Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 91.7%

Time: 14.5s

Alternatives: 20

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-243}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) (- a z)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -2e-112)
     t_1
     (if (<= t_2 1e-243) (+ t (* (- t x) (/ (- a y) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-112) {
		tmp = t_1;
	} else if (t_2 <= 1e-243) {
		tmp = t + ((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) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-2d-112)) then
        tmp = t_1
    else if (t_2 <= 1d-243) then
        tmp = t + ((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 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-112) {
		tmp = t_1;
	} else if (t_2 <= 1e-243) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -2e-112:
		tmp = t_1
	elif t_2 <= 1e-243:
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -2e-112)
		tmp = t_1;
	elseif (t_2 <= 1e-243)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -2e-112)
		tmp = t_1;
	elseif (t_2 <= 1e-243)
		tmp = t + ((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[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-112], t$95$1, If[LessEqual[t$95$2, 1e-243], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.9999999999999999e-112 or 9.99999999999999995e-244 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.4%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 94.9%

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

   4. Applied egg-rr 94.9%

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

   if -1.9999999999999999e-112 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999995e-244

   1. Initial program 12.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. distribute-rgt-out-- N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-112}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-243}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-65}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-49}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+59}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.55e+164)
     t_1
     (if (<= z -3.7e+68)
       (* x (/ y (- z a)))
       (if (<= z -1.52e-65)
         (/ (* (- y z) t) (- a z))
         (if (<= z 1.95e-49)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 1.8e+59) (/ (* y (- t x)) (- a z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.55e+164) {
		tmp = t_1;
	} else if (z <= -3.7e+68) {
		tmp = x * (y / (z - a));
	} else if (z <= -1.52e-65) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 1.95e-49) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.8e+59) {
		tmp = (y * (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 * ((y - z) / (a - z))
    if (z <= (-1.55d+164)) then
        tmp = t_1
    else if (z <= (-3.7d+68)) then
        tmp = x * (y / (z - a))
    else if (z <= (-1.52d-65)) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 1.95d-49) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.8d+59) then
        tmp = (y * (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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.55e+164) {
		tmp = t_1;
	} else if (z <= -3.7e+68) {
		tmp = x * (y / (z - a));
	} else if (z <= -1.52e-65) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 1.95e-49) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.8e+59) {
		tmp = (y * (t - x)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.55e+164:
		tmp = t_1
	elif z <= -3.7e+68:
		tmp = x * (y / (z - a))
	elif z <= -1.52e-65:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 1.95e-49:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.8e+59:
		tmp = (y * (t - x)) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.55e+164)
		tmp = t_1;
	elseif (z <= -3.7e+68)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (z <= -1.52e-65)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 1.95e-49)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.8e+59)
		tmp = Float64(Float64(y * 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 * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.55e+164)
		tmp = t_1;
	elseif (z <= -3.7e+68)
		tmp = x * (y / (z - a));
	elseif (z <= -1.52e-65)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 1.95e-49)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.8e+59)
		tmp = (y * (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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+164], t$95$1, If[LessEqual[z, -3.7e+68], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.52e-65], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-49], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+59], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5500000000000001e164 or 1.7999999999999999e59 < z

   1. Initial program 56.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 41.5%

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

   5. Simplified 41.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 66.5%

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

   7. Applied egg-rr 66.5%

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

   if -1.5500000000000001e164 < z < -3.69999999999999998e68

   1. Initial program 63.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{x \cdot y}{a - z}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot y}{a - z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{y}{a - z}}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{a - z}\right)}\right)\right) \]

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

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

      7. --lowering--.f64 73.8%

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

   8. Simplified 73.8%

      \[\leadsto \color{blue}{0 - x \cdot \frac{y}{a - z}} \]

