg 86.3%

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

      8. associate-/r/ 88.5%

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

   7. Simplified 88.5%

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

   if -5e-297 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. *-commutative 4.4%

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

      3. associate-/l* 4.4%

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

      4. fma-define 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq -5 \cdot 10^{-297} \lor \neg \left(x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-297} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t x) (- y z)) (- a z)))))
   (if (or (<= t_1 -5e-297) (not (<= t_1 0.0)))
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-297) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((t - x) * (y - z)) / (a - z))
    if ((t_1 <= (-5d-297)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-297) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - x) * (y - z)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-297) or not (t_1 <= 0.0):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-297) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - x) * (y - z)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -5e-297) || ~((t_1 <= 0.0)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-297], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5e-297 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.0%

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

      1. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

   if -5e-297 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. +-commutative 4.4%

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

      2. *-commutative 4.4%

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

      3. associate-/l* 4.4%

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

      4. fma-define 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq -5 \cdot 10^{-297} \lor \neg \left(x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.001633:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -2.2e+158)
     (+ x (* t (/ y a)))
     (if (<= a -9.5e+108)
       t_1
       (if (<= a -0.001633)
         (- x (/ (* x y) a))
         (if (<= a -1.1e-298)
           t_1
           (if (<= a 8.2e+108)
             (* y (/ (- t x) (- a z)))
             (+ x (* y (/ t a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -2.2e+158) {
		tmp = x + (t * (y / a));
	} else if (a <= -9.5e+108) {
		tmp = t_1;
	} else if (a <= -0.001633) {
		tmp = x - ((x * y) / a);
	} else if (a <= -1.1e-298) {
		tmp = t_1;
	} else if (a <= 8.2e+108) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-2.2d+158)) then
        tmp = x + (t * (y / a))
    else if (a <= (-9.5d+108)) then
        tmp = t_1
    else if (a <= (-0.001633d0)) then
        tmp = x - ((x * y) / a)
    else if (a <= (-1.1d-298)) then
        tmp = t_1
    else if (a <= 8.2d+108) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -2.2e+158) {
		tmp = x + (t * (y / a));
	} else if (a <= -9.5e+108) {
		tmp = t_1;
	} else if (a <= -0.001633) {
		tmp = x - ((x * y) / a);
	} else if (a <= -1.1e-298) {
		tmp = t_1;
	} else if (a <= 8.2e+108) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -2.2e+158:
		tmp = x + (t * (y / a))
	elif a <= -9.5e+108:
		tmp = t_1
	elif a <= -0.001633:
		tmp = x - ((x * y) / a)
	elif a <= -1.1e-298:
		tmp = t_1
	elif a <= 8.2e+108:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.2e+158)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= -9.5e+108)
		tmp = t_1;
	elseif (a <= -0.001633)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (a <= -1.1e-298)
		tmp = t_1;
	elseif (a <= 8.2e+108)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -2.2e+158)
		tmp = x + (t * (y / a));
	elseif (a <= -9.5e+108)
		tmp = t_1;
	elseif (a <= -0.001633)
		tmp = x - ((x * y) / a);
	elseif (a <= -1.1e-298)
		tmp = t_1;
	elseif (a <= 8.2e+108)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+158], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e+108], t$95$1, If[LessEqual[a, -0.001633], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-298], t$95$1, If[LessEqual[a, 8.2e+108], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.2000000000000001e158

   1. Initial program 64.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 74.1%

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

      1. associate-/l* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in z around 0 71.1%

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

      1. associate-/l* 88.4%

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

   10. Simplified 88.4%

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

   if -2.2000000000000001e158 < a < -9.50000000000000097e108 or -0.0016329999999999999 < a < -1.1e-298

   1. Initial program 63.9%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around 0 58.0%

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

      1. mul-1-neg 58.0%

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

      2. associate-/l* 72.7%

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

      3. distribute-lft-neg-out 72.7%

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

      4. +-commutative 72.7%

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

      5. div-sub 72.7%

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

      6. distribute-rgt-out 74.4%

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

      7. sub-neg 74.4%

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

      8. associate-/r/ 77.3%

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

   7. Simplified 77.3%

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

      1. clear-num 77.3%

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

      2. associate-/r* 63.9%

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

      3. add-cube-cbrt 63.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 63.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 63.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 76.3%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 76.3%

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

      8. div-inv 76.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 76.3%

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

      10. fma-define 76.3%

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

   9. Applied egg-rr 76.3%

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

   10. Taylor expanded in t around inf 71.6%

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

       1. div-sub 71.6%

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

   12. Simplified 71.6%

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

   if -9.50000000000000097e108 < a < -0.0016329999999999999

   1. Initial program 72.8%

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

      1. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around 0 65.3%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. neg-mul-1 64.9%

