Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 94.8%

Time: 13.8s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a - z}{y - z}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\frac{a}{z} - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ (- a z) (- y z)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e-305)
     t_1
     (if (<= t_2 0.0) (+ t (* (- t x) (- (/ a z) (/ y z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / (y - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-305) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((t - x) * ((a / z) - (y / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / ((a - z) / (y - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-5d-305)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + ((t - x) * ((a / z) - (y / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / (y - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-305) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((t - x) * ((a / z) - (y / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / ((a - z) / (y - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -5e-305:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + ((t - x) * ((a / z) - (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(a - z) / Float64(y - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-305)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a / z) - Float64(y / z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / ((a - z) / (y - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -5e-305)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + ((t - x) * ((a / z) - (y / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - 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, -5e-305], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999985e-305 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      9. clear-num N/A

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

      10. flip-- N/A

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

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

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

      12. --lowering--.f64 90.7%

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

   4. Applied egg-rr 90.7%

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

      1. associate-/l/ N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

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

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

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

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

      8. --lowering--.f64 94.9%

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

   6. Applied egg-rr 94.9%

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

   if -4.99999999999999985e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 94.1%

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

   5. Simplified 94.1%

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

      1. div-sub N/A

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

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

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

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

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

      4. /-lowering-/.f64 94.2%

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

   7. Applied egg-rr 94.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-305}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\frac{a}{z} - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a - z}{y - z}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ (- a z) (- y z)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e-305) t_1 (if (<= t_2 0.0) (+ t (* x (/ (- y a) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / (y - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-305) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / ((a - z) / (y - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-5d-305)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / (y - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-305) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / ((a - z) / (y - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -5e-305:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-305)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + 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 = x + ((t - x) / ((a - z) / (y - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -5e-305)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - 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, -5e-305], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(y - a), $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)))) < -4.99999999999999985e-305 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      9. clear-num N/A

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

      10. flip-- N/A

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

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

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

      12. --lowering--.f64 90.7%

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

   4. Applied egg-rr 90.7%

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

      1. associate-/l/ N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

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

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

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

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

      8. --lowering--.f64 94.9%

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

   6. Applied egg-rr 94.9%

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

   if -4.99999999999999985e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 94.1%

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

   8. Simplified 94.1%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-305}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-219}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-226)
     t_1
     (if (<= t_1 1e-219) (+ t (* x (/ (- y a) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-226) {
		tmp = t_1;
	} else if (t_1 <= 1e-219) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-1d-226)) then
        tmp = t_1
    else if (t_1 <= 1d-219) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-226) {
		tmp = t_1;
	} else if (t_1 <= 1e-219) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e-226:
		tmp = t_1
	elif t_1 <= 1e-219:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-226)
		tmp = t_1;
	elseif (t_1 <= 1e-219)
		tmp = Float64(t + 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 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-226)
		tmp = t_1;
	elseif (t_1 <= 1e-219)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-226], t$95$1, If[LessEqual[t$95$1, 1e-219], N[(t + N[(x * N[(N[(y - a), $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)))) < -9.99999999999999921e-227 or 1e-219 < (+.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

   if -9.99999999999999921e-227 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e-219