   if -3.69999999999999998e68 < z < -1.5199999999999999e-65

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 66.2%

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

   5. Simplified 66.2%

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

   if -1.5199999999999999e-65 < z < 1.95000000000000006e-49

   1. Initial program 94.3%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 80.2%

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

   7. Simplified 80.2%

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

   if 1.95000000000000006e-49 < z < 1.7999999999999999e59

   1. Initial program 95.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 69.8%

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

   5. Simplified 69.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-65}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-49}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+59}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.35e+164)
     t_1
     (if (<= z -1.15e+78)
       (* x (/ y (- z a)))
       (if (<= z -1.8e-63)
         (/ (* (- y z) t) (- a z))
         (if (<= z 6.8e-47)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 9.6e+61) (+ x (* y (/ (- x t) z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= -1.15e+78) {
		tmp = x * (y / (z - a));
	} else if (z <= -1.8e-63) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 6.8e-47) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 9.6e+61) {
		tmp = x + (y * ((x - 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 = t * ((y - z) / (a - z))
    if (z <= (-1.35d+164)) then
        tmp = t_1
    else if (z <= (-1.15d+78)) then
        tmp = x * (y / (z - a))
    else if (z <= (-1.8d-63)) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 6.8d-47) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 9.6d+61) then
        tmp = x + (y * ((x - 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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= -1.15e+78) {
		tmp = x * (y / (z - a));
	} else if (z <= -1.8e-63) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 6.8e-47) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 9.6e+61) {
		tmp = x + (y * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.35e+164:
		tmp = t_1
	elif z <= -1.15e+78:
		tmp = x * (y / (z - a))
	elif z <= -1.8e-63:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 6.8e-47:
		tmp = x + ((t - x) * (y / a))
	elif z <= 9.6e+61:
		tmp = x + (y * ((x - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= -1.15e+78)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (z <= -1.8e-63)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 6.8e-47)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 9.6e+61)
		tmp = Float64(x + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= -1.15e+78)
		tmp = x * (y / (z - a));
	elseif (z <= -1.8e-63)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 6.8e-47)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 9.6e+61)
		tmp = x + (y * ((x - t) / 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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+164], t$95$1, If[LessEqual[z, -1.15e+78], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-63], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-47], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+61], N[(x + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.35000000000000003e164 or 9.5999999999999995e61 < z

   1. Initial program 55.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 41.9%

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

   5. Simplified 41.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 67.1%

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

   7. Applied egg-rr 67.1%

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

   if -1.35000000000000003e164 < z < -1.1500000000000001e78

   1. Initial program 63.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{x \cdot y}{a - z}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot y}{a - z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{y}{a - z}}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{a - z}\right)}\right)\right) \]

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

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

      7. --lowering--.f64 73.8%

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

   8. Simplified 73.8%

      \[\leadsto \color{blue}{0 - x \cdot \frac{y}{a - z}} \]

   if -1.1500000000000001e78 < z < -1.80000000000000004e-63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 66.2%

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

   5. Simplified 66.2%

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

   if -1.80000000000000004e-63 < z < 6.8000000000000003e-47

   1. Initial program 94.3%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 80.2%

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

   7. Simplified 80.2%

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

   if 6.8000000000000003e-47 < z < 9.5999999999999995e61

   1. Initial program 95.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 83.6%

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

   8. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 63.0%

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

   10. Simplified 63.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-51}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.4e+164)
     t_1
     (if (<= z -6.5e+77)
       (* x (/ y (- z a)))
       (if (<= z -3.55e-63)
         t_1
         (if (<= z 2.7e-51)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 2.1e+62) (+ x (* y (/ (- x t) z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.4e+164) {
		tmp = t_1;
	} else if (z <= -6.5e+77) {
		tmp = x * (y / (z - a));
	} else if (z <= -3.55e-63) {
		tmp = t_1;
	} else if (z <= 2.7e-51) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.1e+62) {
		tmp = x + (y * ((x - 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 = t * ((y - z) / (a - z))
    if (z <= (-1.4d+164)) then
        tmp = t_1
    else if (z <= (-6.5d+77)) then
        tmp = x * (y / (z - a))
    else if (z <= (-3.55d-63)) then
        tmp = t_1
    else if (z <= 2.7d-51) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 2.1d+62) then
        tmp = x + (y * ((x - 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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.4e+164) {
		tmp = t_1;
	} else if (z <= -6.5e+77) {
		tmp = x * (y / (z - a));
	} else if (z <= -3.55e-63) {
		tmp = t_1;
	} else if (z <= 2.7e-51) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.1e+62) {
		tmp = x + (y * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.4e+164:
		tmp = t_1
	elif z <= -6.5e+77:
		tmp = x * (y / (z - a))
	elif z <= -3.55e-63:
		tmp = t_1
	elif z <= 2.7e-51:
		tmp = x + ((t - x) * (y / a))
	elif z <= 2.1e+62:
		tmp = x + (y * ((x - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.4e+164)
		tmp = t_1;
	elseif (z <= -6.5e+77)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (z <= -3.55e-63)
		tmp = t_1;
	elseif (z <= 2.7e-51)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 2.1e+62)
		tmp = Float64(x + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.4e+164)
		tmp = t_1;
	elseif (z <= -6.5e+77)
		tmp = x * (y / (z - a));
	elseif (z <= -3.55e-63)
		tmp = t_1;
	elseif (z <= 2.7e-51)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 2.1e+62)
		tmp = x + (y * ((x - t) / 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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+164], t$95$1, If[LessEqual[z, -6.5e+77], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.55e-63], t$95$1, If[LessEqual[z, 2.7e-51], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+62], N[(x + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e164 or -6.5e77 < z < -3.5500000000000001e-63 or 2.1e62 < z

   1. Initial program 63.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 46.2%

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

   5. Simplified 46.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 67.0%

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

   7. Applied egg-rr 67.0%

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

   if -1.4000000000000001e164 < z < -6.5e77

   1. Initial program 63.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{x \cdot y}{a - z}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot y}{a - z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{y}{a - z}}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{a - z}\right)}\right)\right) \]

