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

Percentage Accurate: 67.3% → 89.7%

Time: 14.9s

Alternatives: 23

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-208}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -4e-208)
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- y x) (- a z)) t))
       (+ x (/ (- y x) (/ (- a t) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -4e-208) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if (t_1 <= (-4d-208)) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else if (t_1 <= 0.0d0) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -4e-208) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -4e-208:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -4e-208)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -4e-208)
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-208], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.0000000000000004e-208

   1. Initial program 75.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 89.0%

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

   4. Applied egg-rr 89.0%

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

   if -4.0000000000000004e-208 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 70.0%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 91.4%

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

   4. Applied egg-rr 91.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-208}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ (- z t) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -4e-208)
     t_1
     (if (<= t_2 0.0) (+ y (/ (* (- y x) (- a z)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -4e-208) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) * ((z - t) / (a - t)))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-4d-208)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -4e-208) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * ((z - t) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -4e-208:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -4e-208)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * ((z - t) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -4e-208)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	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 - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-208], t$95$1, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.0000000000000004e-208 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 90.3%

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

   4. Applied egg-rr 90.3%

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

   if -4.0000000000000004e-208 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-208}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+59}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.75 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+231}:\\ \;\;\;\;\frac{y \cdot t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+59)
   y
   (if (<= t -3.75e-165)
     (/ y (/ (- a t) z))
     (if (<= t -7.4e-295)
       x
       (if (<= t 9.2e-165)
         (/ y (/ a (- z t)))
         (if (<= t 1.15e-22) x (if (<= t 2.2e+231) (/ (* y t) (- t a)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+59) {
		tmp = y;
	} else if (t <= -3.75e-165) {
		tmp = y / ((a - t) / z);
	} else if (t <= -7.4e-295) {
		tmp = x;
	} else if (t <= 9.2e-165) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.15e-22) {
		tmp = x;
	} else if (t <= 2.2e+231) {
		tmp = (y * t) / (t - a);
	} else {
		tmp = 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 (t <= (-3d+59)) then
        tmp = y
    else if (t <= (-3.75d-165)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-7.4d-295)) then
        tmp = x
    else if (t <= 9.2d-165) then
        tmp = y / (a / (z - t))
    else if (t <= 1.15d-22) then
        tmp = x
    else if (t <= 2.2d+231) then
        tmp = (y * t) / (t - a)
    else
        tmp = 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 (t <= -3e+59) {
		tmp = y;
	} else if (t <= -3.75e-165) {
		tmp = y / ((a - t) / z);
	} else if (t <= -7.4e-295) {
		tmp = x;
	} else if (t <= 9.2e-165) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.15e-22) {
		tmp = x;
	} else if (t <= 2.2e+231) {
		tmp = (y * t) / (t - a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+59:
		tmp = y
	elif t <= -3.75e-165:
		tmp = y / ((a - t) / z)
	elif t <= -7.4e-295:
		tmp = x
	elif t <= 9.2e-165:
		tmp = y / (a / (z - t))
	elif t <= 1.15e-22:
		tmp = x
	elif t <= 2.2e+231:
		tmp = (y * t) / (t - a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+59)
		tmp = y;
	elseif (t <= -3.75e-165)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -7.4e-295)
		tmp = x;
	elseif (t <= 9.2e-165)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 1.15e-22)
		tmp = x;
	elseif (t <= 2.2e+231)
		tmp = Float64(Float64(y * t) / Float64(t - a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+59)
		tmp = y;
	elseif (t <= -3.75e-165)
		tmp = y / ((a - t) / z);
	elseif (t <= -7.4e-295)
		tmp = x;
	elseif (t <= 9.2e-165)
		tmp = y / (a / (z - t));
	elseif (t <= 1.15e-22)
		tmp = x;
	elseif (t <= 2.2e+231)
		tmp = (y * t) / (t - a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+59], y, If[LessEqual[t, -3.75e-165], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.4e-295], x, If[LessEqual[t, 9.2e-165], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-22], x, If[LessEqual[t, 2.2e+231], N[(N[(y * t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3e59 or 2.19999999999999992e231 < t

   1. Initial program 36.6%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 56.6%

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

   if -3e59 < t < -3.7500000000000001e-165

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   5. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 56.6%

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

   7. Applied egg-rr 56.6%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 46.9%

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

   10. Simplified 46.9%

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

   if -3.7500000000000001e-165 < t < -7.3999999999999999e-295 or 9.2000000000000002e-165 < t < 1.1499999999999999e-22