   1. Initial program 12.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 88.0%

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

   8. Simplified 88.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-226}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-219}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.00092:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-296}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.35e+111)
   x
   (if (<= a -0.00092)
     (* t (/ y (- a z)))
     (if (<= a -2.8e-296)
       t
       (if (<= a 9.5e-111) (* x (/ y z)) (if (<= a 1.25e+81) t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.35e+111) {
		tmp = x;
	} else if (a <= -0.00092) {
		tmp = t * (y / (a - z));
	} else if (a <= -2.8e-296) {
		tmp = t;
	} else if (a <= 9.5e-111) {
		tmp = x * (y / z);
	} else if (a <= 1.25e+81) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.35d+111)) then
        tmp = x
    else if (a <= (-0.00092d0)) then
        tmp = t * (y / (a - z))
    else if (a <= (-2.8d-296)) then
        tmp = t
    else if (a <= 9.5d-111) then
        tmp = x * (y / z)
    else if (a <= 1.25d+81) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.35e+111) {
		tmp = x;
	} else if (a <= -0.00092) {
		tmp = t * (y / (a - z));
	} else if (a <= -2.8e-296) {
		tmp = t;
	} else if (a <= 9.5e-111) {
		tmp = x * (y / z);
	} else if (a <= 1.25e+81) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.35e+111:
		tmp = x
	elif a <= -0.00092:
		tmp = t * (y / (a - z))
	elif a <= -2.8e-296:
		tmp = t
	elif a <= 9.5e-111:
		tmp = x * (y / z)
	elif a <= 1.25e+81:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.35e+111)
		tmp = x;
	elseif (a <= -0.00092)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= -2.8e-296)
		tmp = t;
	elseif (a <= 9.5e-111)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.25e+81)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.35e+111)
		tmp = x;
	elseif (a <= -0.00092)
		tmp = t * (y / (a - z));
	elseif (a <= -2.8e-296)
		tmp = t;
	elseif (a <= 9.5e-111)
		tmp = x * (y / z);
	elseif (a <= 1.25e+81)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.35e+111], x, If[LessEqual[a, -0.00092], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.8e-296], t, If[LessEqual[a, 9.5e-111], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+81], t, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.35000000000000004e111 or 1.25e81 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.4%

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

   if -2.35000000000000004e111 < a < -9.2000000000000003e-4

   1. Initial program 75.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 39.6%

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

   5. Simplified 39.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 33.9%

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

   8. Simplified 33.9%

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

   if -9.2000000000000003e-4 < a < -2.7999999999999999e-296 or 9.4999999999999995e-111 < a < 1.25e81

   1. Initial program 75.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 41.9%

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

   if -2.7999999999999999e-296 < a < 9.4999999999999995e-111

   1. Initial program 71.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 41.1%

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

   5. Simplified 41.1%

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

   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 51.7%

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

   8. Simplified 51.7%

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

Alternative 5: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -7e+53)
     t_1
     (if (<= z -1.1e-67)
       (+ x (* (- y z) (/ t (- a z))))
       (if (<= z 5.4e+148) (+ 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 + (x * ((y - a) / z));
	double tmp;
	if (z <= -7e+53) {
		tmp = t_1;
	} else if (z <= -1.1e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 5.4e+148) {
		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 + (x * ((y - a) / z))
    if (z <= (-7d+53)) then
        tmp = t_1
    else if (z <= (-1.1d-67)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 5.4d+148) 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 + (x * ((y - a) / z));
	double tmp;
	if (z <= -7e+53) {
		tmp = t_1;
	} else if (z <= -1.1e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 5.4e+148) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -7e+53:
		tmp = t_1
	elif z <= -1.1e-67:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 5.4e+148:
		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(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -7e+53)
		tmp = t_1;
	elseif (z <= -1.1e-67)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 5.4e+148)
		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 + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -7e+53)
		tmp = t_1;
	elseif (z <= -1.1e-67)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 5.4e+148)
		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[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+53], t$95$1, If[LessEqual[z, -1.1e-67], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+148], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000038e53 or 5.40000000000000038e148 < z

   1. Initial program 62.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 76.9%

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

   8. Simplified 76.9%

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

   if -7.00000000000000038e53 < z < -1.1000000000000001e-67

   1. Initial program 88.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 80.8%

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

   5. Simplified 80.8%

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

   if -1.1000000000000001e-67 < z < 5.40000000000000038e148

   1. Initial program 90.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+53}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+81}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a (- y z))))))
   (if (<= a -2.1e+137)
     t_1
     (if (<= a -1.58e+53)
       (+ x (* y (/ (- t x) a)))
       (if (<= a 1.7e+81) (+ t (* x (/ (- y a) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -2.1e+137) {
		tmp = t_1;
	} else if (a <= -1.58e+53) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 1.7e+81) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / (y - z)))
    if (a <= (-2.1d+137)) then
        tmp = t_1
    else if (a <= (-1.58d+53)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= 1.7d+81) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -2.1e+137) {
		tmp = t_1;
	} else if (a <= -1.58e+53) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 1.7e+81) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / (y - z)))
	tmp = 0
	if a <= -2.1e+137:
		tmp = t_1
	elif a <= -1.58e+53:
		tmp = x + (y * ((t - x) / a))
	elif a <= 1.7e+81:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -2.1e+137)
		tmp = t_1;
	elseif (a <= -1.58e+53)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 1.7e+81)
		tmp = Float64(t + 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 = x + (t / (a / (y - z)));
	tmp = 0.0;
	if (a <= -2.1e+137)
		tmp = t_1;
	elseif (a <= -1.58e+53)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= 1.7e+81)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+137], t$95$1, If[LessEqual[a, -1.58e+53], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+81], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0999999999999999e137 or 1.70000000000000001e81 < a