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

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

      7. --lowering--.f64 73.8%

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

   8. Simplified 73.8%

      \[\leadsto \color{blue}{0 - x \cdot \frac{y}{a - z}} \]

   if -3.5500000000000001e-63 < z < 2.6999999999999997e-51

   1. Initial program 94.3%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 80.2%

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

   7. Simplified 80.2%

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

   if 2.6999999999999997e-51 < z < 2.1e62

   1. Initial program 95.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 83.6%

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

   8. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 63.0%

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

   10. Simplified 63.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-51}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 1.68 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= z -1.4e+164)
     t
     (if (<= z -3.3e+78)
       t_1
       (if (<= z -3.1e-296)
         (* x (+ (/ (- z y) a) 1.0))
         (if (<= z 1.68e-49)
           (+ x (/ t (/ a y)))
           (if (<= z 4.3e+153) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.4e+164) {
		tmp = t;
	} else if (z <= -3.3e+78) {
		tmp = t_1;
	} else if (z <= -3.1e-296) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 1.68e-49) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.3e+153) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (z <= (-1.4d+164)) then
        tmp = t
    else if (z <= (-3.3d+78)) then
        tmp = t_1
    else if (z <= (-3.1d-296)) then
        tmp = x * (((z - y) / a) + 1.0d0)
    else if (z <= 1.68d-49) then
        tmp = x + (t / (a / y))
    else if (z <= 4.3d+153) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.4e+164) {
		tmp = t;
	} else if (z <= -3.3e+78) {
		tmp = t_1;
	} else if (z <= -3.1e-296) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 1.68e-49) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.3e+153) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if z <= -1.4e+164:
		tmp = t
	elif z <= -3.3e+78:
		tmp = t_1
	elif z <= -3.1e-296:
		tmp = x * (((z - y) / a) + 1.0)
	elif z <= 1.68e-49:
		tmp = x + (t / (a / y))
	elif z <= 4.3e+153:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -1.4e+164)
		tmp = t;
	elseif (z <= -3.3e+78)
		tmp = t_1;
	elseif (z <= -3.1e-296)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	elseif (z <= 1.68e-49)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 4.3e+153)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -1.4e+164)
		tmp = t;
	elseif (z <= -3.3e+78)
		tmp = t_1;
	elseif (z <= -3.1e-296)
		tmp = x * (((z - y) / a) + 1.0);
	elseif (z <= 1.68e-49)
		tmp = x + (t / (a / y));
	elseif (z <= 4.3e+153)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+164], t, If[LessEqual[z, -3.3e+78], t$95$1, If[LessEqual[z, -3.1e-296], N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.68e-49], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+153], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e164 or 4.2999999999999998e153 < z

   1. Initial program 53.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 59.5%

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

   if -1.4000000000000001e164 < z < -3.3e78 or 1.6800000000000001e-49 < z < 4.2999999999999998e153

   1. Initial program 74.9%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{a + -1 \cdot y}{z}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a + -1 \cdot y}{z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. --lowering--.f64 50.3%

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

   8. Simplified 50.3%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{a - y}{z}\right)} \]

   if -3.3e78 < z < -3.1000000000000002e-296

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in a around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. --lowering--.f64 57.5%

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

   8. Simplified 57.5%

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

   if -3.1000000000000002e-296 < z < 1.6800000000000001e-49

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 58.9%

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

   8. Simplified 58.9%

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

      1. +-commutative N/A

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

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

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

      7. /-lowering-/.f64 63.2%

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

   10. Applied egg-rr 63.2%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 1.68 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= z -1.45e+164)
     t
     (if (<= z -2.2e+78)
       t_1
       (if (<= z -4e-70)
         (* x (- 1.0 (/ y a)))
         (if (<= z 7.5e-51)
           (+ x (* t (/ y a)))
           (if (<= z 1.08e+154) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.45e+164) {
		tmp = t;
	} else if (z <= -2.2e+78) {
		tmp = t_1;
	} else if (z <= -4e-70) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7.5e-51) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.08e+154) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (z <= (-1.45d+164)) then
        tmp = t
    else if (z <= (-2.2d+78)) then
        tmp = t_1
    else if (z <= (-4d-70)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 7.5d-51) then
        tmp = x + (t * (y / a))
    else if (z <= 1.08d+154) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.45e+164) {
		tmp = t;
	} else if (z <= -2.2e+78) {
		tmp = t_1;
	} else if (z <= -4e-70) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7.5e-51) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.08e+154) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if z <= -1.45e+164:
		tmp = t
	elif z <= -2.2e+78:
		tmp = t_1
	elif z <= -4e-70:
		tmp = x * (1.0 - (y / a))
	elif z <= 7.5e-51:
		tmp = x + (t * (y / a))
	elif z <= 1.08e+154:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -1.45e+164)
		tmp = t;
	elseif (z <= -2.2e+78)
		tmp = t_1;
	elseif (z <= -4e-70)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 7.5e-51)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.08e+154)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -1.45e+164)
		tmp = t;
	elseif (z <= -2.2e+78)
		tmp = t_1;
	elseif (z <= -4e-70)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 7.5e-51)
		tmp = x + (t * (y / a));
	elseif (z <= 1.08e+154)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+164], t, If[LessEqual[z, -2.2e+78], t$95$1, If[LessEqual[z, -4e-70], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-51], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e+154], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4499999999999999e164 or 1.08e154 < z