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

   8. Simplified 64.9%

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

   if -1.1e-298 < a < 8.1999999999999998e108

   1. Initial program 64.2%

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

      1. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/l* 70.7%

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

      3. distribute-lft-neg-out 70.7%

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

      4. +-commutative 70.7%

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

      5. div-sub 70.7%

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

      6. distribute-rgt-out 74.3%

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

      7. sub-neg 74.3%

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

      8. associate-/r/ 76.0%

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

   7. Simplified 76.0%

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

      1. clear-num 75.9%

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

      2. associate-/r* 64.1%

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

      3. add-cube-cbrt 63.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 63.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 63.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 75.1%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 75.1%

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

      8. div-inv 74.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 74.5%

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

      10. fma-define 74.5%

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

   9. Applied egg-rr 74.5%

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

   10. Taylor expanded in y around inf 57.9%

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

       1. div-sub 57.9%

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

   12. Simplified 57.9%

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

   if 8.1999999999999998e108 < a

   1. Initial program 68.9%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around 0 59.0%

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

   6. Taylor expanded in t around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. *-lft-identity 61.1%

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

      3. times-frac 71.5%

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

      4. /-rgt-identity 71.5%

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

   8. Simplified 71.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -0.001633:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+158}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.001633:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -1.45e+158)
     (+ x (* t (/ y a)))
     (if (<= a -9.2e+108)
       t_1
       (if (<= a -0.001633)
         (- x (/ (* x y) a))
         (if (<= a 5e+75) t_1 (+ x (* y (/ t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.45e+158) {
		tmp = x + (t * (y / a));
	} else if (a <= -9.2e+108) {
		tmp = t_1;
	} else if (a <= -0.001633) {
		tmp = x - ((x * y) / a);
	} else if (a <= 5e+75) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-1.45d+158)) then
        tmp = x + (t * (y / a))
    else if (a <= (-9.2d+108)) then
        tmp = t_1
    else if (a <= (-0.001633d0)) then
        tmp = x - ((x * y) / a)
    else if (a <= 5d+75) then
        tmp = t_1
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.45e+158) {
		tmp = x + (t * (y / a));
	} else if (a <= -9.2e+108) {
		tmp = t_1;
	} else if (a <= -0.001633) {
		tmp = x - ((x * y) / a);
	} else if (a <= 5e+75) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -1.45e+158:
		tmp = x + (t * (y / a))
	elif a <= -9.2e+108:
		tmp = t_1
	elif a <= -0.001633:
		tmp = x - ((x * y) / a)
	elif a <= 5e+75:
		tmp = t_1
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.45e+158)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= -9.2e+108)
		tmp = t_1;
	elseif (a <= -0.001633)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (a <= 5e+75)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.45e+158)
		tmp = x + (t * (y / a));
	elseif (a <= -9.2e+108)
		tmp = t_1;
	elseif (a <= -0.001633)
		tmp = x - ((x * y) / a);
	elseif (a <= 5e+75)
		tmp = t_1;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+158], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e+108], t$95$1, If[LessEqual[a, -0.001633], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+75], t$95$1, N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45000000000000012e158

   1. Initial program 64.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 74.1%

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

      1. associate-/l* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in z around 0 71.1%

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

      1. associate-/l* 88.4%

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

   10. Simplified 88.4%

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

   if -1.45000000000000012e158 < a < -9.1999999999999996e108 or -0.0016329999999999999 < a < 5.0000000000000002e75

   1. Initial program 63.4%

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

      1. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-/l* 70.7%

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

      3. distribute-lft-neg-out 70.7%

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

      4. +-commutative 70.7%

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

      5. div-sub 70.7%

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

      6. distribute-rgt-out 73.6%

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

      7. sub-neg 73.6%

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

      8. associate-/r/ 76.0%

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

   7. Simplified 76.0%

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

      1. clear-num 75.9%

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

      2. associate-/r* 63.3%

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

      3. add-cube-cbrt 62.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 62.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 62.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 75.0%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 75.0%

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

      8. div-inv 74.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 74.6%

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

      10. fma-define 74.6%

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

   9. Applied egg-rr 74.6%

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

   10. Taylor expanded in t around inf 59.2%

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

       1. div-sub 59.2%

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

   12. Simplified 59.2%

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

   if -9.1999999999999996e108 < a < -0.0016329999999999999

   1. Initial program 72.8%

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

      1. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around 0 65.3%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. neg-mul-1 64.9%

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

   8. Simplified 64.9%

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

   if 5.0000000000000002e75 < a

   1. Initial program 70.2%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around 0 59.7%

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

   6. Taylor expanded in t around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. *-lft-identity 58.2%

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

      3. times-frac 66.9%

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

      4. /-rgt-identity 66.9%

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

   8. Simplified 66.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+158}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -0.001633:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e+82) (not (<= z 2.55e+79)))
   (- t (* y (/ (- t x) z)))
   (+ x (/ (- t x) (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+82) || !(z <= 2.55e+79)) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.15d+82)) .or. (.not. (z <= 2.55d+79))) then
        tmp = t - (y * ((t - x) / z))
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+82) || !(z <= 2.55e+79)) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e+82) or not (z <= 2.55e+79):
		tmp = t - (y * ((t - x) / z))
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e+82) || !(z <= 2.55e+79))
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e+82) || ~((z <= 2.55e+79)))
		tmp = t - (y * ((t - x) / z));
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e+82], N[Not[LessEqual[z, 2.55e+79]], $MachinePrecision]], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000007e82 or 2.5500000000000001e79 < z