   1. Initial program 90.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 85.8%

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

   5. Simplified 85.8%

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

      1. *-commutative N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 87.8%

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

   7. Applied egg-rr 87.8%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 80.6%

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

   10. Simplified 80.6%

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

   if -2.0999999999999999e137 < a < -1.57999999999999999e53

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 77.9%

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

   5. Simplified 77.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 85.0%

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

   7. Applied egg-rr 85.0%

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

   if -1.57999999999999999e53 < a < 1.70000000000000001e81

   1. Initial program 73.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 68.5%

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

   8. Simplified 68.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+81}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+80}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a (- y z))))))
   (if (<= a -1.4e+137)
     t_1
     (if (<= a -1.55e-10)
       (+ x (* y (/ (- t x) a)))
       (if (<= a 9.2e+80) (+ t (/ (* x y) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -1.4e+137) {
		tmp = t_1;
	} else if (a <= -1.55e-10) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 9.2e+80) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / (y - z)))
    if (a <= (-1.4d+137)) then
        tmp = t_1
    else if (a <= (-1.55d-10)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= 9.2d+80) then
        tmp = t + ((x * 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 / (a / (y - z)));
	double tmp;
	if (a <= -1.4e+137) {
		tmp = t_1;
	} else if (a <= -1.55e-10) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 9.2e+80) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / (y - z)))
	tmp = 0
	if a <= -1.4e+137:
		tmp = t_1
	elif a <= -1.55e-10:
		tmp = x + (y * ((t - x) / a))
	elif a <= 9.2e+80:
		tmp = t + ((x * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -1.4e+137)
		tmp = t_1;
	elseif (a <= -1.55e-10)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 9.2e+80)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / (y - z)));
	tmp = 0.0;
	if (a <= -1.4e+137)
		tmp = t_1;
	elseif (a <= -1.55e-10)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= 9.2e+80)
		tmp = t + ((x * 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[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+137], t$95$1, If[LessEqual[a, -1.55e-10], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+80], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4e137 or 9.20000000000000016e80 < a

   1. Initial program 90.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 85.8%

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

   5. Simplified 85.8%

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

      1. *-commutative N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 87.8%

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

   7. Applied egg-rr 87.8%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 80.6%

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

   10. Simplified 80.6%

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

   if -1.4e137 < a < -1.55000000000000008e-10

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 63.0%

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

   5. Simplified 63.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 67.3%

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

   7. Applied egg-rr 67.3%

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

   if -1.55000000000000008e-10 < a < 9.20000000000000016e80

   1. Initial program 74.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 61.3%

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

   11. Simplified 61.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+80}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+107)
   t
   (if (<= z 1.2e-51)
     (* x (- 1.0 (/ y a)))
     (if (<= z 3.3e+122) (* x (/ (- y a) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+107) {
		tmp = t;
	} else if (z <= 1.2e-51) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.3e+122) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.15d+107)) then
        tmp = t
    else if (z <= 1.2d-51) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.3d+122) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+107) {
		tmp = t;
	} else if (z <= 1.2e-51) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.3e+122) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+107:
		tmp = t
	elif z <= 1.2e-51:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.3e+122:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+107)
		tmp = t;
	elseif (z <= 1.2e-51)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.3e+122)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.15e+107)
		tmp = t;
	elseif (z <= 1.2e-51)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.3e+122)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+107], t, If[LessEqual[z, 1.2e-51], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+122], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e107 or 3.2999999999999999e122 < z

