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

Percentage Accurate: 67.8% → 89.0%

Time: 14.4s

Alternatives: 19

Speedup: 0.6×

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: 67.8% 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: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{1}{\frac{\frac{z}{t - x}}{a - y}}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ 1.0 (/ (/ z (- t x)) (- a y))))))
   (if (<= z -6.8e+137)
     t_1
     (if (<= z 3.1e+157) (+ x (/ (- t x) (/ (- a z) (- y z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (1.0 / ((z / (t - x)) / (a - y)));
	double tmp;
	if (z <= -6.8e+137) {
		tmp = t_1;
	} else if (z <= 3.1e+157) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (1.0d0 / ((z / (t - x)) / (a - y)))
    if (z <= (-6.8d+137)) then
        tmp = t_1
    else if (z <= 3.1d+157) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (1.0 / ((z / (t - x)) / (a - y)));
	double tmp;
	if (z <= -6.8e+137) {
		tmp = t_1;
	} else if (z <= 3.1e+157) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (1.0 / ((z / (t - x)) / (a - y)))
	tmp = 0
	if z <= -6.8e+137:
		tmp = t_1
	elif z <= 3.1e+157:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(1.0 / Float64(Float64(z / Float64(t - x)) / Float64(a - y))))
	tmp = 0.0
	if (z <= -6.8e+137)
		tmp = t_1;
	elseif (z <= 3.1e+157)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (1.0 / ((z / (t - x)) / (a - y)));
	tmp = 0.0;
	if (z <= -6.8e+137)
		tmp = t_1;
	elseif (z <= 3.1e+157)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(1.0 / N[(N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+137], t$95$1, If[LessEqual[z, 3.1e+157], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.79999999999999973e137 or 3.0999999999999997e157 < z

   1. Initial program 21.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 61.0%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 61.0%

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

      1. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{1}{\color{blue}{\frac{z}{\left(t - x\right) \cdot \left(y - a\right)}}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z}{\left(t - x\right) \cdot \left(y - a\right)}\right)}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(1, \left(\frac{\frac{z}{t - x}}{\color{blue}{y - a}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{z}{t - x}\right), \color{blue}{\left(y - a\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{y} - a\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(y - a\right)\right)\right)\right) \]

      7. --lowering--.f64 94.2%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{a}\right)\right)\right)\right) \]

   7. Applied egg-rr 94.2%

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

   if -6.79999999999999973e137 < z < 3.0999999999999997e157

   1. Initial program 84.7%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{t \cdot t - x \cdot x}{t + x}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - z}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{\frac{t \cdot t - x \cdot x}{t + x}}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{t - x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \left(t - x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      9. --lowering--.f64 84.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   4. Applied egg-rr 84.7%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - z}{1} \cdot \left(t - x\right)}{\color{blue}{a} - z}\right)\right) \]

      2. /-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      11. --lowering--.f64 93.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 93.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;t + \frac{1}{\frac{\frac{z}{t - x}}{a - y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{1}{\frac{\frac{z}{t - x}}{a - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 42.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t - x\right) \cdot y}{a}\\ t_2 := x - t \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4200000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- t x) y) a)) (t_2 (- x (* t (/ z a)))))
   (if (<= a -3.6e+43)
     t_2
     (if (<= a -3.7e-52)
       t_1
       (if (<= a -4.6e-284)
         t
         (if (<= a 5e-145)
           (* x (/ (- y a) z))
           (if (<= a 4200000000000.0) t (if (<= a 2.7e+107) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) * y) / a;
	double t_2 = x - (t * (z / a));
	double tmp;
	if (a <= -3.6e+43) {
		tmp = t_2;
	} else if (a <= -3.7e-52) {
		tmp = t_1;
	} else if (a <= -4.6e-284) {
		tmp = t;
	} else if (a <= 5e-145) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4200000000000.0) {
		tmp = t;
	} else if (a <= 2.7e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t - x) * y) / a
    t_2 = x - (t * (z / a))
    if (a <= (-3.6d+43)) then
        tmp = t_2
    else if (a <= (-3.7d-52)) then
        tmp = t_1
    else if (a <= (-4.6d-284)) then
        tmp = t
    else if (a <= 5d-145) then
        tmp = x * ((y - a) / z)
    else if (a <= 4200000000000.0d0) then
        tmp = t
    else if (a <= 2.7d+107) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) * y) / a;
	double t_2 = x - (t * (z / a));
	double tmp;
	if (a <= -3.6e+43) {
		tmp = t_2;
	} else if (a <= -3.7e-52) {
		tmp = t_1;
	} else if (a <= -4.6e-284) {
		tmp = t;
	} else if (a <= 5e-145) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4200000000000.0) {
		tmp = t;
	} else if (a <= 2.7e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((t - x) * y) / a
	t_2 = x - (t * (z / a))
	tmp = 0
	if a <= -3.6e+43:
		tmp = t_2
	elif a <= -3.7e-52:
		tmp = t_1
	elif a <= -4.6e-284:
		tmp = t
	elif a <= 5e-145:
		tmp = x * ((y - a) / z)
	elif a <= 4200000000000.0:
		tmp = t
	elif a <= 2.7e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) * y) / a)
	t_2 = Float64(x - Float64(t * Float64(z / a)))
	tmp = 0.0
	if (a <= -3.6e+43)
		tmp = t_2;
	elseif (a <= -3.7e-52)
		tmp = t_1;
	elseif (a <= -4.6e-284)
		tmp = t;
	elseif (a <= 5e-145)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 4200000000000.0)
		tmp = t;
	elseif (a <= 2.7e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((t - x) * y) / a;
	t_2 = x - (t * (z / a));
	tmp = 0.0;
	if (a <= -3.6e+43)
		tmp = t_2;
	elseif (a <= -3.7e-52)
		tmp = t_1;
	elseif (a <= -4.6e-284)
		tmp = t;
	elseif (a <= 5e-145)
		tmp = x * ((y - a) / z);
	elseif (a <= 4200000000000.0)
		tmp = t;
	elseif (a <= 2.7e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+43], t$95$2, If[LessEqual[a, -3.7e-52], t$95$1, If[LessEqual[a, -4.6e-284], t, If[LessEqual[a, 5e-145], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4200000000000.0], t, If[LessEqual[a, 2.7e+107], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6000000000000001e43 or 2.7000000000000001e107 < a