   1. Initial program 26.2%

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

      1. +-commutative 26.2%

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

      2. *-commutative 26.2%

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

      3. associate-/l* 59.7%

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

      4. fma-define 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. associate-*r/ 60.6%

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

      3. associate-*r/ 60.6%

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

      4. mul-1-neg 60.6%

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

      5. div-sub 60.6%

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

      6. mul-1-neg 60.6%

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

      7. distribute-lft-out-- 60.6%

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

      8. associate-*r/ 60.6%

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

      9. mul-1-neg 60.6%

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

      10. unsub-neg 60.6%

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

      11. distribute-rgt-out-- 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around inf 61.2%

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

      1. associate-/l* 72.7%

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

   10. Simplified 72.7%

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

   if -2.15000000000000007e82 < z < 2.5500000000000001e79

   1. Initial program 84.8%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. associate-/l* 88.7%

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

      3. distribute-lft-neg-out 88.7%

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

      4. +-commutative 88.7%

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

      5. div-sub 88.7%

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

      6. distribute-rgt-out 91.2%

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

      7. sub-neg 91.2%

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

      8. associate-/r/ 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in y around inf 84.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82} \lor \neg \left(z \leq 2.15 \cdot 10^{+79}\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.48e+82) (not (<= z 2.15e+79)))
   (- t (* y (/ (- t x) z)))
   (+ x (* y (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.48e+82) || !(z <= 2.15e+79)) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.48d+82)) .or. (.not. (z <= 2.15d+79))) then
        tmp = t - (y * ((t - x) / z))
    else
        tmp = x + (y * ((t - x) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.48e+82) || !(z <= 2.15e+79)) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.48e+82) or not (z <= 2.15e+79):
		tmp = t - (y * ((t - x) / z))
	else:
		tmp = x + (y * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.48e+82) || !(z <= 2.15e+79))
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.48e+82) || ~((z <= 2.15e+79)))
		tmp = t - (y * ((t - x) / z));
	else
		tmp = x + (y * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.48e+82], N[Not[LessEqual[z, 2.15e+79]], $MachinePrecision]], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.48e82 or 2.1500000000000002e79 < z

   1. Initial program 26.2%

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

      1. +-commutative 26.2%

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

      2. *-commutative 26.2%

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

      3. associate-/l* 59.7%

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

      4. fma-define 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. associate-*r/ 60.6%

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

      3. associate-*r/ 60.6%

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

      4. mul-1-neg 60.6%

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

      5. div-sub 60.6%

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

      6. mul-1-neg 60.6%

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

      7. distribute-lft-out-- 60.6%

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

      8. associate-*r/ 60.6%

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

      9. mul-1-neg 60.6%

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

      10. unsub-neg 60.6%

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

      11. distribute-rgt-out-- 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around inf 61.2%

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

      1. associate-/l* 72.7%

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

   10. Simplified 72.7%

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

   if -1.48e82 < z < 2.1500000000000002e79

   1. Initial program 84.8%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around inf 78.1%

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

      1. associate-*r/ 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82} \lor \neg \left(z \leq 2.15 \cdot 10^{+79}\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67} \lor \neg \left(a \leq 4.4 \cdot 10^{-40}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e-67) (not (<= a 4.4e-40)))
   (+ x (* t (/ (- y z) (- a z))))
   (- t (* y (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e-67) || !(a <= 4.4e-40)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7d-67)) .or. (.not. (a <= 4.4d-40))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t - (y * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e-67) || !(a <= 4.4e-40)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e-67) or not (a <= 4.4e-40):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7e-67) || !(a <= 4.4e-40))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7e-67) || ~((a <= 4.4e-40)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e-67], N[Not[LessEqual[a, 4.4e-40]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.0000000000000001e-67 or 4.40000000000000018e-40 < a

   1. Initial program 68.0%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 60.9%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   if -7.0000000000000001e-67 < a < 4.40000000000000018e-40

   1. Initial program 62.7%

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

      1. +-commutative 62.7%

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

      2. *-commutative 62.7%

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

      3. associate-/l* 72.8%

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

      4. fma-define 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in z around inf 73.9%

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

      1. associate--l+ 73.9%

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

      2. associate-*r/ 73.9%

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

      3. associate-*r/ 73.9%

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

      4. mul-1-neg 73.9%

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

      5. div-sub 73.9%

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

      6. mul-1-neg 73.9%

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

      7. distribute-lft-out-- 73.9%

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

      8. associate-*r/ 73.9%

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

      9. mul-1-neg 73.9%

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

      10. unsub-neg 73.9%

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

      11. distribute-rgt-out-- 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 75.8%