   1. Initial program 53.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 59.5%

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

   if -1.4499999999999999e164 < z < -2.20000000000000014e78 or 7.49999999999999976e-51 < z < 1.08e154

   1. Initial program 74.9%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{a + -1 \cdot y}{z}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a + -1 \cdot y}{z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. --lowering--.f64 50.3%

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

   8. Simplified 50.3%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{a - y}{z}\right)} \]

   if -2.20000000000000014e78 < z < -3.99999999999999998e-70

   1. Initial program 99.8%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 39.4%

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

   7. Simplified 39.4%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(\frac{y}{a}\right)\right)\right) \]

      2. sub-neg N/A

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

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

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

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

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

      5. /-lowering-/.f64 44.2%

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

   10. Simplified 44.2%

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

   if -3.99999999999999998e-70 < z < 7.49999999999999976e-51

   1. Initial program 94.3%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 63.2%

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

   10. Applied egg-rr 63.2%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= z -1.35e+164)
     t
     (if (<= z -1.2e+78)
       t_1
       (if (<= z -1e-72)
         (* x (- 1.0 (/ y a)))
         (if (<= z 3.5e-47)
           (+ x (* t (/ y a)))
           (if (<= z 3.3e+129) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t;
	} else if (z <= -1.2e+78) {
		tmp = t_1;
	} else if (z <= -1e-72) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.5e-47) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.3e+129) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (z <= (-1.35d+164)) then
        tmp = t
    else if (z <= (-1.2d+78)) then
        tmp = t_1
    else if (z <= (-1d-72)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.5d-47) then
        tmp = x + (t * (y / a))
    else if (z <= 3.3d+129) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t;
	} else if (z <= -1.2e+78) {
		tmp = t_1;
	} else if (z <= -1e-72) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.5e-47) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.3e+129) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if z <= -1.35e+164:
		tmp = t
	elif z <= -1.2e+78:
		tmp = t_1
	elif z <= -1e-72:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.5e-47:
		tmp = x + (t * (y / a))
	elif z <= 3.3e+129:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -1.35e+164)
		tmp = t;
	elseif (z <= -1.2e+78)
		tmp = t_1;
	elseif (z <= -1e-72)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.5e-47)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.3e+129)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -1.35e+164)
		tmp = t;
	elseif (z <= -1.2e+78)
		tmp = t_1;
	elseif (z <= -1e-72)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.5e-47)
		tmp = x + (t * (y / a));
	elseif (z <= 3.3e+129)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+164], t, If[LessEqual[z, -1.2e+78], t$95$1, If[LessEqual[z, -1e-72], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-47], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+129], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35000000000000003e164 or 3.2999999999999999e129 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 56.3%

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

   if -1.35000000000000003e164 < z < -1.1999999999999999e78 or 3.4999999999999998e-47 < z < 3.2999999999999999e129

   1. Initial program 79.3%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 50.1%

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

   8. Simplified 50.1%

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

   if -1.1999999999999999e78 < z < -9.9999999999999997e-73

   1. Initial program 99.8%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 39.4%

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

   7. Simplified 39.4%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(\frac{y}{a}\right)\right)\right) \]

      2. sub-neg N/A

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

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

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

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

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

      5. /-lowering-/.f64 44.2%

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

   10. Simplified 44.2%

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

   if -9.9999999999999997e-73 < z < 3.4999999999999998e-47

   1. Initial program 94.3%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 63.2%

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

   10. Applied egg-rr 63.2%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+60}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.35e+164)
     t_1
     (if (<= z -9e+75)
       (* x (/ y (- z a)))
       (if (<= z -3.1e-66)
         t_1
         (if (<= z 6.4e+60) (+ x (* (- t x) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= -9e+75) {
		tmp = x * (y / (z - a));
	} else if (z <= -3.1e-66) {
		tmp = t_1;
	} else if (z <= 6.4e+60) {
		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 * ((y - z) / (a - z))
    if (z <= (-1.35d+164)) then
        tmp = t_1
    else if (z <= (-9d+75)) then
        tmp = x * (y / (z - a))
    else if (z <= (-3.1d-66)) then
        tmp = t_1
    else if (z <= 6.4d+60) 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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= -9e+75) {
		tmp = x * (y / (z - a));
	} else if (z <= -3.1e-66) {
		tmp = t_1;
	} else if (z <= 6.4e+60) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.35e+164:
		tmp = t_1
	elif z <= -9e+75:
		tmp = x * (y / (z - a))
	elif z <= -3.1e-66:
		tmp = t_1
	elif z <= 6.4e+60:
		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(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= -9e+75)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (z <= -3.1e-66)
		tmp = t_1;
	elseif (z <= 6.4e+60)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= -9e+75)
		tmp = x * (y / (z - a));
	elseif (z <= -3.1e-66)
		tmp = t_1;
	elseif (z <= 6.4e+60)
		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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+164], t$95$1, If[LessEqual[z, -9e+75], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-66], t$95$1, If[LessEqual[z, 6.4e+60], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000003e164 or -9.0000000000000007e75 < z < -3.0999999999999997e-66 or 6.39999999999999982e60 < z