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.6%

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

   if -7.3999999999999999e-295 < t < 9.2000000000000002e-165

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.1%

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

   5. Simplified 58.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 70.6%

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

   10. Simplified 70.6%

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

   if 1.1499999999999999e-22 < t < 2.19999999999999992e231

   1. Initial program 59.8%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

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

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

      4. *-commutative N/A

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

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

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

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

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

      7. --lowering--.f64 38.8%

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

   8. Simplified 38.8%

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

   9. Taylor expanded in a around 0

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

       1. mul-1-neg N/A

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

       2. sub-neg N/A

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

       3. --lowering--.f64 38.8%

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

   11. Simplified 38.8%

       \[\leadsto \frac{y \cdot t}{\color{blue}{t - a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-166}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+66)
   y
   (if (<= t -5.5e-165)
     (/ y (/ (- a t) z))
     (if (<= t -2.25e-297)
       x
       (if (<= t 4e-166)
         (/ y (/ a (- z t)))
         (if (<= t 1.5e-24) x (* t (/ y (- t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+66) {
		tmp = y;
	} else if (t <= -5.5e-165) {
		tmp = y / ((a - t) / z);
	} else if (t <= -2.25e-297) {
		tmp = x;
	} else if (t <= 4e-166) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.5e-24) {
		tmp = x;
	} else {
		tmp = t * (y / (t - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+66)) then
        tmp = y
    else if (t <= (-5.5d-165)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-2.25d-297)) then
        tmp = x
    else if (t <= 4d-166) then
        tmp = y / (a / (z - t))
    else if (t <= 1.5d-24) then
        tmp = x
    else
        tmp = t * (y / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+66) {
		tmp = y;
	} else if (t <= -5.5e-165) {
		tmp = y / ((a - t) / z);
	} else if (t <= -2.25e-297) {
		tmp = x;
	} else if (t <= 4e-166) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.5e-24) {
		tmp = x;
	} else {
		tmp = t * (y / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+66:
		tmp = y
	elif t <= -5.5e-165:
		tmp = y / ((a - t) / z)
	elif t <= -2.25e-297:
		tmp = x
	elif t <= 4e-166:
		tmp = y / (a / (z - t))
	elif t <= 1.5e-24:
		tmp = x
	else:
		tmp = t * (y / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+66)
		tmp = y;
	elseif (t <= -5.5e-165)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -2.25e-297)
		tmp = x;
	elseif (t <= 4e-166)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 1.5e-24)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+66)
		tmp = y;
	elseif (t <= -5.5e-165)
		tmp = y / ((a - t) / z);
	elseif (t <= -2.25e-297)
		tmp = x;
	elseif (t <= 4e-166)
		tmp = y / (a / (z - t));
	elseif (t <= 1.5e-24)
		tmp = x;
	else
		tmp = t * (y / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+66], y, If[LessEqual[t, -5.5e-165], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.25e-297], x, If[LessEqual[t, 4e-166], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-24], x, N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.8000000000000001e66

   1. Initial program 43.5%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 53.1%

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

   if -2.8000000000000001e66 < t < -5.49999999999999969e-165

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   5. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 56.6%

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

   7. Applied egg-rr 56.6%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 46.9%

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

   10. Simplified 46.9%

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

   if -5.49999999999999969e-165 < t < -2.24999999999999988e-297 or 4.00000000000000016e-166 < t < 1.49999999999999998e-24

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.6%

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

   if -2.24999999999999988e-297 < t < 4.00000000000000016e-166

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.1%

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

   5. Simplified 58.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 70.6%

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

   10. Simplified 70.6%

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

   if 1.49999999999999998e-24 < t

   1. Initial program 51.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

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

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

      4. *-commutative N/A

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

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

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

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

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

      7. --lowering--.f64 35.1%

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

   8. Simplified 35.1%

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

      1. distribute-frac-neg2 N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 42.5%

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

   10. Applied egg-rr 42.5%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-166}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-166}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+59)
   y
   (if (<= t -2e-165)
     (/ y (/ (- a t) z))
     (if (<= t -1.7e-294)
       x
       (if (<= t 6.7e-166) (/ y (/ a (- z t))) (if (<= t 1.45e-22) x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+59) {
		tmp = y;
	} else if (t <= -2e-165) {
		tmp = y / ((a - t) / z);
	} else if (t <= -1.7e-294) {
		tmp = x;
	} else if (t <= 6.7e-166) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.45e-22) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-4.2d+59)) then
        tmp = y
    else if (t <= (-2d-165)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-1.7d-294)) then
        tmp = x
    else if (t <= 6.7d-166) then
        tmp = y / (a / (z - t))
    else if (t <= 1.45d-22) then
        tmp = x
    else
        tmp = 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 (t <= -4.2e+59) {
		tmp = y;
	} else if (t <= -2e-165) {
		tmp = y / ((a - t) / z);
	} else if (t <= -1.7e-294) {
		tmp = x;
	} else if (t <= 6.7e-166) {
		tmp = y / (a / (z - t));
	} else if (t <= 1.45e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+59:
		tmp = y
	elif t <= -2e-165:
		tmp = y / ((a - t) / z)
	elif t <= -1.7e-294:
		tmp = x
	elif t <= 6.7e-166:
		tmp = y / (a / (z - t))
	elif t <= 1.45e-22:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+59)
		tmp = y;
	elseif (t <= -2e-165)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -1.7e-294)
		tmp = x;
	elseif (t <= 6.7e-166)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 1.45e-22)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+59)
		tmp = y;
	elseif (t <= -2e-165)
		tmp = y / ((a - t) / z);
	elseif (t <= -1.7e-294)
		tmp = x;
	elseif (t <= 6.7e-166)
		tmp = y / (a / (z - t));
	elseif (t <= 1.45e-22)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+59], y, If[LessEqual[t, -2e-165], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-294], x, If[LessEqual[t, 6.7e-166], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-22], x, y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.19999999999999968e59 or 1.4500000000000001e-22 < t

   1. Initial program 48.8%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 42.8%

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

   if -4.19999999999999968e59 < t < -2e-165

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   5. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 56.6%

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

   7. Applied egg-rr 56.6%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 46.9%

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

   10. Simplified 46.9%

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

   if -2e-165 < t < -1.69999999999999991e-294 or 6.70000000000000052e-166 < t < 1.4500000000000001e-22