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

   10. Simplified 75.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67} \lor \neg \left(a \leq 4.4 \cdot 10^{-40}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-298}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-67)
   x
   (if (<= a -1.75e-298) t (if (<= a 5.2e-57) (* x (/ y z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-67) {
		tmp = x;
	} else if (a <= -1.75e-298) {
		tmp = t;
	} else if (a <= 5.2e-57) {
		tmp = x * (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 <= (-7d-67)) then
        tmp = x
    else if (a <= (-1.75d-298)) then
        tmp = t
    else if (a <= 5.2d-57) then
        tmp = x * (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 <= -7e-67) {
		tmp = x;
	} else if (a <= -1.75e-298) {
		tmp = t;
	} else if (a <= 5.2e-57) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-67:
		tmp = x
	elif a <= -1.75e-298:
		tmp = t
	elif a <= 5.2e-57:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-67)
		tmp = x;
	elseif (a <= -1.75e-298)
		tmp = t;
	elseif (a <= 5.2e-57)
		tmp = Float64(x * 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 <= -7e-67)
		tmp = x;
	elseif (a <= -1.75e-298)
		tmp = t;
	elseif (a <= 5.2e-57)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-67], x, If[LessEqual[a, -1.75e-298], t, If[LessEqual[a, 5.2e-57], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000001e-67 or 5.19999999999999971e-57 < a

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-/l* 87.5%

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

      4. fma-define 87.6%

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

   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 inf 41.1%

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

   if -7.0000000000000001e-67 < a < -1.7499999999999999e-298

   1. Initial program 63.6%

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

      1. associate-/l* 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in y around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-/l* 66.6%

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

      3. distribute-lft-neg-out 66.6%

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

      4. +-commutative 66.6%

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

      5. div-sub 66.6%

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

      6. distribute-rgt-out 69.1%

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

      7. sub-neg 69.1%

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

      8. associate-/r/ 71.6%

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

   7. Simplified 71.6%

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

      1. clear-num 71.6%

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

      2. associate-/r* 63.5%

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

      3. add-cube-cbrt 62.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 62.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 62.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 70.9%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 70.8%

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

      8. div-inv 70.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 70.8%

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

      10. fma-define 70.7%

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

   9. Applied egg-rr 70.7%

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

   10. Taylor expanded in z around inf 49.2%

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

   if -1.7499999999999999e-298 < a < 5.19999999999999971e-57

   1. Initial program 63.1%

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

      1. +-commutative 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-/l* 74.2%

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

      4. fma-define 74.2%

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

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   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-- 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in t around 0 42.3%

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

      1. associate-/l* 46.6%

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

   10. Simplified 46.6%

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

   11. Taylor expanded in y around inf 39.0%

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

       1. associate-/l* 43.3%

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

   13. Simplified 43.3%

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

Alternative 10: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-20} \lor \neg \left(z \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.3e-20) (not (<= z 1.6e+16)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e-20) || !(z <= 1.6e+16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.3d-20)) .or. (.not. (z <= 1.6d+16))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e-20) || !(z <= 1.6e+16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.3e-20) or not (z <= 1.6e+16):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.3e-20) || !(z <= 1.6e+16))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.3e-20) || ~((z <= 1.6e+16)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.3e-20], N[Not[LessEqual[z, 1.6e+16]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3000000000000002e-20 or 1.6e16 < z

   1. Initial program 40.8%

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

      1. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in y around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. associate-/l* 67.1%

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

      3. distribute-lft-neg-out 67.1%

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

      4. +-commutative 67.1%

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

      5. div-sub 67.1%

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

      6. distribute-rgt-out 67.1%

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

      7. sub-neg 67.1%

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

      8. associate-/r/ 69.5%

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

   7. Simplified 69.5%

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

      1. clear-num 69.4%

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

      2. associate-/r* 40.7%

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

      3. add-cube-cbrt 40.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 40.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 40.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 68.5%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 68.4%

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

      8. div-inv 68.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 68.4%

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

      10. fma-define 68.4%

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

   9. Applied egg-rr 68.4%

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

   10. Taylor expanded in t around inf 59.7%

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

       1. div-sub 59.7%

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

   12. Simplified 59.7%

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

   if -5.3000000000000002e-20 < z < 1.6e16

   1. Initial program 88.9%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in y around 0 90.8%

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

      1. mul-1-neg 90.8%

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

      2. associate-/l* 88.4%

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

      3. distribute-lft-neg-out 88.4%

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

      4. +-commutative 88.4%

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

      5. div-sub 88.4%

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

      6. distribute-rgt-out 91.6%

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

      7. sub-neg 91.6%

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

      8. associate-/r/ 93.4%

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

   7. Simplified 93.4%

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

   8. Taylor expanded in z around 0 76.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-20} \lor \neg \left(z \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-20} \lor \neg \left(z \leq 2.5 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e-20) (not (<= z 2.5e+16)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e-20) || !(z <= 2.5e+16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d-20)) .or. (.not. (z <= 2.5d+16))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e-20) || !(z <= 2.5e+16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e-20) or not (z <= 2.5e+16):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e-20) || !(z <= 2.5e+16))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e-20) || ~((z <= 2.5e+16)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e-20], N[Not[LessEqual[z, 2.5e+16]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e-20 or 2.5e16 < z