   1. Initial program 63.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 46.2%

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

   5. Simplified 46.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 67.0%

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

   7. Applied egg-rr 67.0%

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

   if -1.35000000000000003e164 < z < -9.0000000000000007e75

   1. Initial program 63.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{x \cdot y}{a - z}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot y}{a - z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{y}{a - z}}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{a - z}\right)}\right)\right) \]

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

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

      7. --lowering--.f64 73.8%

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

   8. Simplified 73.8%

      \[\leadsto \color{blue}{0 - x \cdot \frac{y}{a - z}} \]

   if -3.0999999999999997e-66 < z < 6.39999999999999982e60

   1. Initial program 94.6%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+60}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= z -1.35e+164)
     t
     (if (<= z -4.4e+78)
       t_1
       (if (<= z 9e-46) (* x (- 1.0 (/ y a))) (if (<= z 1.02e+129) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t;
	} else if (z <= -4.4e+78) {
		tmp = t_1;
	} else if (z <= 9e-46) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.02e+129) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (z <= (-1.35d+164)) then
        tmp = t
    else if (z <= (-4.4d+78)) then
        tmp = t_1
    else if (z <= 9d-46) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.02d+129) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t;
	} else if (z <= -4.4e+78) {
		tmp = t_1;
	} else if (z <= 9e-46) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.02e+129) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if z <= -1.35e+164:
		tmp = t
	elif z <= -4.4e+78:
		tmp = t_1
	elif z <= 9e-46:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.02e+129:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -1.35e+164)
		tmp = t;
	elseif (z <= -4.4e+78)
		tmp = t_1;
	elseif (z <= 9e-46)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.02e+129)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -1.35e+164)
		tmp = t;
	elseif (z <= -4.4e+78)
		tmp = t_1;
	elseif (z <= 9e-46)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.02e+129)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+164], t, If[LessEqual[z, -4.4e+78], t$95$1, If[LessEqual[z, 9e-46], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+129], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000003e164 or 1.01999999999999996e129 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 56.3%

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

   if -1.35000000000000003e164 < z < -4.40000000000000028e78 or 9.00000000000000001e-46 < z < 1.01999999999999996e129

   1. Initial program 79.3%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 50.1%

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

   8. Simplified 50.1%

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

   if -4.40000000000000028e78 < z < 9.00000000000000001e-46

   1. Initial program 95.3%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(\frac{y}{a}\right)\right)\right) \]

      2. sub-neg N/A

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

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

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

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

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

      5. /-lowering-/.f64 54.4%

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

   10. Simplified 54.4%

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

Alternative 10: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -7 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-242}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x - t}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -7e-61)
     t_1
     (if (<= t -1.1e-242)
       (- x (/ y (/ a (- x t))))
       (if (<= t 2.9e-98) (* x (/ (- y a) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -7e-61) {
		tmp = t_1;
	} else if (t <= -1.1e-242) {
		tmp = x - (y / (a / (x - t)));
	} else if (t <= 2.9e-98) {
		tmp = 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 = t * ((y - z) / (a - z))
    if (t <= (-7d-61)) then
        tmp = t_1
    else if (t <= (-1.1d-242)) then
        tmp = x - (y / (a / (x - t)))
    else if (t <= 2.9d-98) then
        tmp = 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 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -7e-61) {
		tmp = t_1;
	} else if (t <= -1.1e-242) {
		tmp = x - (y / (a / (x - t)));
	} else if (t <= 2.9e-98) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -7e-61:
		tmp = t_1
	elif t <= -1.1e-242:
		tmp = x - (y / (a / (x - t)))
	elif t <= 2.9e-98:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -7e-61)
		tmp = t_1;
	elseif (t <= -1.1e-242)
		tmp = Float64(x - Float64(y / Float64(a / Float64(x - t))));
	elseif (t <= 2.9e-98)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -7e-61)
		tmp = t_1;
	elseif (t <= -1.1e-242)
		tmp = x - (y / (a / (x - t)));
	elseif (t <= 2.9e-98)
		tmp = 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[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-61], t$95$1, If[LessEqual[t, -1.1e-242], N[(x - N[(y / N[(a / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-98], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000006e-61 or 2.9e-98 < t