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.6%

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

   if -1.69999999999999991e-294 < t < 6.70000000000000052e-166

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.1%

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

   5. Simplified 58.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 70.6%

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

   10. Simplified 70.6%

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

Alternative 6: 38.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+58}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.3e+58)
   y
   (if (<= t -2.7e-165)
     (* y (/ z (- a t)))
     (if (<= t -5.4e-301)
       x
       (if (<= t 1.9e-165) (/ y (/ a (- z t))) (if (<= t 8.6e-31) x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.3e+58) {
		tmp = y;
	} else if (t <= -2.7e-165) {
		tmp = y * (z / (a - t));
	} else if (t <= -5.4e-301) {
		tmp = x;
	} else if (t <= 1.9e-165) {
		tmp = y / (a / (z - t));
	} else if (t <= 8.6e-31) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-4.3d+58)) then
        tmp = y
    else if (t <= (-2.7d-165)) then
        tmp = y * (z / (a - t))
    else if (t <= (-5.4d-301)) then
        tmp = x
    else if (t <= 1.9d-165) then
        tmp = y / (a / (z - t))
    else if (t <= 8.6d-31) then
        tmp = x
    else
        tmp = 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 (t <= -4.3e+58) {
		tmp = y;
	} else if (t <= -2.7e-165) {
		tmp = y * (z / (a - t));
	} else if (t <= -5.4e-301) {
		tmp = x;
	} else if (t <= 1.9e-165) {
		tmp = y / (a / (z - t));
	} else if (t <= 8.6e-31) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.3e+58:
		tmp = y
	elif t <= -2.7e-165:
		tmp = y * (z / (a - t))
	elif t <= -5.4e-301:
		tmp = x
	elif t <= 1.9e-165:
		tmp = y / (a / (z - t))
	elif t <= 8.6e-31:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.3e+58)
		tmp = y;
	elseif (t <= -2.7e-165)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= -5.4e-301)
		tmp = x;
	elseif (t <= 1.9e-165)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t <= 8.6e-31)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.3e+58)
		tmp = y;
	elseif (t <= -2.7e-165)
		tmp = y * (z / (a - t));
	elseif (t <= -5.4e-301)
		tmp = x;
	elseif (t <= 1.9e-165)
		tmp = y / (a / (z - t));
	elseif (t <= 8.6e-31)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.3e+58], y, If[LessEqual[t, -2.7e-165], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e-301], x, If[LessEqual[t, 1.9e-165], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e-31], x, y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.29999999999999991e58 or 8.6e-31 < t

   1. Initial program 48.8%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 42.8%

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

   if -4.29999999999999991e58 < t < -2.6999999999999998e-165

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   5. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 56.6%

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

   7. Applied egg-rr 56.6%

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

   8. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 46.9%

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

   10. Simplified 46.9%

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

   if -2.6999999999999998e-165 < t < -5.3999999999999999e-301 or 1.90000000000000009e-165 < t < 8.6e-31

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.6%

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

   if -5.3999999999999999e-301 < t < 1.90000000000000009e-165

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.1%

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

   5. Simplified 58.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 70.6%

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

   10. Simplified 70.6%

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

Alternative 7: 38.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+59)
   y
   (if (<= t -2.6e-165)
     (* y (/ z (- a t)))
     (if (<= t -4.7e-301)
       x
       (if (<= t 1.12e-166) (* y (/ (- z t) a)) (if (<= t 5e-23) x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+59) {
		tmp = y;
	} else if (t <= -2.6e-165) {
		tmp = y * (z / (a - t));
	} else if (t <= -4.7e-301) {
		tmp = x;
	} else if (t <= 1.12e-166) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5e-23) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1.25d+59)) then
        tmp = y
    else if (t <= (-2.6d-165)) then
        tmp = y * (z / (a - t))
    else if (t <= (-4.7d-301)) then
        tmp = x
    else if (t <= 1.12d-166) then
        tmp = y * ((z - t) / a)
    else if (t <= 5d-23) then
        tmp = x
    else
        tmp = 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 (t <= -1.25e+59) {
		tmp = y;
	} else if (t <= -2.6e-165) {
		tmp = y * (z / (a - t));
	} else if (t <= -4.7e-301) {
		tmp = x;
	} else if (t <= 1.12e-166) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5e-23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+59:
		tmp = y
	elif t <= -2.6e-165:
		tmp = y * (z / (a - t))
	elif t <= -4.7e-301:
		tmp = x
	elif t <= 1.12e-166:
		tmp = y * ((z - t) / a)
	elif t <= 5e-23:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+59)
		tmp = y;
	elseif (t <= -2.6e-165)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= -4.7e-301)
		tmp = x;
	elseif (t <= 1.12e-166)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 5e-23)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+59)
		tmp = y;
	elseif (t <= -2.6e-165)
		tmp = y * (z / (a - t));
	elseif (t <= -4.7e-301)
		tmp = x;
	elseif (t <= 1.12e-166)
		tmp = y * ((z - t) / a);
	elseif (t <= 5e-23)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+59], y, If[LessEqual[t, -2.6e-165], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-301], x, If[LessEqual[t, 1.12e-166], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-23], x, y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2499999999999999e59 or 5.0000000000000002e-23 < t

   1. Initial program 48.8%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 42.8%

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

   if -1.2499999999999999e59 < t < -2.60000000000000007e-165

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   5. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 56.6%

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

   7. Applied egg-rr 56.6%

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

   8. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 46.9%

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

   10. Simplified 46.9%

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

   if -2.60000000000000007e-165 < t < -4.6999999999999997e-301 or 1.11999999999999994e-166 < t < 5.0000000000000002e-23