   1. Initial program 66.7%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 57.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 57.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 54.8%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 60.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 60.5%

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

   if -3.6000000000000001e43 < a < -3.6999999999999997e-52 or 4.2e12 < a < 2.7000000000000001e107

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 54.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 54.6%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right) \]

      3. --lowering--.f64 48.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right) \]

   8. Simplified 48.6%

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

   if -3.6999999999999997e-52 < a < -4.6e-284 or 4.9999999999999998e-145 < a < 4.2e12

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 41.6%

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

   if -4.6e-284 < a < 4.9999999999999998e-145

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 88.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 88.3%

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

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. div-sub N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{a - y}{z}\right)}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot \left(a - y\right)}{\color{blue}{z}}\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot a - -1 \cdot y}{z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot a - -1 \cdot y\right), \color{blue}{z}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(a\right)\right) - -1 \cdot y\right), z\right)\right) \]

      10. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(a\right)\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot y\right), z\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(a\right)\right) + 1 \cdot y\right), z\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(a\right)\right) + y\right), z\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\mathsf{neg}\left(a\right)\right), y\right), z\right)\right) \]

      14. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - a\right), y\right), z\right)\right) \]

      15. --lowering--.f64 51.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, a\right), y\right), z\right)\right) \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{x \cdot \frac{\left(0 - a\right) + y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-52}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4200000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+107}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+107}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ z a)))))
   (if (<= a -8e-57)
     t_1
     (if (<= a -4.7e-284)
       t
       (if (<= a 3e-144)
         (/ (* x (- y a)) z)
         (if (<= a 2.7e+107) (+ t (* a (/ t z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (z / a));
	double tmp;
	if (a <= -8e-57) {
		tmp = t_1;
	} else if (a <= -4.7e-284) {
		tmp = t;
	} else if (a <= 3e-144) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 2.7e+107) {
		tmp = t + (a * (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (z / a))
    if (a <= (-8d-57)) then
        tmp = t_1
    else if (a <= (-4.7d-284)) then
        tmp = t
    else if (a <= 3d-144) then
        tmp = (x * (y - a)) / z
    else if (a <= 2.7d+107) then
        tmp = t + (a * (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (z / a));
	double tmp;
	if (a <= -8e-57) {
		tmp = t_1;
	} else if (a <= -4.7e-284) {
		tmp = t;
	} else if (a <= 3e-144) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 2.7e+107) {
		tmp = t + (a * (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (z / a))
	tmp = 0
	if a <= -8e-57:
		tmp = t_1
	elif a <= -4.7e-284:
		tmp = t
	elif a <= 3e-144:
		tmp = (x * (y - a)) / z
	elif a <= 2.7e+107:
		tmp = t + (a * (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(z / a)))
	tmp = 0.0
	if (a <= -8e-57)
		tmp = t_1;
	elseif (a <= -4.7e-284)
		tmp = t;
	elseif (a <= 3e-144)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 2.7e+107)
		tmp = Float64(t + Float64(a * Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (z / a));
	tmp = 0.0;
	if (a <= -8e-57)
		tmp = t_1;
	elseif (a <= -4.7e-284)
		tmp = t;
	elseif (a <= 3e-144)
		tmp = (x * (y - a)) / z;
	elseif (a <= 2.7e+107)
		tmp = t + (a * (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-57], t$95$1, If[LessEqual[a, -4.7e-284], t, If[LessEqual[a, 3e-144], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.7e+107], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.99999999999999964e-57 or 2.7000000000000001e107 < a