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 54.4%

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

   5. Simplified 54.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 70.3%

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

   7. Applied egg-rr 70.3%

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

   if -7.0000000000000006e-61 < t < -1.10000000000000001e-242

   1. Initial program 78.1%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 78.2%

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

   4. Applied egg-rr 78.2%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 72.1%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 68.6%

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

   10. Simplified 68.6%

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

   if -1.10000000000000001e-242 < t < 2.9e-98

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{a + -1 \cdot y}{z}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a + -1 \cdot y}{z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. --lowering--.f64 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-242}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x - t}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-240}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -4e-61)
     t_1
     (if (<= t -2.9e-240)
       (+ x (* (- t x) (/ y a)))
       (if (<= t 2e-99) (* x (/ (- y a) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -4e-61) {
		tmp = t_1;
	} else if (t <= -2.9e-240) {
		tmp = x + ((t - x) * (y / a));
	} else if (t <= 2e-99) {
		tmp = 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 = t * ((y - z) / (a - z))
    if (t <= (-4d-61)) then
        tmp = t_1
    else if (t <= (-2.9d-240)) then
        tmp = x + ((t - x) * (y / a))
    else if (t <= 2d-99) then
        tmp = 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 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -4e-61) {
		tmp = t_1;
	} else if (t <= -2.9e-240) {
		tmp = x + ((t - x) * (y / a));
	} else if (t <= 2e-99) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -4e-61:
		tmp = t_1
	elif t <= -2.9e-240:
		tmp = x + ((t - x) * (y / a))
	elif t <= 2e-99:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -4e-61)
		tmp = t_1;
	elseif (t <= -2.9e-240)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (t <= 2e-99)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -4e-61)
		tmp = t_1;
	elseif (t <= -2.9e-240)
		tmp = x + ((t - x) * (y / a));
	elseif (t <= 2e-99)
		tmp = 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[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e-61], t$95$1, If[LessEqual[t, -2.9e-240], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-99], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000002e-61 or 2e-99 < t

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 54.4%

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

   5. Simplified 54.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 70.3%

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

   7. Applied egg-rr 70.3%

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

   if -4.0000000000000002e-61 < t < -2.9000000000000002e-240

   1. Initial program 78.1%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 81.5%

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

   4. Applied egg-rr 81.5%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 68.5%

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

   7. Simplified 68.5%

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

   if -2.9000000000000002e-240 < t < 2e-99

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{a + -1 \cdot y}{z}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a + -1 \cdot y}{z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. --lowering--.f64 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-240}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.2e-59)
     t_1
     (if (<= t -1.7e-238)
       (* x (- 1.0 (/ y a)))
       (if (<= t 7e-99) (* x (/ (- y a) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.2e-59) {
		tmp = t_1;
	} else if (t <= -1.7e-238) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 7e-99) {
		tmp = 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 = t * ((y - z) / (a - z))
    if (t <= (-1.2d-59)) then
        tmp = t_1
    else if (t <= (-1.7d-238)) then
        tmp = x * (1.0d0 - (y / a))
    else if (t <= 7d-99) then
        tmp = 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 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.2e-59) {
		tmp = t_1;
	} else if (t <= -1.7e-238) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 7e-99) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.2e-59:
		tmp = t_1
	elif t <= -1.7e-238:
		tmp = x * (1.0 - (y / a))
	elif t <= 7e-99:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.2e-59)
		tmp = t_1;
	elseif (t <= -1.7e-238)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (t <= 7e-99)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.2e-59)
		tmp = t_1;
	elseif (t <= -1.7e-238)
		tmp = x * (1.0 - (y / a));
	elseif (t <= 7e-99)
		tmp = 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[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e-59], t$95$1, If[LessEqual[t, -1.7e-238], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-99], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000008e-59 or 6.9999999999999997e-99 < t

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 54.4%

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

   5. Simplified 54.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 70.3%

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

   7. Applied egg-rr 70.3%

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

   if -1.20000000000000008e-59 < t < -1.69999999999999992e-238

   1. Initial program 78.1%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 81.5%

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

   4. Applied egg-rr 81.5%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(\frac{y}{a}\right)\right)\right) \]

      2. sub-neg N/A

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

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

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

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

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

      5. /-lowering-/.f64 66.0%

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

   10. Simplified 66.0%

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

   if -1.69999999999999992e-238 < t < 6.9999999999999997e-99

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 59.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{a + -1 \cdot y}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{a + -1 \cdot y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{a + -1 \cdot y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a + \left(\mathsf{neg}\left(y\right)\right)\right), z\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\left(a - y\right), z\right)\right)\right) \]

      7. --lowering--.f64 63.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, y\right), z\right)\right)\right) \]