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.6%

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

   if -4.6999999999999997e-301 < t < 1.11999999999999994e-166

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.1%

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

   5. Simplified 58.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 70.4%

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

   10. Simplified 70.4%

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

Alternative 8: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+65}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-220}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+65)
   y
   (if (<= t -2.05e-165)
     (* y (/ z (- a t)))
     (if (<= t -2.8e-298)
       x
       (if (<= t 6.3e-220) (/ y (/ a z)) (if (<= t 1.7e-22) x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+65) {
		tmp = y;
	} else if (t <= -2.05e-165) {
		tmp = y * (z / (a - t));
	} else if (t <= -2.8e-298) {
		tmp = x;
	} else if (t <= 6.3e-220) {
		tmp = y / (a / z);
	} else if (t <= 1.7e-22) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1d+65)) then
        tmp = y
    else if (t <= (-2.05d-165)) then
        tmp = y * (z / (a - t))
    else if (t <= (-2.8d-298)) then
        tmp = x
    else if (t <= 6.3d-220) then
        tmp = y / (a / z)
    else if (t <= 1.7d-22) then
        tmp = x
    else
        tmp = 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 (t <= -1e+65) {
		tmp = y;
	} else if (t <= -2.05e-165) {
		tmp = y * (z / (a - t));
	} else if (t <= -2.8e-298) {
		tmp = x;
	} else if (t <= 6.3e-220) {
		tmp = y / (a / z);
	} else if (t <= 1.7e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+65:
		tmp = y
	elif t <= -2.05e-165:
		tmp = y * (z / (a - t))
	elif t <= -2.8e-298:
		tmp = x
	elif t <= 6.3e-220:
		tmp = y / (a / z)
	elif t <= 1.7e-22:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+65)
		tmp = y;
	elseif (t <= -2.05e-165)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= -2.8e-298)
		tmp = x;
	elseif (t <= 6.3e-220)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.7e-22)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e+65)
		tmp = y;
	elseif (t <= -2.05e-165)
		tmp = y * (z / (a - t));
	elseif (t <= -2.8e-298)
		tmp = x;
	elseif (t <= 6.3e-220)
		tmp = y / (a / z);
	elseif (t <= 1.7e-22)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+65], y, If[LessEqual[t, -2.05e-165], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-298], x, If[LessEqual[t, 6.3e-220], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-22], x, y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.9999999999999999e64 or 1.6999999999999999e-22 < t

   1. Initial program 48.8%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 42.8%

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

   if -9.9999999999999999e64 < t < -2.0500000000000001e-165

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.2%

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

   5. Simplified 51.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 56.6%

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

   7. Applied egg-rr 56.6%

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

   8. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 46.9%

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

   10. Simplified 46.9%

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

   if -2.0500000000000001e-165 < t < -2.79999999999999992e-298 or 6.30000000000000017e-220 < t < 1.6999999999999999e-22

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.3%

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

   if -2.79999999999999992e-298 < t < 6.30000000000000017e-220

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 59.5%

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

   5. Simplified 59.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 74.6%

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

   7. Applied egg-rr 74.6%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 69.4%

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

   10. Simplified 69.4%

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

Alternative 9: 37.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= t -1.9e+17)
     y
     (if (<= t -2.8e-165)
       t_1
       (if (<= t -2.8e-294)
         x
         (if (<= t 2.55e-220) t_1 (if (<= t 1.12e-26) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (t <= -1.9e+17) {
		tmp = y;
	} else if (t <= -2.8e-165) {
		tmp = t_1;
	} else if (t <= -2.8e-294) {
		tmp = x;
	} else if (t <= 2.55e-220) {
		tmp = t_1;
	} else if (t <= 1.12e-26) {
		tmp = x;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y / (a / z)
    if (t <= (-1.9d+17)) then
        tmp = y
    else if (t <= (-2.8d-165)) then
        tmp = t_1
    else if (t <= (-2.8d-294)) then
        tmp = x
    else if (t <= 2.55d-220) then
        tmp = t_1
    else if (t <= 1.12d-26) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (t <= -1.9e+17) {
		tmp = y;
	} else if (t <= -2.8e-165) {
		tmp = t_1;
	} else if (t <= -2.8e-294) {
		tmp = x;
	} else if (t <= 2.55e-220) {
		tmp = t_1;
	} else if (t <= 1.12e-26) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if t <= -1.9e+17:
		tmp = y
	elif t <= -2.8e-165:
		tmp = t_1
	elif t <= -2.8e-294:
		tmp = x
	elif t <= 2.55e-220:
		tmp = t_1
	elif t <= 1.12e-26:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (t <= -1.9e+17)
		tmp = y;
	elseif (t <= -2.8e-165)
		tmp = t_1;
	elseif (t <= -2.8e-294)
		tmp = x;
	elseif (t <= 2.55e-220)
		tmp = t_1;
	elseif (t <= 1.12e-26)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (t <= -1.9e+17)
		tmp = y;
	elseif (t <= -2.8e-165)
		tmp = t_1;
	elseif (t <= -2.8e-294)
		tmp = x;
	elseif (t <= 2.55e-220)
		tmp = t_1;
	elseif (t <= 1.12e-26)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+17], y, If[LessEqual[t, -2.8e-165], t$95$1, If[LessEqual[t, -2.8e-294], x, If[LessEqual[t, 2.55e-220], t$95$1, If[LessEqual[t, 1.12e-26], x, y]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e17 or 1.12e-26 < t