   1. Initial program 69.7%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 53.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 53.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 49.6%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 54.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 54.2%

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

   if -7.99999999999999964e-57 < a < -4.70000000000000022e-284

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 38.5%

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

   if -4.70000000000000022e-284 < a < 2.9999999999999999e-144

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 88.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 88.3%

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

   6. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - a\right)\right), \color{blue}{z}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - a\right)\right), z\right) \]

      3. --lowering--.f64 47.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, a\right)\right), z\right) \]

   8. Simplified 47.3%

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

   if 2.9999999999999999e-144 < a < 2.7000000000000001e107

   1. Initial program 72.9%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 34.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 34.3%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{t \cdot z}{a - z}\right) \]

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(\left(a - z\right)\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot t\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{neg.f64}\left(\left(a - z\right)\right)\right) \]

      7. --lowering--.f64 22.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   8. Simplified 22.5%

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

   9. Taylor expanded in z around inf

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

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot t}{z}\right)}\right) \]

       2. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(t, \left(a \cdot \color{blue}{\frac{t}{z}}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

       4. /-lowering-/.f64 36.7%

          \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 36.7%

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

Alternative 4: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-94}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -2.8e-15)
     t_1
     (if (<= z -1.9e-94)
       (* (- t x) (/ y (- a z)))
       (if (<= z 1.65e+25) (+ x (/ (- t x) (/ a (- y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -2.8e-15) {
		tmp = t_1;
	} else if (z <= -1.9e-94) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.65e+25) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * ((a - y) / z))
    if (z <= (-2.8d-15)) then
        tmp = t_1
    else if (z <= (-1.9d-94)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.65d+25) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -2.8e-15) {
		tmp = t_1;
	} else if (z <= -1.9e-94) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.65e+25) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -2.8e-15:
		tmp = t_1
	elif z <= -1.9e-94:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.65e+25:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -2.8e-15)
		tmp = t_1;
	elseif (z <= -1.9e-94)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.65e+25)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -2.8e-15)
		tmp = t_1;
	elseif (z <= -1.9e-94)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.65e+25)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-15], t$95$1, If[LessEqual[z, -1.9e-94], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+25], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.80000000000000014e-15 or 1.6500000000000001e25 < z

   1. Initial program 42.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 62.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 62.3%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 80.5%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 80.5%

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

   if -2.80000000000000014e-15 < z < -1.9e-94

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 78.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 78.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 82.5%

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

   if -1.9e-94 < z < 1.6500000000000001e25

   1. Initial program 92.5%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{t \cdot t - x \cdot x}{t + x}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - z}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{\frac{t \cdot t - x \cdot x}{t + x}}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{t - x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \left(t - x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      9. --lowering--.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   4. Applied egg-rr 92.5%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - z}{1} \cdot \left(t - x\right)}{\color{blue}{a} - z}\right)\right) \]

      2. /-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      11. --lowering--.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y - z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 82.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   9. Simplified 82.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-94}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-97}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ a z)))))
   (if (<= z -5.6e-15)
     t_1
     (if (<= z -2.6e-97)
       (* (- t x) (/ y (- a z)))
       (if (<= z 1.8e+38) (+ x (/ (- t x) (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -5.6e-15) {
		tmp = t_1;
	} else if (z <= -2.6e-97) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.8e+38) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * (a / z))
    if (z <= (-5.6d-15)) then
        tmp = t_1
    else if (z <= (-2.6d-97)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.8d+38) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -5.6e-15) {
		tmp = t_1;
	} else if (z <= -2.6e-97) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.8e+38) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * (a / z))
	tmp = 0
	if z <= -5.6e-15:
		tmp = t_1
	elif z <= -2.6e-97:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.8e+38:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(a / z)))
	tmp = 0.0
	if (z <= -5.6e-15)
		tmp = t_1;
	elseif (z <= -2.6e-97)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.8e+38)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * (a / z));
	tmp = 0.0;
	if (z <= -5.6e-15)
		tmp = t_1;
	elseif (z <= -2.6e-97)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.8e+38)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-15], t$95$1, If[LessEqual[z, -2.6e-97], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+38], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000028e-15 or 1.79999999999999985e38 < z

   1. Initial program 42.0%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 62.0%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 62.0%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t - x\right)\right), z\right)\right) \]

      7. --lowering--.f64 46.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(t, x\right)\right), z\right)\right) \]

   8. Simplified 46.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{\left(t - x\right) \cdot a}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{a}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 55.5%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 55.5%