   8. Simplified 63.1%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{a - y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+76}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -2.7e+78)
     t_1
     (if (<= z 2.2e+76) (+ 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 <= -2.7e+78) {
		tmp = t_1;
	} else if (z <= 2.2e+76) {
		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 <= (-2.7d+78)) then
        tmp = t_1
    else if (z <= 2.2d+76) 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 <= -2.7e+78) {
		tmp = t_1;
	} else if (z <= 2.2e+76) {
		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 <= -2.7e+78:
		tmp = t_1
	elif z <= 2.2e+76:
		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 <= -2.7e+78)
		tmp = t_1;
	elseif (z <= 2.2e+76)
		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 <= -2.7e+78)
		tmp = t_1;
	elseif (z <= 2.2e+76)
		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, -2.7e+78], t$95$1, If[LessEqual[z, 2.2e+76], 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 < -2.70000000000000004e78 or 2.2e76 < z

   1. Initial program 55.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - a}{z}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - a}}{z}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - a\right), \color{blue}{z}\right)\right)\right) \]

      12. --lowering--.f64 89.5%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right)\right)\right) \]

   5. Simplified 89.5%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]

   if -2.70000000000000004e78 < z < 2.2e76

   1. Initial program 95.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+76}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -4.5e+36)
     t_1
     (if (<= z 8.6e+70) (+ x (/ y (/ (- a z) (- t x)))) 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 <= -4.5e+36) {
		tmp = t_1;
	} else if (z <= 8.6e+70) {
		tmp = x + (y / ((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 + ((t - x) * ((a - y) / z))
    if (z <= (-4.5d+36)) then
        tmp = t_1
    else if (z <= 8.6d+70) then
        tmp = x + (y / ((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 + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -4.5e+36) {
		tmp = t_1;
	} else if (z <= 8.6e+70) {
		tmp = x + (y / ((a - z) / (t - x)));
	} 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 <= -4.5e+36:
		tmp = t_1
	elif z <= 8.6e+70:
		tmp = x + (y / ((a - z) / (t - x)))
	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 <= -4.5e+36)
		tmp = t_1;
	elseif (z <= 8.6e+70)
		tmp = Float64(x + Float64(y / 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 + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -4.5e+36)
		tmp = t_1;
	elseif (z <= 8.6e+70)
		tmp = x + (y / ((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[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+36], t$95$1, If[LessEqual[z, 8.6e+70], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999997e36 or 8.6000000000000002e70 < z

   1. Initial program 58.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - a}{z}\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - a}}{z}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - a\right), \color{blue}{z}\right)\right)\right) \]

      12. --lowering--.f64 88.6%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right)\right)\right) \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{t - \left(t - x\right) \cdot \frac{y - a}{z}} \]

   if -4.49999999999999997e36 < z < 8.6000000000000002e70

   1. Initial program 95.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{t - x}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - z}{\color{blue}{\frac{a - z}{t - x}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{a - z}{t - x}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{a - z}}{t - x}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{t} - x\right)\right)\right)\right) \]

      7. --lowering--.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right)\right) \]

   4. Applied egg-rr 95.2%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(t, x\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 84.9%

      \[\leadsto x + \frac{\color{blue}{y}}{\frac{a - z}{t - x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.35e+164)
     t_1
     (if (<= z 3.45e+69) (+ x (/ y (/ (- 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) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= 3.45e+69) {
		tmp = x + (y / ((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) / (a - z))
    if (z <= (-1.35d+164)) then
        tmp = t_1
    else if (z <= 3.45d+69) then
        tmp = x + (y / ((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) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= 3.45e+69) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.35e+164:
		tmp = t_1
	elif z <= 3.45e+69:
		tmp = x + (y / ((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(a - z)))
	tmp = 0.0
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= 3.45e+69)
		tmp = Float64(x + Float64(y / 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) / (a - z));
	tmp = 0.0;
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= 3.45e+69)
		tmp = x + (y / ((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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+164], t$95$1, If[LessEqual[z, 3.45e+69], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000003e164 or 3.4500000000000001e69 < z

   1. Initial program 55.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 41.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y - z}{a - z} \cdot \color{blue}{t} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 67.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 67.1%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -1.35000000000000003e164 < z < 3.4500000000000001e69

   1. Initial program 92.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{t - x}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - z}{\color{blue}{\frac{a - z}{t - x}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{a - z}{t - x}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{a - z}}{t - x}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{t} - x\right)\right)\right)\right) \]

      7. --lowering--.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right)\right) \]

   4. Applied egg-rr 92.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(t, x\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 81.2%

      \[\leadsto x + \frac{\color{blue}{y}}{\frac{a - z}{t - x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.35e+164)
     t_1
     (if (<= z 1.22e+68) (+ x (* y (/ (- t x) (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= 1.22e+68) {
		tmp = x + (y * ((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 * ((y - z) / (a - z))
    if (z <= (-1.35d+164)) then
        tmp = t_1
    else if (z <= 1.22d+68) then
        tmp = x + (y * ((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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+164) {
		tmp = t_1;
	} else if (z <= 1.22e+68) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.35e+164:
		tmp = t_1
	elif z <= 1.22e+68:
		tmp = x + (y * ((t - x) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= 1.22e+68)
		tmp = Float64(x + Float64(y * 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 * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.35e+164)
		tmp = t_1;
	elseif (z <= 1.22e+68)
		tmp = x + (y * ((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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+164], t$95$1, If[LessEqual[z, 1.22e+68], N[(x + N[(y * 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 < -1.35000000000000003e164 or 1.22e68 < z