   1. Initial program 50.1%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 41.0%

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

   if -1.9e17 < t < -2.7999999999999999e-165 or -2.79999999999999991e-294 < t < 2.55e-220

   1. Initial program 84.2%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 55.9%

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

   5. Simplified 55.9%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 63.7%

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

   7. Applied egg-rr 63.7%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 51.4%

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

   10. Simplified 51.4%

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

   if -2.7999999999999999e-165 < t < -2.79999999999999991e-294 or 2.55e-220 < t < 1.12e-26

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.3%

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

Alternative 10: 37.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -4.8e+23)
     y
     (if (<= t -3.2e-165)
       t_1
       (if (<= t -1e-295)
         x
         (if (<= t 7.5e-220) t_1 (if (<= t 1.35e-22) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -4.8e+23) {
		tmp = y;
	} else if (t <= -3.2e-165) {
		tmp = t_1;
	} else if (t <= -1e-295) {
		tmp = x;
	} else if (t <= 7.5e-220) {
		tmp = t_1;
	} else if (t <= 1.35e-22) {
		tmp = x;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (t <= (-4.8d+23)) then
        tmp = y
    else if (t <= (-3.2d-165)) then
        tmp = t_1
    else if (t <= (-1d-295)) then
        tmp = x
    else if (t <= 7.5d-220) then
        tmp = t_1
    else if (t <= 1.35d-22) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -4.8e+23) {
		tmp = y;
	} else if (t <= -3.2e-165) {
		tmp = t_1;
	} else if (t <= -1e-295) {
		tmp = x;
	} else if (t <= 7.5e-220) {
		tmp = t_1;
	} else if (t <= 1.35e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -4.8e+23:
		tmp = y
	elif t <= -3.2e-165:
		tmp = t_1
	elif t <= -1e-295:
		tmp = x
	elif t <= 7.5e-220:
		tmp = t_1
	elif t <= 1.35e-22:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -4.8e+23)
		tmp = y;
	elseif (t <= -3.2e-165)
		tmp = t_1;
	elseif (t <= -1e-295)
		tmp = x;
	elseif (t <= 7.5e-220)
		tmp = t_1;
	elseif (t <= 1.35e-22)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (t <= -4.8e+23)
		tmp = y;
	elseif (t <= -3.2e-165)
		tmp = t_1;
	elseif (t <= -1e-295)
		tmp = x;
	elseif (t <= 7.5e-220)
		tmp = t_1;
	elseif (t <= 1.35e-22)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+23], y, If[LessEqual[t, -3.2e-165], t$95$1, If[LessEqual[t, -1e-295], x, If[LessEqual[t, 7.5e-220], t$95$1, If[LessEqual[t, 1.35e-22], x, y]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8e23 or 1.3500000000000001e-22 < t

   1. Initial program 50.1%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 41.0%

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

   if -4.8e23 < t < -3.20000000000000013e-165 or -1.00000000000000006e-295 < t < 7.5000000000000002e-220

   1. Initial program 84.2%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 55.9%

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

   5. Simplified 55.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 63.6%

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

   7. Applied egg-rr 63.6%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 51.2%

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

   10. Simplified 51.2%

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

   if -3.20000000000000013e-165 < t < -1.00000000000000006e-295 or 7.5000000000000002e-220 < t < 1.3500000000000001e-22

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.3%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-142}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t))))))
   (if (<= a -5.4e-145)
     t_1
     (if (<= a 1.75e-142) (+ y (/ (* (- y x) (- a z)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double tmp;
	if (a <= -5.4e-145) {
		tmp = t_1;
	} else if (a <= 1.75e-142) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / (a - t)))
    if (a <= (-5.4d-145)) then
        tmp = t_1
    else if (a <= 1.75d-142) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double tmp;
	if (a <= -5.4e-145) {
		tmp = t_1;
	} else if (a <= 1.75e-142) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	tmp = 0
	if a <= -5.4e-145:
		tmp = t_1
	elif a <= 1.75e-142:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (a <= -5.4e-145)
		tmp = t_1;
	elseif (a <= 1.75e-142)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	tmp = 0.0;
	if (a <= -5.4e-145)
		tmp = t_1;
	elseif (a <= 1.75e-142)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e-145], t$95$1, If[LessEqual[a, 1.75e-142], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4000000000000001e-145 or 1.75000000000000007e-142 < a

   1. Initial program 67.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 86.3%

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

   4. Applied egg-rr 86.3%

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

   if -5.4000000000000001e-145 < a < 1.75000000000000007e-142

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 84.0%

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

   5. Simplified 84.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-145}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-142}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -72000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+60}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a (- z t))))))
   (if (<= a -72000.0)
     t_1
     (if (<= a 6.5e+60) (+ y (/ (* (- y x) (- a z)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -72000.0) {
		tmp = t_1;
	} else if (a <= 6.5e+60) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a / (z - t)))
    if (a <= (-72000.0d0)) then
        tmp = t_1
    else if (a <= 6.5d+60) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -72000.0) {
		tmp = t_1;
	} else if (a <= 6.5e+60) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / (z - t)))
	tmp = 0
	if a <= -72000.0:
		tmp = t_1
	elif a <= 6.5e+60:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -72000.0)
		tmp = t_1;
	elseif (a <= 6.5e+60)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -72000.0)
		tmp = t_1;
	elseif (a <= 6.5e+60)
		tmp = y + (((y - x) * (a - z)) / t);
	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 - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -72000.0], t$95$1, If[LessEqual[a, 6.5e+60], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -72000 or 6.49999999999999931e60 < a