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

   if -5.60000000000000028e-15 < z < -2.60000000000000007e-97

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 78.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 78.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 82.5%

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

   if -2.60000000000000007e-97 < z < 1.79999999999999985e38

   1. Initial program 92.6%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{t \cdot t - x \cdot x}{t + x}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - z}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{\frac{t \cdot t - x \cdot x}{t + x}}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{t - x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \left(t - x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      9. --lowering--.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   4. Applied egg-rr 92.5%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - z}{1} \cdot \left(t - x\right)}{\color{blue}{a} - z}\right)\right) \]

      2. /-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      11. --lowering--.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 77.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   9. Simplified 77.9%

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

Alternative 6: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-133}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ a z)))))
   (if (<= z -1.02e-13)
     t_1
     (if (<= z -2.8e-133)
       (* (- t x) (/ y (- a z)))
       (if (<= z 1.4e+34) (+ x (/ (* (- t x) y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -1.02e-13) {
		tmp = t_1;
	} else if (z <= -2.8e-133) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.4e+34) {
		tmp = x + (((t - x) * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * (a / z))
    if (z <= (-1.02d-13)) then
        tmp = t_1
    else if (z <= (-2.8d-133)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.4d+34) then
        tmp = x + (((t - x) * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -1.02e-13) {
		tmp = t_1;
	} else if (z <= -2.8e-133) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.4e+34) {
		tmp = x + (((t - x) * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * (a / z))
	tmp = 0
	if z <= -1.02e-13:
		tmp = t_1
	elif z <= -2.8e-133:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.4e+34:
		tmp = x + (((t - x) * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(a / z)))
	tmp = 0.0
	if (z <= -1.02e-13)
		tmp = t_1;
	elseif (z <= -2.8e-133)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.4e+34)
		tmp = Float64(x + Float64(Float64(Float64(t - x) * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * (a / z));
	tmp = 0.0;
	if (z <= -1.02e-13)
		tmp = t_1;
	elseif (z <= -2.8e-133)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.4e+34)
		tmp = x + (((t - x) * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e-13], t$95$1, If[LessEqual[z, -2.8e-133], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+34], N[(x + N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0199999999999999e-13 or 1.40000000000000004e34 < z

   1. Initial program 42.0%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 62.0%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 62.0%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t - x\right)\right), z\right)\right) \]

      7. --lowering--.f64 46.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(t, x\right)\right), z\right)\right) \]

   8. Simplified 46.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{\left(t - x\right) \cdot a}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{a}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 55.5%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 55.5%

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

   if -1.0199999999999999e-13 < z < -2.7999999999999999e-133

   1. Initial program 86.7%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 67.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 67.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 77.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 77.0%

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

   if -2.7999999999999999e-133 < z < 1.40000000000000004e34

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right)\right) \]

      4. --lowering--.f64 73.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right)\right) \]

   5. Simplified 73.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-13}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-133}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-129}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.95e-13)
   (* y (/ (- t x) (- a z)))
   (if (<= y -1.5e-129)
     (- x (* t (/ z a)))
     (if (<= y 3.3e-96) (+ t (* (- t x) (/ a z))) (* (- t x) (/ y (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.95e-13) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -1.5e-129) {
		tmp = x - (t * (z / a));
	} else if (y <= 3.3e-96) {
		tmp = t + ((t - x) * (a / z));
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.95d-13)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= (-1.5d-129)) then
        tmp = x - (t * (z / a))
    else if (y <= 3.3d-96) then
        tmp = t + ((t - x) * (a / z))
    else
        tmp = (t - x) * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.95e-13) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -1.5e-129) {
		tmp = x - (t * (z / a));
	} else if (y <= 3.3e-96) {
		tmp = t + ((t - x) * (a / z));
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.95e-13:
		tmp = y * ((t - x) / (a - z))
	elif y <= -1.5e-129:
		tmp = x - (t * (z / a))
	elif y <= 3.3e-96:
		tmp = t + ((t - x) * (a / z))
	else:
		tmp = (t - x) * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.95e-13)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= -1.5e-129)
		tmp = Float64(x - Float64(t * Float64(z / a)));
	elseif (y <= 3.3e-96)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(a / z)));
	else
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.95e-13)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= -1.5e-129)
		tmp = x - (t * (z / a));
	elseif (y <= 3.3e-96)
		tmp = t + ((t - x) * (a / z));
	else
		tmp = (t - x) * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.95e-13], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-129], N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-96], N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.95000000000000002e-13

   1. Initial program 66.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 53.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 53.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), y\right) \]

      6. --lowering--.f64 69.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), y\right) \]

   7. Applied egg-rr 69.8%

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

   if -1.95000000000000002e-13 < y < -1.4999999999999999e-129

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 54.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 54.4%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 49.8%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 53.1%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 53.1%