   1. Initial program 40.8%

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

      1. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in y around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. associate-/l* 67.1%

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

      3. distribute-lft-neg-out 67.1%

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

      4. +-commutative 67.1%

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

      5. div-sub 67.1%

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

      6. distribute-rgt-out 67.1%

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

      7. sub-neg 67.1%

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

      8. associate-/r/ 69.5%

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

   7. Simplified 69.5%

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

      1. clear-num 69.4%

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

      2. associate-/r* 40.7%

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

      3. add-cube-cbrt 40.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 40.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 40.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 68.5%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 68.4%

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

      8. div-inv 68.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 68.4%

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

      10. fma-define 68.4%

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

   9. Applied egg-rr 68.4%

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

   10. Taylor expanded in t around inf 59.7%

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

       1. div-sub 59.7%

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

   12. Simplified 59.7%

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

   if -2.0999999999999999e-20 < z < 2.5e16

   1. Initial program 88.9%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in z around 0 72.1%

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

      1. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-20} \lor \neg \left(z \leq 2.5 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-20} \lor \neg \left(z \leq 3 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.3e-20) (not (<= z 3e+16)))
   (* t (/ (- y z) (- a z)))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e-20) || !(z <= 3e+16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.3d-20)) .or. (.not. (z <= 3d+16))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e-20) || !(z <= 3e+16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.3e-20) or not (z <= 3e+16):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.3e-20) || !(z <= 3e+16))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.3e-20) || ~((z <= 3e+16)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.3e-20], N[Not[LessEqual[z, 3e+16]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3000000000000002e-20 or 3e16 < z

   1. Initial program 40.8%

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

      1. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in y around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. associate-/l* 67.1%

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

      3. distribute-lft-neg-out 67.1%

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

      4. +-commutative 67.1%

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

      5. div-sub 67.1%

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

      6. distribute-rgt-out 67.1%

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

      7. sub-neg 67.1%

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

      8. associate-/r/ 69.5%

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

   7. Simplified 69.5%

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

      1. clear-num 69.4%

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

      2. associate-/r* 40.7%

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

      3. add-cube-cbrt 40.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 40.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 40.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 68.5%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 68.4%

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

      8. div-inv 68.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 68.4%

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

      10. fma-define 68.4%

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

   9. Applied egg-rr 68.4%

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

   10. Taylor expanded in t around inf 59.7%

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

       1. div-sub 59.7%

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

   12. Simplified 59.7%

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

   if -5.3000000000000002e-20 < z < 3e16

   1. Initial program 88.9%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in t around inf 67.7%

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

      1. associate-/l* 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around inf 65.5%

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

      1. associate-/l* 69.4%

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

   10. Simplified 69.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-20} \lor \neg \left(z \leq 3 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.001633:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-53}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.001633)
   (+ x (/ (- t x) (/ a y)))
   (if (<= a 1.02e-53) (- t (* y (/ (- t x) z))) (+ x (* y (/ (- t x) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.001633) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 1.02e-53) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.001633d0)) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 1.02d-53) then
        tmp = t - (y * ((t - x) / z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.001633) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 1.02e-53) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.001633:
		tmp = x + ((t - x) / (a / y))
	elif a <= 1.02e-53:
		tmp = t - (y * ((t - x) / z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.001633)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 1.02e-53)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.001633)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 1.02e-53)
		tmp = t - (y * ((t - x) / z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.001633], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-53], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0016329999999999999

   1. Initial program 63.6%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in y around 0 72.5%

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

      1. mul-1-neg 72.5%

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

      2. associate-/l* 84.9%

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

      3. distribute-lft-neg-out 84.9%

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

      4. +-commutative 84.9%

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

      5. div-sub 84.9%

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

      6. distribute-rgt-out 84.9%

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

      7. sub-neg 84.9%

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

      8. associate-/r/ 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in z around 0 73.8%

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

   if -0.0016329999999999999 < a < 1.02000000000000002e-53

   1. Initial program 65.9%

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

      1. +-commutative 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-/l* 75.0%

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

      4. fma-define 75.0%

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

   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 71.9%

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

      1. associate--l+ 71.9%

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

      2. associate-*r/ 71.9%

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

      3. associate-*r/ 71.9%

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

      4. mul-1-neg 71.9%

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

      5. div-sub 72.7%

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

      6. mul-1-neg 72.7%

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

      7. distribute-lft-out-- 72.7%

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

      8. associate-*r/ 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. distribute-rgt-out-- 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in y around inf 70.7%