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 58.3%

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

   if -2.15e107 < z < 1.2e-51

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. 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 52.0%

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

   8. Simplified 52.0%

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

   if 1.2e-51 < z < 3.2999999999999999e122

   1. Initial program 92.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 57.1%

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

   5. Simplified 57.1%

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

   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

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

      2. sub-neg N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-lft-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. div-sub N/A

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

      14. /-lowering-/.f64 N/A

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

      15. --lowering--.f64 41.7%

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

   8. Simplified 41.7%

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

Alternative 9: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.4e-34)
   (* x (+ (/ z a) 1.0))
   (if (<= a -1.15e-295)
     t
     (if (<= a 4.8e-110) (* x (/ y z)) (if (<= a 9.5e+80) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.4e-34) {
		tmp = x * ((z / a) + 1.0);
	} else if (a <= -1.15e-295) {
		tmp = t;
	} else if (a <= 4.8e-110) {
		tmp = x * (y / z);
	} else if (a <= 9.5e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.4d-34)) then
        tmp = x * ((z / a) + 1.0d0)
    else if (a <= (-1.15d-295)) then
        tmp = t
    else if (a <= 4.8d-110) then
        tmp = x * (y / z)
    else if (a <= 9.5d+80) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.4e-34) {
		tmp = x * ((z / a) + 1.0);
	} else if (a <= -1.15e-295) {
		tmp = t;
	} else if (a <= 4.8e-110) {
		tmp = x * (y / z);
	} else if (a <= 9.5e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.4e-34:
		tmp = x * ((z / a) + 1.0)
	elif a <= -1.15e-295:
		tmp = t
	elif a <= 4.8e-110:
		tmp = x * (y / z)
	elif a <= 9.5e+80:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.4e-34)
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	elseif (a <= -1.15e-295)
		tmp = t;
	elseif (a <= 4.8e-110)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 9.5e+80)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.4e-34)
		tmp = x * ((z / a) + 1.0);
	elseif (a <= -1.15e-295)
		tmp = t;
	elseif (a <= 4.8e-110)
		tmp = x * (y / z);
	elseif (a <= 9.5e+80)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.4e-34], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e-295], t, If[LessEqual[a, 4.8e-110], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+80], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.39999999999999976e-34

   1. Initial program 84.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in a around inf

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

   11. Simplified 40.1%

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

   if -7.39999999999999976e-34 < a < -1.15e-295 or 4.80000000000000013e-110 < a < 9.499999999999999e80

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 43.0%

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

   if -1.15e-295 < a < 4.80000000000000013e-110

   1. Initial program 71.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 41.1%

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

   5. Simplified 41.1%

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

   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 51.7%

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

   8. Simplified 51.7%

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

   if 9.499999999999999e80 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 55.3%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-303}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.55e-10)
   x
   (if (<= a -7.5e-303)
     t
     (if (<= a 2.3e-110) (* x (/ y z)) (if (<= a 9.4e+80) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e-10) {
		tmp = x;
	} else if (a <= -7.5e-303) {
		tmp = t;
	} else if (a <= 2.3e-110) {
		tmp = x * (y / z);
	} else if (a <= 9.4e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.55d-10)) then
        tmp = x
    else if (a <= (-7.5d-303)) then
        tmp = t
    else if (a <= 2.3d-110) then
        tmp = x * (y / z)
    else if (a <= 9.4d+80) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e-10) {
		tmp = x;
	} else if (a <= -7.5e-303) {
		tmp = t;
	} else if (a <= 2.3e-110) {
		tmp = x * (y / z);
	} else if (a <= 9.4e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.55e-10:
		tmp = x
	elif a <= -7.5e-303:
		tmp = t
	elif a <= 2.3e-110:
		tmp = x * (y / z)
	elif a <= 9.4e+80:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.55e-10)
		tmp = x;
	elseif (a <= -7.5e-303)
		tmp = t;
	elseif (a <= 2.3e-110)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 9.4e+80)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.55e-10)
		tmp = x;
	elseif (a <= -7.5e-303)
		tmp = t;
	elseif (a <= 2.3e-110)
		tmp = x * (y / z);
	elseif (a <= 9.4e+80)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.55e-10], x, If[LessEqual[a, -7.5e-303], t, If[LessEqual[a, 2.3e-110], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.4e+80], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.55000000000000008e-10 or 9.40000000000000019e80 < a