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

   if -1.4999999999999999e-129 < y < 3.2999999999999999e-96

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 51.9%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 51.9%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t - x\right)\right), z\right)\right) \]

      7. --lowering--.f64 52.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(t, x\right)\right), z\right)\right) \]

   8. Simplified 52.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{\left(t - x\right) \cdot a}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{a}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 58.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 58.1%

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

   if 3.2999999999999999e-96 < y

   1. Initial program 80.1%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 63.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 63.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 70.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 70.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-129}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5e-13)
   (* y (/ (- t x) (- a z)))
   (if (<= y -5e-155)
     (- x (* t (/ z a)))
     (if (<= y 4e-82) t (* (- t x) (/ y (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e-13) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -5e-155) {
		tmp = x - (t * (z / a));
	} else if (y <= 4e-82) {
		tmp = t;
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5d-13)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= (-5d-155)) then
        tmp = x - (t * (z / a))
    else if (y <= 4d-82) then
        tmp = t
    else
        tmp = (t - x) * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e-13) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= -5e-155) {
		tmp = x - (t * (z / a));
	} else if (y <= 4e-82) {
		tmp = t;
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5e-13:
		tmp = y * ((t - x) / (a - z))
	elif y <= -5e-155:
		tmp = x - (t * (z / a))
	elif y <= 4e-82:
		tmp = t
	else:
		tmp = (t - x) * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5e-13)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= -5e-155)
		tmp = Float64(x - Float64(t * Float64(z / a)));
	elseif (y <= 4e-82)
		tmp = t;
	else
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5e-13)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= -5e-155)
		tmp = x - (t * (z / a));
	elseif (y <= 4e-82)
		tmp = t;
	else
		tmp = (t - x) * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5e-13], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-155], N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-82], t, N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9999999999999999e-13

   1. Initial program 66.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 53.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 53.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), y\right) \]

      6. --lowering--.f64 69.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), y\right) \]

   7. Applied egg-rr 69.8%

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

   if -4.9999999999999999e-13 < y < -4.9999999999999999e-155

   1. Initial program 81.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 56.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 56.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 50.0%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 52.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 52.9%

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

   if -4.9999999999999999e-155 < y < 4e-82

   1. Initial program 64.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 46.2%

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

   if 4e-82 < y

   1. Initial program 79.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 65.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 73.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 73.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -2.5e-11)
     t_1
     (if (<= y -2.4e-153) (- x (* t (/ z a))) (if (<= y 2.5e-82) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -2.5e-11) {
		tmp = t_1;
	} else if (y <= -2.4e-153) {
		tmp = x - (t * (z / a));
	} else if (y <= 2.5e-82) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-2.5d-11)) then
        tmp = t_1
    else if (y <= (-2.4d-153)) then
        tmp = x - (t * (z / a))
    else if (y <= 2.5d-82) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -2.5e-11) {
		tmp = t_1;
	} else if (y <= -2.4e-153) {
		tmp = x - (t * (z / a));
	} else if (y <= 2.5e-82) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -2.5e-11:
		tmp = t_1
	elif y <= -2.4e-153:
		tmp = x - (t * (z / a))
	elif y <= 2.5e-82:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.5e-11)
		tmp = t_1;
	elseif (y <= -2.4e-153)
		tmp = Float64(x - Float64(t * Float64(z / a)));
	elseif (y <= 2.5e-82)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -2.5e-11)
		tmp = t_1;
	elseif (y <= -2.4e-153)
		tmp = x - (t * (z / a));
	elseif (y <= 2.5e-82)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-11], t$95$1, If[LessEqual[y, -2.4e-153], N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-82], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000009e-11 or 2.4999999999999999e-82 < y

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 60.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 71.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 71.1%

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

   if -2.50000000000000009e-11 < y < -2.4000000000000002e-153

   1. Initial program 81.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 56.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 56.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 50.0%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 52.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 52.9%

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

   if -2.4000000000000002e-153 < y < 2.4999999999999999e-82

   1. Initial program 64.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 46.2%

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

Alternative 10: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -1.02e+138)
     t_1
     (if (<= z 2.3e+153) (+ x (/ (- t x) (/ (- a z) (- y z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -1.02e+138) {
		tmp = t_1;
	} else if (z <= 2.3e+153) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * ((a - y) / z))
    if (z <= (-1.02d+138)) then
        tmp = t_1
    else if (z <= 2.3d+153) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -1.02e+138) {
		tmp = t_1;
	} else if (z <= 2.3e+153) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -1.02e+138:
		tmp = t_1
	elif z <= 2.3e+153:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -1.02e+138)
		tmp = t_1;
	elseif (z <= 2.3e+153)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -1.02e+138)
		tmp = t_1;
	elseif (z <= 2.3e+153)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+138], t$95$1, If[LessEqual[z, 2.3e+153], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e138 or 2.3000000000000001e153 < z