   1. Initial program 67.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 93.5%

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

   4. Applied egg-rr 93.5%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      10. --lowering--.f64 93.0%

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 81.8%

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

   9. Simplified 81.8%

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

   if -72000 < a < 6.49999999999999931e60

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -72000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+60}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -1 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+60}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a (- z t))))))
   (if (<= a -1e-64)
     t_1
     (if (<= a 4e+60) (+ x (* (- y x) (/ (- t z) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -1e-64) {
		tmp = t_1;
	} else if (a <= 4e+60) {
		tmp = x + ((y - x) * ((t - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a / (z - t)))
    if (a <= (-1d-64)) then
        tmp = t_1
    else if (a <= 4d+60) then
        tmp = x + ((y - x) * ((t - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -1e-64) {
		tmp = t_1;
	} else if (a <= 4e+60) {
		tmp = x + ((y - x) * ((t - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / (z - t)))
	tmp = 0
	if a <= -1e-64:
		tmp = t_1
	elif a <= 4e+60:
		tmp = x + ((y - x) * ((t - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -1e-64)
		tmp = t_1;
	elseif (a <= 4e+60)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(t - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -1e-64)
		tmp = t_1;
	elseif (a <= 4e+60)
		tmp = x + ((y - x) * ((t - z) / t));
	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 - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-64], t$95$1, If[LessEqual[a, 4e+60], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.99999999999999965e-65 or 3.9999999999999998e60 < a

   1. Initial program 68.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      10. --lowering--.f64 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in a around inf

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

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

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

      2. --lowering--.f64 79.0%

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

   9. Simplified 79.0%

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

   if -9.99999999999999965e-65 < a < 3.9999999999999998e60

   1. Initial program 65.5%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

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

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

      13. --lowering--.f64 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+60}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+60}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) a)))))
   (if (<= a -8e-67)
     t_1
     (if (<= a 4.9e+60) (+ x (* (- y x) (/ (- t z) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / a));
	double tmp;
	if (a <= -8e-67) {
		tmp = t_1;
	} else if (a <= 4.9e+60) {
		tmp = x + ((y - x) * ((t - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / a))
    if (a <= (-8d-67)) then
        tmp = t_1
    else if (a <= 4.9d+60) then
        tmp = x + ((y - x) * ((t - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / a));
	double tmp;
	if (a <= -8e-67) {
		tmp = t_1;
	} else if (a <= 4.9e+60) {
		tmp = x + ((y - x) * ((t - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / a))
	tmp = 0
	if a <= -8e-67:
		tmp = t_1
	elif a <= 4.9e+60:
		tmp = x + ((y - x) * ((t - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -8e-67)
		tmp = t_1;
	elseif (a <= 4.9e+60)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(t - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / a));
	tmp = 0.0;
	if (a <= -8e-67)
		tmp = t_1;
	elseif (a <= 4.9e+60)
		tmp = x + ((y - x) * ((t - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-67], t$95$1, If[LessEqual[a, 4.9e+60], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.99999999999999954e-67 or 4.9000000000000003e60 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 77.8%

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

   5. Simplified 77.8%

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

   if -7.99999999999999954e-67 < a < 4.9000000000000003e60

   1. Initial program 65.5%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

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

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

      13. --lowering--.f64 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-67}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+60}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.9e+14)
   (/ y (/ (- a t) (- z t)))
   (if (<= y 2.5e-30)
     (* x (+ (/ (- z t) (- t a)) 1.0))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.9e+14) {
		tmp = y / ((a - t) / (z - t));
	} else if (y <= 2.5e-30) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.9d+14)) then
        tmp = y / ((a - t) / (z - t))
    else if (y <= 2.5d-30) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.9e+14) {
		tmp = y / ((a - t) / (z - t));
	} else if (y <= 2.5e-30) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.9e+14:
		tmp = y / ((a - t) / (z - t))
	elif y <= 2.5e-30:
		tmp = x * (((z - t) / (t - a)) + 1.0)
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.9e+14)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (y <= 2.5e-30)
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.9e+14)
		tmp = y / ((a - t) / (z - t));
	elseif (y <= 2.5e-30)
		tmp = x * (((z - t) / (t - a)) + 1.0);
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.9e+14], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-30], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e14

   1. Initial program 67.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 59.4%

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

   5. Simplified 59.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 80.7%

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

   7. Applied egg-rr 80.7%

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

   if -3.9e14 < y < 2.49999999999999986e-30

   1. Initial program 73.6%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 62.0%

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

   5. Simplified 62.0%

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

   if 2.49999999999999986e-30 < y

   1. Initial program 56.3%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 40.8%

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

   5. Simplified 40.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), y\right) \]

      6. --lowering--.f64 69.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), y\right) \]

   7. Applied egg-rr 69.9%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+36)
   (* y (/ (- z t) (- a t)))
   (if (<= t 4.8e-27) (+ x (* (- y x) (/ z a))) (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+36) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 4.8e-27) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y / ((a - t) / (z - 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 (t <= (-2.1d+36)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 4.8d-27) then
        tmp = x + ((y - x) * (z / a))
    else
        tmp = y / ((a - t) / (z - 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 (t <= -2.1e+36) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 4.8e-27) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+36:
		tmp = y * ((z - t) / (a - t))
	elif t <= 4.8e-27:
		tmp = x + ((y - x) * (z / a))
	else:
		tmp = y / ((a - t) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+36)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 4.8e-27)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+36)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 4.8e-27)
		tmp = x + ((y - x) * (z / a));
	else
		tmp = y / ((a - t) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+36], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-27], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.10000000000000004e36