   1. Initial program 88.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 46.7%

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

   if -1.55000000000000008e-10 < a < -7.49999999999999972e-303 or 2.3000000000000001e-110 < a < 9.40000000000000019e80

   1. Initial program 75.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 42.2%

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

   if -7.49999999999999972e-303 < a < 2.3000000000000001e-110

   1. Initial program 71.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 41.1%

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

   5. Simplified 41.1%

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

   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 51.7%

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

   8. Simplified 51.7%

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

Alternative 11: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.86 \cdot 10^{+50}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.86e+50)
   (+ x (* (- t x) (/ (- y z) a)))
   (if (<= a 6.2e-55)
     (+ t (* (- t x) (/ (- a y) z)))
     (+ x (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.86e+50) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (a <= 6.2e-55) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.86d+50)) then
        tmp = x + ((t - x) * ((y - z) / a))
    else if (a <= 6.2d-55) then
        tmp = t + ((t - x) * ((a - y) / z))
    else
        tmp = x + (t / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.86e+50) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (a <= 6.2e-55) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.86e+50:
		tmp = x + ((t - x) * ((y - z) / a))
	elif a <= 6.2e-55:
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = x + (t / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.86e+50)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	elseif (a <= 6.2e-55)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.86e+50)
		tmp = x + ((t - x) * ((y - z) / a));
	elseif (a <= 6.2e-55)
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = x + (t / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.86e+50], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-55], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.86000000000000006e50

   1. Initial program 87.8%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      9. clear-num N/A

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

      10. flip-- N/A

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

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

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

      12. --lowering--.f64 87.8%

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

   4. Applied egg-rr 87.8%

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

   5. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 82.1%

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

   7. Simplified 82.1%

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

   if -1.86000000000000006e50 < a < 6.19999999999999993e-55

   1. Initial program 71.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 83.4%

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

   5. Simplified 83.4%

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

   if 6.19999999999999993e-55 < a

   1. Initial program 89.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 75.3%

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

   5. Simplified 75.3%

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

      1. *-commutative N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 78.6%

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

   7. Applied egg-rr 78.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.86 \cdot 10^{+50}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32500000000000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -32500000000000.0)
   (+ x (* y (/ (- t x) (- a z))))
   (if (<= y 2.3e+159)
     (+ x (/ t (/ (- a z) (- y z))))
     (+ x (/ (- t x) (/ (- a z) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -32500000000000.0) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else if (y <= 2.3e+159) {
		tmp = x + (t / ((a - z) / (y - z)));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-32500000000000.0d0)) then
        tmp = x + (y * ((t - x) / (a - z)))
    else if (y <= 2.3d+159) then
        tmp = x + (t / ((a - z) / (y - z)))
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -32500000000000.0) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else if (y <= 2.3e+159) {
		tmp = x + (t / ((a - z) / (y - z)));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -32500000000000.0:
		tmp = x + (y * ((t - x) / (a - z)))
	elif y <= 2.3e+159:
		tmp = x + (t / ((a - z) / (y - z)))
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -32500000000000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	elseif (y <= 2.3e+159)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -32500000000000.0)
		tmp = x + (y * ((t - x) / (a - z)));
	elseif (y <= 2.3e+159)
		tmp = x + (t / ((a - z) / (y - z)));
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -32500000000000.0], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+159], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.25e13

   1. Initial program 91.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 83.6%

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

   if -3.25e13 < y < 2.29999999999999995e159

   1. Initial program 74.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 69.2%

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

   5. Simplified 69.2%

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

      1. *-commutative N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 74.8%

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

   7. Applied egg-rr 74.8%

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

   if 2.29999999999999995e159 < y

   1. Initial program 88.7%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      9. clear-num N/A

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

      10. flip-- N/A

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

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

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

      12. --lowering--.f64 88.6%

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

   4. Applied egg-rr 88.6%

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

      1. associate-/l/ N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. div-inv N/A