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

      1. associate-/l* 75.6%

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

   10. Simplified 75.6%

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

   if 1.02000000000000002e-53 < a

   1. Initial program 67.7%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in z around 0 56.0%

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

      1. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

Alternative 14: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+99}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.48e+82)
   (- t (/ (* x a) z))
   (if (<= z 3.3e+99) (+ x (* t (/ y a))) (/ x (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 3.3e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x / (z / (y - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.48d+82)) then
        tmp = t - ((x * a) / z)
    else if (z <= 3.3d+99) then
        tmp = x + (t * (y / a))
    else
        tmp = x / (z / (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 3.3e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x / (z / (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.48e+82:
		tmp = t - ((x * a) / z)
	elif z <= 3.3e+99:
		tmp = x + (t * (y / a))
	else:
		tmp = x / (z / (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.48e+82)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 3.3e+99)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x / Float64(z / Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.48e+82)
		tmp = t - ((x * a) / z);
	elseif (z <= 3.3e+99)
		tmp = x + (t * (y / a));
	else
		tmp = x / (z / (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.48e+82], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+99], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.48e82

   1. Initial program 17.8%

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

      1. +-commutative 17.8%

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

      2. *-commutative 17.8%

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

      3. associate-/l* 57.4%

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

      4. fma-define 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate-*r/ 66.6%

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

      3. associate-*r/ 66.6%

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

      4. mul-1-neg 66.6%

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

      5. div-sub 66.6%

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

      6. mul-1-neg 66.6%

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

      7. distribute-lft-out-- 66.6%

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

      8. associate-*r/ 66.6%

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

      9. mul-1-neg 66.6%

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

      10. unsub-neg 66.6%

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

      11. distribute-rgt-out-- 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in t around 0 64.9%

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

       1. *-commutative 64.9%

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

   13. Simplified 64.9%

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

   if -1.48e82 < z < 3.2999999999999999e99

   1. Initial program 85.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around inf 65.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in z around 0 50.4%

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

      1. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

   if 3.2999999999999999e99 < z

   1. Initial program 31.8%

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

      1. +-commutative 31.8%

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

      2. *-commutative 31.8%

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

      3. associate-/l* 60.2%

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

      4. fma-define 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. associate-*r/ 51.8%

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

      3. associate-*r/ 51.8%

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

      4. mul-1-neg 51.8%

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

      5. div-sub 51.8%

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

      6. mul-1-neg 51.8%

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

      7. distribute-lft-out-- 51.8%

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

      8. associate-*r/ 51.8%

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

      9. mul-1-neg 51.8%

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

      10. unsub-neg 51.8%

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

      11. distribute-rgt-out-- 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

       1. clear-num 43.1%

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

       2. un-div-inv 43.2%

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

   12. Applied egg-rr 43.2%

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

Alternative 15: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+82}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+97}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.48e+82)
   (- t (/ (* x a) z))
   (if (<= z 1.75e+97) (+ x (* t (/ y a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.75e+97) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.48d+82)) then
        tmp = t - ((x * a) / z)
    else if (z <= 1.75d+97) then
        tmp = x + (t * (y / a))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.48e+82) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.75e+97) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.48e+82:
		tmp = t - ((x * a) / z)
	elif z <= 1.75e+97:
		tmp = x + (t * (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.48e+82)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 1.75e+97)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.48e+82)
		tmp = t - ((x * a) / z);
	elseif (z <= 1.75e+97)
		tmp = x + (t * (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.48e+82], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+97], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.48e82

   1. Initial program 17.8%

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

      1. +-commutative 17.8%

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

      2. *-commutative 17.8%

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

      3. associate-/l* 57.4%

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

      4. fma-define 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate-*r/ 66.6%

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

      3. associate-*r/ 66.6%

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

      4. mul-1-neg 66.6%

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

      5. div-sub 66.6%

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

      6. mul-1-neg 66.6%

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

      7. distribute-lft-out-- 66.6%

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

      8. associate-*r/ 66.6%

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

      9. mul-1-neg 66.6%

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

      10. unsub-neg 66.6%

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

      11. distribute-rgt-out-- 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. neg-mul-1 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in t around 0 64.9%

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

       1. *-commutative 64.9%

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

   13. Simplified 64.9%

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

   if -1.48e82 < z < 1.75e97

   1. Initial program 85.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around inf 65.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in z around 0 50.4%

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

      1. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

   if 1.75e97 < z

   1. Initial program 31.8%

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

      1. +-commutative 31.8%

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

      2. *-commutative 31.8%

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

      3. associate-/l* 60.2%

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

      4. fma-define 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. associate-*r/ 51.8%