   1. Initial program 21.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 61.0%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 61.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 94.0%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 94.0%

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

   if -1.02e138 < z < 2.3000000000000001e153

   1. Initial program 84.7%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{t \cdot t - x \cdot x}{t + x}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - z}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{\frac{t \cdot t - x \cdot x}{t + x}}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{t - x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \left(t - x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      9. --lowering--.f64 84.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   4. Applied egg-rr 84.7%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - z}{1} \cdot \left(t - x\right)}{\color{blue}{a} - z}\right)\right) \]

      2. /-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      11. --lowering--.f64 93.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 93.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+138}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+129}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -6.7e+137)
     t_1
     (if (<= z 3.4e+129) (+ x (* (- y z) (/ (- t x) (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -6.7e+137) {
		tmp = t_1;
	} else if (z <= 3.4e+129) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * ((a - y) / z))
    if (z <= (-6.7d+137)) then
        tmp = t_1
    else if (z <= 3.4d+129) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -6.7e+137) {
		tmp = t_1;
	} else if (z <= 3.4e+129) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -6.7e+137:
		tmp = t_1
	elif z <= 3.4e+129:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -6.7e+137)
		tmp = t_1;
	elseif (z <= 3.4e+129)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -6.7e+137)
		tmp = t_1;
	elseif (z <= 3.4e+129)
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.7e+137], t$95$1, If[LessEqual[z, 3.4e+129], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6999999999999999e137 or 3.40000000000000018e129 < z

   1. Initial program 24.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 63.1%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 63.1%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 94.3%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 94.3%

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

   if -6.6999999999999999e137 < z < 3.40000000000000018e129

   1. Initial program 85.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{a - z} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), \left(y - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right)\right)\right) \]

      7. --lowering--.f64 91.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 91.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+137}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+129}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+129}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.85e-15)
   t
   (if (<= z 7.5e-42)
     (/ (* (- t x) y) a)
     (if (<= z 2.1e+129) (- x (* t (/ z a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.85e-15) {
		tmp = t;
	} else if (z <= 7.5e-42) {
		tmp = ((t - x) * y) / a;
	} else if (z <= 2.1e+129) {
		tmp = x - (t * (z / 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 <= (-2.85d-15)) then
        tmp = t
    else if (z <= 7.5d-42) then
        tmp = ((t - x) * y) / a
    else if (z <= 2.1d+129) then
        tmp = x - (t * (z / 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 <= -2.85e-15) {
		tmp = t;
	} else if (z <= 7.5e-42) {
		tmp = ((t - x) * y) / a;
	} else if (z <= 2.1e+129) {
		tmp = x - (t * (z / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.85e-15:
		tmp = t
	elif z <= 7.5e-42:
		tmp = ((t - x) * y) / a
	elif z <= 2.1e+129:
		tmp = x - (t * (z / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.85e-15)
		tmp = t;
	elseif (z <= 7.5e-42)
		tmp = Float64(Float64(Float64(t - x) * y) / a);
	elseif (z <= 2.1e+129)
		tmp = Float64(x - Float64(t * Float64(z / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.85e-15)
		tmp = t;
	elseif (z <= 7.5e-42)
		tmp = ((t - x) * y) / a;
	elseif (z <= 2.1e+129)
		tmp = x - (t * (z / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.85e-15], t, If[LessEqual[z, 7.5e-42], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.1e+129], N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8500000000000002e-15 or 2.09999999999999997e129 < z

   1. Initial program 37.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 50.5%

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

   if -2.8500000000000002e-15 < z < 7.49999999999999972e-42

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 57.7%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right) \]

      3. --lowering--.f64 43.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right) \]

   8. Simplified 43.5%

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

   if 7.49999999999999972e-42 < z < 2.09999999999999997e129

   1. Initial program 71.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 49.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 49.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 39.4%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 44.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 44.6%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+129}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -9e+56) t_1 (if (<= y -1.35e-154) x (if (<= y 6.6e-60) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -9e+56) {
		tmp = t_1;
	} else if (y <= -1.35e-154) {
		tmp = x;
	} else if (y <= 6.6e-60) {
		tmp = t;
	} 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 / (a - z))
    if (y <= (-9d+56)) then
        tmp = t_1
    else if (y <= (-1.35d-154)) then
        tmp = x
    else if (y <= 6.6d-60) then
        tmp = t
    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 / (a - z));
	double tmp;
	if (y <= -9e+56) {
		tmp = t_1;
	} else if (y <= -1.35e-154) {
		tmp = x;
	} else if (y <= 6.6e-60) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -9e+56:
		tmp = t_1
	elif y <= -1.35e-154:
		tmp = x
	elif y <= 6.6e-60:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -9e+56)
		tmp = t_1;
	elseif (y <= -1.35e-154)
		tmp = x;
	elseif (y <= 6.6e-60)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -9e+56)
		tmp = t_1;
	elseif (y <= -1.35e-154)
		tmp = x;
	elseif (y <= 6.6e-60)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+56], t$95$1, If[LessEqual[y, -1.35e-154], x, If[LessEqual[y, 6.6e-60], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000006e56 or 6.5999999999999996e-60 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 63.6%