   1. Initial program 45.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 32.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 32.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z - t}{a - t} \cdot \color{blue}{y} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{a - t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(a - t\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), y\right) \]

      6. --lowering--.f64 67.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), y\right) \]

   7. Applied egg-rr 67.7%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} \]

   if -2.10000000000000004e36 < t < 4.80000000000000004e-27

   1. Initial program 85.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z - t}{a - t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(a - t\right)\right), \left(\color{blue}{y} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), \left(y - x\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), \left(y - x\right)\right)\right) \]

      7. --lowering--.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   4. Applied egg-rr 92.5%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{z}{a}\right)}, \mathsf{\_.f64}\left(y, x\right)\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 73.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \mathsf{\_.f64}\left(\color{blue}{y}, x\right)\right)\right) \]

   7. Simplified 73.7%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]

   if 4.80000000000000004e-27 < t

   1. Initial program 51.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 41.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 41.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{a - t}{z - t}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{y}{\color{blue}{\frac{a - t}{z - t}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a - t}{z - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(a - t\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      7. --lowering--.f64 58.8%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 58.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-25}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.5e+35) t_1 (if (<= t 3e-25) (+ x (* (- y x) (/ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.5e+35) {
		tmp = t_1;
	} else if (t <= 3e-25) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-4.5d+35)) then
        tmp = t_1
    else if (t <= 3d-25) then
        tmp = x + ((y - x) * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.5e+35) {
		tmp = t_1;
	} else if (t <= 3e-25) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -4.5e+35:
		tmp = t_1
	elif t <= 3e-25:
		tmp = x + ((y - x) * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.5e+35)
		tmp = t_1;
	elseif (t <= 3e-25)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -4.5e+35)
		tmp = t_1;
	elseif (t <= 3e-25)
		tmp = x + ((y - x) * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+35], t$95$1, If[LessEqual[t, 3e-25], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999997e35 or 2.9999999999999998e-25 < t

   1. Initial program 49.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 38.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 38.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z - t}{a - t} \cdot \color{blue}{y} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{a - t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(a - t\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), y\right) \]

      6. --lowering--.f64 61.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), y\right) \]

   7. Applied egg-rr 61.9%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} \]

   if -4.4999999999999997e35 < t < 2.9999999999999998e-25

   1. Initial program 85.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z - t}{a - t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(a - t\right)\right), \left(\color{blue}{y} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), \left(y - x\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), \left(y - x\right)\right)\right) \]

      7. --lowering--.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   4. Applied egg-rr 92.5%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{z}{a}\right)}, \mathsf{\_.f64}\left(y, x\right)\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 73.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \mathsf{\_.f64}\left(\color{blue}{y}, x\right)\right)\right) \]

   7. Simplified 73.7%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-25}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -300000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y a)))))
   (if (<= a -300000.0) t_1 (if (<= a 6e+57) (* y (/ (- z t) (- a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / a));
	double tmp;
	if (a <= -300000.0) {
		tmp = t_1;
	} else if (a <= 6e+57) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / a))
    if (a <= (-300000.0d0)) then
        tmp = t_1
    else if (a <= 6d+57) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / a));
	double tmp;
	if (a <= -300000.0) {
		tmp = t_1;
	} else if (a <= 6e+57) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / a))
	tmp = 0
	if a <= -300000.0:
		tmp = t_1
	elif a <= 6e+57:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / a)))
	tmp = 0.0
	if (a <= -300000.0)
		tmp = t_1;
	elseif (a <= 6e+57)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / a));
	tmp = 0.0;
	if (a <= -300000.0)
		tmp = t_1;
	elseif (a <= 6e+57)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -300000.0], t$95$1, If[LessEqual[a, 6e+57], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3e5 or 5.9999999999999999e57 < a

   1. Initial program 67.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{\left(y - x\right) \cdot \left(z - t\right)}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(z - t\right) \cdot \left(y - x\right)}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(z - t\right) \cdot \color{blue}{\frac{y - x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(z - t\right), \color{blue}{\left(\frac{y - x}{a}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{\color{blue}{y - x}}{a}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{a}\right)\right)\right) \]

      7. --lowering--.f64 79.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), a\right)\right)\right) \]

   5. Simplified 79.1%

      \[\leadsto \color{blue}{x + \left(z - t\right) \cdot \frac{y - x}{a}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 74.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 74.0%

      \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y}{a}} \]

   if -3e5 < a < 5.9999999999999999e57

   1. Initial program 66.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 47.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z - t}{a - t} \cdot \color{blue}{y} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{a - t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(a - t\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), y\right) \]

      6. --lowering--.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), y\right) \]

   7. Applied egg-rr 60.5%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -300000:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+180) x (if (<= a 6e+178) (* y (/ (- z t) (- a t))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+180) {
		tmp = x;
	} else if (a <= 6e+178) {
		tmp = y * ((z - t) / (a - 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 <= (-6.2d+180)) then
        tmp = x
    else if (a <= 6d+178) then
        tmp = y * ((z - t) / (a - 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 <= -6.2e+180) {
		tmp = x;
	} else if (a <= 6e+178) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+180:
		tmp = x
	elif a <= 6e+178:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+180)
		tmp = x;
	elseif (a <= 6e+178)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+180)
		tmp = x;
	elseif (a <= 6e+178)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+180], x, If[LessEqual[a, 6e+178], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999997e180 or 6.00000000000000031e178 < a