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

      3. associate-*r/ 51.8%

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

      4. mul-1-neg 51.8%

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

      5. div-sub 51.8%

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

      6. mul-1-neg 51.8%

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

      7. distribute-lft-out-- 51.8%

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

      8. associate-*r/ 51.8%

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

      9. mul-1-neg 51.8%

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

      10. unsub-neg 51.8%

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

      11. distribute-rgt-out-- 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

Alternative 16: 49.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+99}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+82)
   t
   (if (<= z 8.4e+99) (+ x (* t (/ y a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+82) {
		tmp = t;
	} else if (z <= 8.4e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.35d+82)) then
        tmp = t
    else if (z <= 8.4d+99) then
        tmp = x + (t * (y / a))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+82) {
		tmp = t;
	} else if (z <= 8.4e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+82:
		tmp = t
	elif z <= 8.4e+99:
		tmp = x + (t * (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+82)
		tmp = t;
	elseif (z <= 8.4e+99)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+82)
		tmp = t;
	elseif (z <= 8.4e+99)
		tmp = x + (t * (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+82], t, If[LessEqual[z, 8.4e+99], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35e82

   1. Initial program 17.8%

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

      1. associate-/l* 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in y around 0 22.1%

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

      1. mul-1-neg 22.1%

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

      2. associate-/l* 55.1%

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

      3. distribute-lft-neg-out 55.1%

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

      4. +-commutative 55.1%

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

      5. div-sub 55.1%

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

      6. distribute-rgt-out 55.1%

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

      7. sub-neg 55.1%

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

      8. associate-/r/ 57.4%

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

   7. Simplified 57.4%

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

      1. clear-num 57.3%

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

      2. associate-/r* 17.7%

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

      3. add-cube-cbrt 17.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 17.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 17.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 56.2%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 56.0%

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

      8. div-inv 56.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 56.0%

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

      10. fma-define 56.0%

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

   9. Applied egg-rr 56.0%

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

   10. Taylor expanded in z around inf 57.3%

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

   if -2.35e82 < z < 8.40000000000000041e99

   1. Initial program 85.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around inf 65.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in z around 0 50.4%

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

      1. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

   if 8.40000000000000041e99 < z

   1. Initial program 31.8%

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

      1. +-commutative 31.8%

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

      2. *-commutative 31.8%

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

      3. associate-/l* 60.2%

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

      4. fma-define 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. associate-*r/ 51.8%

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

      3. associate-*r/ 51.8%

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

      4. mul-1-neg 51.8%

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

      5. div-sub 51.8%

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

      6. mul-1-neg 51.8%

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

      7. distribute-lft-out-- 51.8%

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

      8. associate-*r/ 51.8%

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

      9. mul-1-neg 51.8%

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

      10. unsub-neg 51.8%

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

      11. distribute-rgt-out-- 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

Alternative 17: 45.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+82)
   t
   (if (<= z 8.2e+93) (* x (- 1.0 (/ y a))) (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+82) {
		tmp = t;
	} else if (z <= 8.2e+93) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+82)) then
        tmp = t
    else if (z <= 8.2d+93) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+82) {
		tmp = t;
	} else if (z <= 8.2e+93) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+82:
		tmp = t
	elif z <= 8.2e+93:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+82)
		tmp = t;
	elseif (z <= 8.2e+93)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+82)
		tmp = t;
	elseif (z <= 8.2e+93)
		tmp = x * (1.0 - (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+82], t, If[LessEqual[z, 8.2e+93], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999998e82

   1. Initial program 17.8%

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

      1. associate-/l* 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in y around 0 22.1%

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

      1. mul-1-neg 22.1%

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

      2. associate-/l* 55.1%

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

      3. distribute-lft-neg-out 55.1%

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

      4. +-commutative 55.1%

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

      5. div-sub 55.1%

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

      6. distribute-rgt-out 55.1%

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

      7. sub-neg 55.1%

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

      8. associate-/r/ 57.4%

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

   7. Simplified 57.4%

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

      1. clear-num 57.3%

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

      2. associate-/r* 17.7%

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

      3. add-cube-cbrt 17.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 17.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 17.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 56.2%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 56.0%

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

      8. div-inv 56.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 56.0%

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

      10. fma-define 56.0%

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

   9. Applied egg-rr 56.0%

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

   10. Taylor expanded in z around inf 57.3%

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

   if -2.39999999999999998e82 < z < 8.2000000000000002e93

   1. Initial program 85.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around 0 62.2%

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

   6. Taylor expanded in x around inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

   8. Simplified 53.1%

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

   if 8.2000000000000002e93 < z

   1. Initial program 31.8%

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

      1. +-commutative 31.8%

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

      2. *-commutative 31.8%

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

      3. associate-/l* 60.2%

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

      4. fma-define 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. associate--l+ 51.8%