   1. Initial program 55.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 41.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y - z}{a - z} \cdot \color{blue}{t} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 67.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 67.1%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -1.35000000000000003e164 < z < 1.22e68

   1. Initial program 92.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 81.1%

      \[\leadsto x + \color{blue}{y} \cdot \frac{t - x}{a - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- y z) (- z a)) 1.0))))
   (if (<= x -5.8e+39) t_1 (if (<= x 5.8e-9) (* t (/ (- y z) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((y - z) / (z - a)) + 1.0);
	double tmp;
	if (x <= -5.8e+39) {
		tmp = t_1;
	} else if (x <= 5.8e-9) {
		tmp = t * ((y - z) / (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 * (((y - z) / (z - a)) + 1.0d0)
    if (x <= (-5.8d+39)) then
        tmp = t_1
    else if (x <= 5.8d-9) then
        tmp = t * ((y - z) / (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 * (((y - z) / (z - a)) + 1.0);
	double tmp;
	if (x <= -5.8e+39) {
		tmp = t_1;
	} else if (x <= 5.8e-9) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((y - z) / (z - a)) + 1.0)
	tmp = 0
	if x <= -5.8e+39:
		tmp = t_1
	elif x <= 5.8e-9:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0))
	tmp = 0.0
	if (x <= -5.8e+39)
		tmp = t_1;
	elseif (x <= 5.8e-9)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((y - z) / (z - a)) + 1.0);
	tmp = 0.0;
	if (x <= -5.8e+39)
		tmp = t_1;
	elseif (x <= 5.8e-9)
		tmp = t * ((y - z) / (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[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+39], t$95$1, If[LessEqual[x, 5.8e-9], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000059e39 or 5.79999999999999982e-9 < x

   1. Initial program 74.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   if -5.80000000000000059e39 < x < 5.79999999999999982e-9

   1. Initial program 82.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 57.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 57.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y - z}{a - z} \cdot \color{blue}{t} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 71.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 71.9%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+184}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+16)
   x
   (if (<= a 1.4e-183) (* x (/ y z)) (if (<= a 1.05e+184) (+ x t) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+16) {
		tmp = x;
	} else if (a <= 1.4e-183) {
		tmp = x * (y / z);
	} else if (a <= 1.05e+184) {
		tmp = x + 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 <= (-3.8d+16)) then
        tmp = x
    else if (a <= 1.4d-183) then
        tmp = x * (y / z)
    else if (a <= 1.05d+184) then
        tmp = x + 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 <= -3.8e+16) {
		tmp = x;
	} else if (a <= 1.4e-183) {
		tmp = x * (y / z);
	} else if (a <= 1.05e+184) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+16:
		tmp = x
	elif a <= 1.4e-183:
		tmp = x * (y / z)
	elif a <= 1.05e+184:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+16)
		tmp = x;
	elseif (a <= 1.4e-183)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.05e+184)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+16)
		tmp = x;
	elseif (a <= 1.4e-183)
		tmp = x * (y / z);
	elseif (a <= 1.05e+184)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+16], x, If[LessEqual[a, 1.4e-183], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+184], N[(x + t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8e16 or 1.05e184 < a

   1. Initial program 83.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 44.6%

      \[\leadsto \color{blue}{x} \]

   if -3.8e16 < a < 1.39999999999999992e-183

   1. Initial program 73.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 35.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 35.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 43.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 43.4%

      \[\leadsto x \cdot \color{blue}{\frac{y}{z}} \]

   if 1.39999999999999992e-183 < a < 1.05e184

   1. Initial program 82.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a - z}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 66.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 66.1%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   7. Step-by-step derivation

   8. Simplified 38.4%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e+37) t (if (<= z 1.2e+71) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+37) {
		tmp = t;
	} else if (z <= 1.2e+71) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.15d+37)) then
        tmp = t
    else if (z <= 1.2d+71) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e+37) {
		tmp = t;
	} else if (z <= 1.2e+71) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e+37:
		tmp = t
	elif z <= 1.2e+71:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e+37)
		tmp = t;
	elseif (z <= 1.2e+71)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.15e+37)
		tmp = t;
	elseif (z <= 1.2e+71)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e+37], t, If[LessEqual[z, 1.2e+71], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.14999999999999992e37 or 1.1999999999999999e71 < z

   1. Initial program 58.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 46.4%

      \[\leadsto \color{blue}{t} \]

   if -3.14999999999999992e37 < z < 1.1999999999999999e71

   1. Initial program 95.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 30.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 25.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 79.1%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 25.5%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))