   1. Initial program 62.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 59.9%

      \[\leadsto \color{blue}{x} \]

   if -6.19999999999999997e180 < a < 6.00000000000000031e178

   1. Initial program 68.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 45.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{z - t}{a - t} \cdot \color{blue}{y} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{a - t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(a - t\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(a - t\right)\right), y\right) \]

      6. --lowering--.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(a, t\right)\right), y\right) \]

   7. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- a t)))))
   (if (<= y -7.5e-87) t_1 (if (<= y 7.5e-32) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double tmp;
	if (y <= -7.5e-87) {
		tmp = t_1;
	} else if (y <= 7.5e-32) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / (a - t))
    if (y <= (-7.5d-87)) then
        tmp = t_1
    else if (y <= 7.5d-32) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (a - t));
	double tmp;
	if (y <= -7.5e-87) {
		tmp = t_1;
	} else if (y <= 7.5e-32) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (a - t))
	tmp = 0
	if y <= -7.5e-87:
		tmp = t_1
	elif y <= 7.5e-32:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (y <= -7.5e-87)
		tmp = t_1;
	elseif (y <= 7.5e-32)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (y <= -7.5e-87)
		tmp = t_1;
	elseif (y <= 7.5e-32)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e-87], t$95$1, If[LessEqual[y, 7.5e-32], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000002e-87 or 7.49999999999999953e-32 < y

   1. Initial program 62.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 47.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(z - t\right) \cdot y}{\color{blue}{a} - t} \]

      2. associate-/l* N/A

         \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z - t\right), \color{blue}{\left(\frac{y}{a - t}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{\color{blue}{y}}{a - t}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - t\right)}\right)\right) \]

      6. --lowering--.f64 68.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 68.1%

      \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   if -7.5000000000000002e-87 < y < 7.49999999999999953e-32

   1. Initial program 74.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 35.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 48.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -100000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -100000.0) x (if (<= a 4.5e+58) (* y (- 1.0 (/ z t))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -100000.0) {
		tmp = x;
	} else if (a <= 4.5e+58) {
		tmp = y * (1.0 - (z / 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 <= (-100000.0d0)) then
        tmp = x
    else if (a <= 4.5d+58) then
        tmp = y * (1.0d0 - (z / 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 <= -100000.0) {
		tmp = x;
	} else if (a <= 4.5e+58) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -100000.0:
		tmp = x
	elif a <= 4.5e+58:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -100000.0)
		tmp = x;
	elseif (a <= 4.5e+58)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -100000.0)
		tmp = x;
	elseif (a <= 4.5e+58)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -100000.0], x, If[LessEqual[a, 4.5e+58], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1e5 or 4.4999999999999998e58 < a

   1. Initial program 67.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 48.0%

      \[\leadsto \color{blue}{x} \]

   if -1e5 < a < 4.4999999999999998e58

   1. Initial program 66.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - t\right)\right), \color{blue}{\left(a - t\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), \left(\color{blue}{a} - t\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \left(a - t\right)\right) \]

      4. --lowering--.f64 47.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

      2. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{a - t}{z - t}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{y}{\color{blue}{\frac{a - t}{z - t}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a - t}{z - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(a - t\right), \color{blue}{\left(z - t\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \left(\color{blue}{z} - t\right)\right)\right) \]

      7. --lowering--.f64 60.5%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, t\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 60.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{t}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(y \cdot \frac{z - t}{t}\right) \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\frac{z - t}{t}} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot y\right) \cdot \frac{\color{blue}{z - t}}{t} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\frac{z - t}{t}\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y\right)\right), \left(\frac{\color{blue}{z - t}}{t}\right)\right) \]

      7. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \left(\frac{\color{blue}{z - t}}{t}\right)\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \left(\frac{z}{t} - \color{blue}{\frac{t}{t}}\right)\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \left(\frac{z}{t} - 1\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \left(\frac{z}{t} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \left(\frac{z}{t} + -1\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \mathsf{+.f64}\left(\left(\frac{z}{t}\right), \color{blue}{-1}\right)\right) \]

      13. /-lowering-/.f64 52.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(z, t\right), -1\right)\right) \]

   10. Simplified 52.4%

       \[\leadsto \color{blue}{\left(-y\right) \cdot \left(\frac{z}{t} + -1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -100000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -78000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+57}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -78000.0) x (if (<= a 1.8e+57) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -78000.0) {
		tmp = x;
	} else if (a <= 1.8e+57) {
		tmp = y;
	} 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 <= (-78000.0d0)) then
        tmp = x
    else if (a <= 1.8d+57) then
        tmp = y
    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 <= -78000.0) {
		tmp = x;
	} else if (a <= 1.8e+57) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -78000.0:
		tmp = x
	elif a <= 1.8e+57:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -78000.0)
		tmp = x;
	elseif (a <= 1.8e+57)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -78000.0)
		tmp = x;
	elseif (a <= 1.8e+57)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -78000.0], x, If[LessEqual[a, 1.8e+57], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -78000 or 1.8000000000000001e57 < a

   1. Initial program 67.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 48.0%

      \[\leadsto \color{blue}{x} \]

   if -78000 < a < 1.8000000000000001e57

   1. Initial program 66.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 35.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 25.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 66.8%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 24.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))