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

   6. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      4. --lowering--.f64 40.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 40.2%

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

   if -9.0000000000000006e56 < y < -1.34999999999999995e-154

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 42.5%

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

   if -1.34999999999999995e-154 < y < 6.5999999999999996e-60

   1. Initial program 66.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 45.4%

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

Alternative 14: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ a z)))))
   (if (<= z -5.6e+76)
     t_1
     (if (<= z 2.25e+36) (+ x (/ (- t x) (/ a (- y z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -5.6e+76) {
		tmp = t_1;
	} else if (z <= 2.25e+36) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * (a / z))
    if (z <= (-5.6d+76)) then
        tmp = t_1
    else if (z <= 2.25d+36) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -5.6e+76) {
		tmp = t_1;
	} else if (z <= 2.25e+36) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * (a / z))
	tmp = 0
	if z <= -5.6e+76:
		tmp = t_1
	elif z <= 2.25e+36:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(a / z)))
	tmp = 0.0
	if (z <= -5.6e+76)
		tmp = t_1;
	elseif (z <= 2.25e+36)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * (a / z));
	tmp = 0.0;
	if (z <= -5.6e+76)
		tmp = t_1;
	elseif (z <= 2.25e+36)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+76], t$95$1, If[LessEqual[z, 2.25e+36], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5999999999999997e76 or 2.24999999999999998e36 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 63.1%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 63.1%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t - x\right)\right), z\right)\right) \]

      7. --lowering--.f64 48.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(t, x\right)\right), z\right)\right) \]

   8. Simplified 48.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{\left(t - x\right) \cdot a}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{a}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 59.7%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 59.7%

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

   if -5.5999999999999997e76 < z < 2.24999999999999998e36

   1. Initial program 89.7%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{t \cdot t - x \cdot x}{t + x}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - z}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{\frac{t \cdot t - x \cdot x}{t + x}}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{t - x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \left(t - x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      9. --lowering--.f64 89.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   4. Applied egg-rr 89.6%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - z}{1} \cdot \left(t - x\right)}{\color{blue}{a} - z}\right)\right) \]

      2. /-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      11. --lowering--.f64 96.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y - z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 75.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   9. Simplified 75.2%

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

Alternative 15: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+34}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ a z)))))
   (if (<= z -1.3e+89)
     t_1
     (if (<= z 2.2e+34) (+ x (* (- t x) (/ (- y z) a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -1.3e+89) {
		tmp = t_1;
	} else if (z <= 2.2e+34) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * (a / z))
    if (z <= (-1.3d+89)) then
        tmp = t_1
    else if (z <= 2.2d+34) then
        tmp = x + ((t - x) * ((y - z) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * (a / z));
	double tmp;
	if (z <= -1.3e+89) {
		tmp = t_1;
	} else if (z <= 2.2e+34) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * (a / z))
	tmp = 0
	if z <= -1.3e+89:
		tmp = t_1
	elif z <= 2.2e+34:
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(a / z)))
	tmp = 0.0
	if (z <= -1.3e+89)
		tmp = t_1;
	elseif (z <= 2.2e+34)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * (a / z));
	tmp = 0.0;
	if (z <= -1.3e+89)
		tmp = t_1;
	elseif (z <= 2.2e+34)
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+89], t$95$1, If[LessEqual[z, 2.2e+34], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e89 or 2.2000000000000002e34 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 63.1%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 63.1%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t - x\right)\right), z\right)\right) \]

      7. --lowering--.f64 48.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(t, x\right)\right), z\right)\right) \]

   8. Simplified 48.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{\left(t - x\right) \cdot a}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{a}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 59.7%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 59.7%

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

   if -1.3e89 < z < 2.2000000000000002e34

   1. Initial program 89.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. fma-define N/A

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

      5. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}, x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right), x\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right), x\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right), x\right) \]

      9. --lowering--.f64 96.6%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right), x\right) \]

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in a around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{a}\right)\right)\right) \]

      6. --lowering--.f64 75.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), a\right)\right)\right) \]