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

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

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

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

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

      8. --lowering--.f64 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 90.6%

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

   9. Simplified 90.6%

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

Alternative 13: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+159}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t x) (- a z))))))
   (if (<= y -1.2e+20)
     t_1
     (if (<= y 3.1e+159) (+ x (/ t (/ (- a z) (- y z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / (a - z)));
	double tmp;
	if (y <= -1.2e+20) {
		tmp = t_1;
	} else if (y <= 3.1e+159) {
		tmp = x + (t / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((t - x) / (a - z)))
    if (y <= (-1.2d+20)) then
        tmp = t_1
    else if (y <= 3.1d+159) then
        tmp = x + (t / ((a - z) / (y - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / (a - z)));
	double tmp;
	if (y <= -1.2e+20) {
		tmp = t_1;
	} else if (y <= 3.1e+159) {
		tmp = x + (t / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - x) / (a - z)))
	tmp = 0
	if y <= -1.2e+20:
		tmp = t_1
	elif y <= 3.1e+159:
		tmp = x + (t / ((a - z) / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (y <= -1.2e+20)
		tmp = t_1;
	elseif (y <= 3.1e+159)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - x) / (a - z)));
	tmp = 0.0;
	if (y <= -1.2e+20)
		tmp = t_1;
	elseif (y <= 3.1e+159)
		tmp = x + (t / ((a - z) / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+20], t$95$1, If[LessEqual[y, 3.1e+159], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e20 or 3.0999999999999998e159 < y

   1. Initial program 90.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 85.0%

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

   if -1.2e20 < y < 3.0999999999999998e159

   1. Initial program 74.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 69.2%

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

   5. Simplified 69.2%

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

      1. *-commutative N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 74.8%

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

   7. Applied egg-rr 74.8%

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

Alternative 14: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -3.1e+53)
     t_1
     (if (<= z 5.5e+148) (+ 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 + (x * ((y - a) / z));
	double tmp;
	if (z <= -3.1e+53) {
		tmp = t_1;
	} else if (z <= 5.5e+148) {
		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 + (x * ((y - a) / z))
    if (z <= (-3.1d+53)) then
        tmp = t_1
    else if (z <= 5.5d+148) 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 + (x * ((y - a) / z));
	double tmp;
	if (z <= -3.1e+53) {
		tmp = t_1;
	} else if (z <= 5.5e+148) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -3.1e+53:
		tmp = t_1
	elif z <= 5.5e+148:
		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(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -3.1e+53)
		tmp = t_1;
	elseif (z <= 5.5e+148)
		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 + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -3.1e+53)
		tmp = t_1;
	elseif (z <= 5.5e+148)
		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[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+53], t$95$1, If[LessEqual[z, 5.5e+148], 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 < -3.10000000000000019e53 or 5.5e148 < z

   1. Initial program 62.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 76.9%

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

   8. Simplified 76.9%

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

   if -3.10000000000000019e53 < z < 5.5e148

   1. Initial program 90.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 77.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+80}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.3e-11)
   (+ x (* y (/ (- t x) a)))
   (if (<= a 8.4e+80) (+ t (/ (* x y) z)) (+ x (* (- y z) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e-11) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 8.4e+80) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.3d-11)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= 8.4d+80) then
        tmp = t + ((x * y) / z)
    else
        tmp = x + ((y - z) * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e-11) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 8.4e+80) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.3e-11:
		tmp = x + (y * ((t - x) / a))
	elif a <= 8.4e+80:
		tmp = t + ((x * y) / z)
	else:
		tmp = x + ((y - z) * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.3e-11)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 8.4e+80)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.3e-11)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= 8.4e+80)
		tmp = t + ((x * y) / z);
	else
		tmp = x + ((y - z) * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.3e-11], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e+80], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3000000000000002e-11

   1. Initial program 84.4%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 63.0%

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

   5. Simplified 63.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 66.4%

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

   7. Applied egg-rr 66.4%

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

   if -3.3000000000000002e-11 < a < 8.40000000000000005e80

   1. Initial program 74.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 61.3%

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

   11. Simplified 61.3%

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

   if 8.40000000000000005e80 < a

   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 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 81.5%