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

      2. associate-*r/ 51.8%

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

      3. associate-*r/ 51.8%

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

      4. mul-1-neg 51.8%

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

      5. div-sub 51.8%

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

      6. mul-1-neg 51.8%

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

      7. distribute-lft-out-- 51.8%

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

      8. associate-*r/ 51.8%

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

      9. mul-1-neg 51.8%

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

      10. unsub-neg 51.8%

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

      11. distribute-rgt-out-- 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in t around 0 24.4%

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

      1. associate-/l* 43.1%

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

   10. Simplified 43.1%

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

Alternative 18: 48.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+82) t (if (<= z 1.4e+17) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+82) {
		tmp = t;
	} else if (z <= 1.4e+17) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+82)) then
        tmp = t
    else if (z <= 1.4d+17) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+82) {
		tmp = t;
	} else if (z <= 1.4e+17) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+82:
		tmp = t
	elif z <= 1.4e+17:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+82)
		tmp = t;
	elseif (z <= 1.4e+17)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+82)
		tmp = t;
	elseif (z <= 1.4e+17)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+82], t, If[LessEqual[z, 1.4e+17], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999998e82 or 1.4e17 < z

   1. Initial program 33.2%

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

      1. associate-/l* 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. associate-/l* 62.0%

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

      3. distribute-lft-neg-out 62.0%

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

      4. +-commutative 62.0%

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

      5. div-sub 62.0%

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

      6. distribute-rgt-out 62.0%

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

      7. sub-neg 62.0%

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

      8. associate-/r/ 65.0%

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

   7. Simplified 65.0%

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

      1. clear-num 65.0%

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

      2. associate-/r* 33.1%

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

      3. add-cube-cbrt 32.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 32.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 32.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 64.0%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 63.9%

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

      8. div-inv 63.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 63.9%

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

      10. fma-define 64.0%

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

   9. Applied egg-rr 64.0%

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

   10. Taylor expanded in z around inf 44.0%

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

   if -2.39999999999999998e82 < z < 1.4e17

   1. Initial program 85.3%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around 0 64.7%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   8. Simplified 55.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+82) t (if (<= z 6.5e+16) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+82) {
		tmp = t;
	} else if (z <= 6.5e+16) {
		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 <= (-1.95d+82)) then
        tmp = t
    else if (z <= 6.5d+16) 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 <= -1.95e+82) {
		tmp = t;
	} else if (z <= 6.5e+16) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+82:
		tmp = t
	elif z <= 6.5e+16:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+82)
		tmp = t;
	elseif (z <= 6.5e+16)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+82)
		tmp = t;
	elseif (z <= 6.5e+16)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+82], t, If[LessEqual[z, 6.5e+16], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999988e82 or 6.5e16 < z

   1. Initial program 33.2%

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

      1. associate-/l* 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. associate-/l* 62.0%

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

      3. distribute-lft-neg-out 62.0%

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

      4. +-commutative 62.0%

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

      5. div-sub 62.0%

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

      6. distribute-rgt-out 62.0%

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

      7. sub-neg 62.0%

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

      8. associate-/r/ 65.0%

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

   7. Simplified 65.0%

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

      1. clear-num 65.0%

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

      2. associate-/r* 33.1%

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

      3. add-cube-cbrt 32.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

      4. pow3 32.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

      5. +-commutative 32.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

      6. associate-/r* 64.0%

         \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

      7. clear-num 63.9%

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

      8. div-inv 63.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

      9. clear-num 63.9%

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

      10. fma-define 64.0%

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

   9. Applied egg-rr 64.0%

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

   10. Taylor expanded in z around inf 44.0%

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

   if -1.94999999999999988e82 < z < 6.5e16

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-/l* 92.0%

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

      4. fma-define 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in a around inf 38.7%

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

Alternative 20: 24.9% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 65.8%

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

   1. associate-/l* 79.8%

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

3. Simplified 79.8%

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

5. Taylor expanded in y around 0 68.5%

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

   1. mul-1-neg 68.5%

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

   2. associate-/l* 78.2%

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

   3. distribute-lft-neg-out 78.2%

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

   4. +-commutative 78.2%

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

   5. div-sub 78.2%

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

   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/ 81.9%

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

7. Simplified 81.9%

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

   1. clear-num 81.9%

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

   2. associate-/r* 65.7%

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

   3. add-cube-cbrt 64.9%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right) \cdot \sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}} \]

   4. pow3 64.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}}\right)}^{3}} \]

   5. +-commutative 64.9%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}} + x}}\right)}^{3} \]

   6. associate-/r* 80.8%

      \[\leadsto {\left(\sqrt[3]{\frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} + x}\right)}^{3} \]

   7. clear-num 80.7%

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

   8. div-inv 80.5%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}} + x}\right)}^{3} \]

   9. clear-num 80.7%

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

   10. fma-define 80.7%

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

9. Applied egg-rr 80.7%

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

10. Taylor expanded in z around inf 21.7%

    \[\leadsto \color{blue}{t} \]
11. Add Preprocessing

Developer Target 1: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (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 - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (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 - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (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[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))