   7. Simplified 75.2%

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

Alternative 16: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-53}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a (- y z))))))
   (if (<= a -1.15e+102) t_1 (if (<= a 1e-53) (* (- t x) (/ y (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -1.15e+102) {
		tmp = t_1;
	} else if (a <= 1e-53) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / (y - z)))
    if (a <= (-1.15d+102)) then
        tmp = t_1
    else if (a <= 1d-53) then
        tmp = (t - x) * (y / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -1.15e+102) {
		tmp = t_1;
	} else if (a <= 1e-53) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / (y - z)))
	tmp = 0
	if a <= -1.15e+102:
		tmp = t_1
	elif a <= 1e-53:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -1.15e+102)
		tmp = t_1;
	elseif (a <= 1e-53)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / (y - z)));
	tmp = 0.0;
	if (a <= -1.15e+102)
		tmp = t_1;
	elseif (a <= 1e-53)
		tmp = (t - x) * (y / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+102], t$95$1, If[LessEqual[a, 1e-53], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1499999999999999e102 or 1.00000000000000003e-53 < a

   1. Initial program 67.3%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{t \cdot t - x \cdot x}{t + x}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - z}{\frac{t + x}{t \cdot t - x \cdot x}}\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(\color{blue}{a}, z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t + x}{t \cdot t - x \cdot x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{\frac{t \cdot t - x \cdot x}{t + x}}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1}{t - x}\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \left(t - x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

      9. --lowering--.f64 67.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, x\right)\right)\right), \mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   4. Applied egg-rr 67.4%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - z}{1} \cdot \left(t - x\right)}{\color{blue}{a} - z}\right)\right) \]

      2. /-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      11. --lowering--.f64 88.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 88.0%

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

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y - z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 77.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   9. Simplified 77.8%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right)\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 70.6%

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

   if -1.1499999999999999e102 < a < 1.00000000000000003e-53

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 56.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 56.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 59.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 59.2%

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

Alternative 17: 42.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+107}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ z a)))))
   (if (<= a -1.15e-45) t_1 (if (<= a 2.7e+107) (+ t (* a (/ t z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (z / a));
	double tmp;
	if (a <= -1.15e-45) {
		tmp = t_1;
	} else if (a <= 2.7e+107) {
		tmp = t + (a * (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (z / a))
    if (a <= (-1.15d-45)) then
        tmp = t_1
    else if (a <= 2.7d+107) then
        tmp = t + (a * (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (z / a));
	double tmp;
	if (a <= -1.15e-45) {
		tmp = t_1;
	} else if (a <= 2.7e+107) {
		tmp = t + (a * (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (z / a))
	tmp = 0
	if a <= -1.15e-45:
		tmp = t_1
	elif a <= 2.7e+107:
		tmp = t + (a * (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(z / a)))
	tmp = 0.0
	if (a <= -1.15e-45)
		tmp = t_1;
	elseif (a <= 2.7e+107)
		tmp = Float64(t + Float64(a * Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (z / a));
	tmp = 0.0;
	if (a <= -1.15e-45)
		tmp = t_1;
	elseif (a <= 2.7e+107)
		tmp = t + (a * (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-45], t$95$1, If[LessEqual[a, 2.7e+107], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.14999999999999996e-45 or 2.7000000000000001e107 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 54.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 54.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \color{blue}{a}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 50.4%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       3. /-lowering-/.f64 55.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 55.2%

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

   if -1.14999999999999996e-45 < a < 2.7000000000000001e107

   1. Initial program 73.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{z \cdot \left(t - x\right)}{a - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(z \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right)\right) \]

      7. --lowering--.f64 25.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 25.3%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{t \cdot z}{a - z}\right) \]

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(\left(a - z\right)\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot t\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{neg.f64}\left(\left(a - z\right)\right)\right) \]

      7. --lowering--.f64 24.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   8. Simplified 24.9%

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

   9. Taylor expanded in z around inf

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

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot t}{z}\right)}\right) \]

       2. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(t, \left(a \cdot \color{blue}{\frac{t}{z}}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

       4. /-lowering-/.f64 34.7%

          \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 34.7%

       \[\leadsto \color{blue}{t + a \cdot \frac{t}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 38.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.08e-39) x (if (<= a 3e+17) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-39) {
		tmp = x;
	} else if (a <= 3e+17) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.08d-39)) then
        tmp = x
    else if (a <= 3d+17) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-39) {
		tmp = x;
	} else if (a <= 3e+17) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.08e-39:
		tmp = x
	elif a <= 3e+17:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.08e-39)
		tmp = x;
	elseif (a <= 3e+17)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.08e-39)
		tmp = x;
	elseif (a <= 3e+17)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.08e-39], x, If[LessEqual[a, 3e+17], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.08e-39 or 3e17 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 42.1%

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

   if -1.08e-39 < a < 3e17

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 36.2%

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

Alternative 19: 25.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 71.9%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 23.9%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 84.0% 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 2024161 
(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))))