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

   8. Simplified 81.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+80}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+80}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t a)))))
   (if (<= a -2.35e-11) t_1 (if (<= a 8.4e+80) (+ t (/ (* x y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.35e-11) {
		tmp = t_1;
	} else if (a <= 8.4e+80) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / a))
    if (a <= (-2.35d-11)) then
        tmp = t_1
    else if (a <= 8.4d+80) then
        tmp = t + ((x * 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 + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.35e-11) {
		tmp = t_1;
	} else if (a <= 8.4e+80) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -2.35e-11:
		tmp = t_1
	elif a <= 8.4e+80:
		tmp = t + ((x * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.35e-11)
		tmp = t_1;
	elseif (a <= 8.4e+80)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -2.35e-11)
		tmp = t_1;
	elseif (a <= 8.4e+80)
		tmp = t + ((x * 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[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.35e-11], t$95$1, If[LessEqual[a, 8.4e+80], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.34999999999999996e-11 or 8.40000000000000005e80 < a

   1. Initial program 88.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 72.4%

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

   8. Simplified 72.4%

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

   if -2.34999999999999996e-11 < a < 8.40000000000000005e80

   1. Initial program 74.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 61.3%

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

   11. Simplified 61.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+80}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+81}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.55e-34) t_1 (if (<= a 1.55e+81) (+ t (/ (* x y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.55e-34) {
		tmp = t_1;
	} else if (a <= 1.55e+81) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-1.55d-34)) then
        tmp = t_1
    else if (a <= 1.55d+81) then
        tmp = t + ((x * 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 * (1.0 - (y / a));
	double tmp;
	if (a <= -1.55e-34) {
		tmp = t_1;
	} else if (a <= 1.55e+81) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.55e-34:
		tmp = t_1
	elif a <= 1.55e+81:
		tmp = t + ((x * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.55e-34)
		tmp = t_1;
	elseif (a <= 1.55e+81)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.55e-34)
		tmp = t_1;
	elseif (a <= 1.55e+81)
		tmp = t + ((x * 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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-34], t$95$1, If[LessEqual[a, 1.55e+81], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5499999999999999e-34 or 1.55e81 < a

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. 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 58.4%

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

   8. Simplified 58.4%

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

   if -1.5499999999999999e-34 < a < 1.55e81

   1. Initial program 74.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. div-sub N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. div-sub N/A

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

      16. /-lowering-/.f64 N/A

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

      17. --lowering--.f64 69.6%

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

   8. Simplified 69.6%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 61.9%

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

   11. Simplified 61.9%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+81}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.9e+105) t (if (<= z 6e+148) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.9e+105) {
		tmp = t;
	} else if (z <= 6e+148) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.9d+105)) then
        tmp = t
    else if (z <= 6d+148) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.9e+105) {
		tmp = t;
	} else if (z <= 6e+148) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.9e+105:
		tmp = t
	elif z <= 6e+148:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.9e+105)
		tmp = t;
	elseif (z <= 6e+148)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.9e+105)
		tmp = t;
	elseif (z <= 6e+148)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.9e+105], t, If[LessEqual[z, 6e+148], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999978e105 or 6.00000000000000029e148 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 59.9%

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

   if -3.89999999999999978e105 < z < 6.00000000000000029e148

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. 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 46.6%

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

   8. Simplified 46.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-10) x (if (<= a 9e+80) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-10) {
		tmp = x;
	} else if (a <= 9e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-10)) then
        tmp = x
    else if (a <= 9d+80) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-10) {
		tmp = x;
	} else if (a <= 9e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-10:
		tmp = x
	elif a <= 9e+80:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-10)
		tmp = x;
	elseif (a <= 9e+80)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-10)
		tmp = x;
	elseif (a <= 9e+80)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-10], x, If[LessEqual[a, 9e+80], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5999999999999999e-10 or 9.00000000000000013e80 < a

   1. Initial program 88.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 46.7%

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

   if -1.5999999999999999e-10 < a < 9.00000000000000013e80

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 37.4%

      \[\leadsto \color{blue}{t} \]
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 80.2%

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

3. Taylor expanded in z around inf

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

5. Simplified 26.7%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(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)))))