Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.3% → 98.4%

Time: 10.0s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

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

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

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

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

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

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

   6. --lowering--.f64 97.2%

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

4. Applied egg-rr 97.2%

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

Alternative 2: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+73}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (+ -1.0 (/ z t))))))
   (if (<= t -1.3e+212)
     t_1
     (if (<= t -2.45e-47)
       (+ x (* t (/ y (- t a))))
       (if (<= t 3e+73) (+ x (* z (/ y (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (-1.0 + (z / t)));
	double tmp;
	if (t <= -1.3e+212) {
		tmp = t_1;
	} else if (t <= -2.45e-47) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 3e+73) {
		tmp = x + (z * (y / (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 - (y * ((-1.0d0) + (z / t)))
    if (t <= (-1.3d+212)) then
        tmp = t_1
    else if (t <= (-2.45d-47)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 3d+73) then
        tmp = x + (z * (y / (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 - (y * (-1.0 + (z / t)));
	double tmp;
	if (t <= -1.3e+212) {
		tmp = t_1;
	} else if (t <= -2.45e-47) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 3e+73) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (-1.0 + (z / t)))
	tmp = 0
	if t <= -1.3e+212:
		tmp = t_1
	elif t <= -2.45e-47:
		tmp = x + (t * (y / (t - a)))
	elif t <= 3e+73:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(-1.0 + Float64(z / t))))
	tmp = 0.0
	if (t <= -1.3e+212)
		tmp = t_1;
	elseif (t <= -2.45e-47)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 3e+73)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (-1.0 + (z / t)));
	tmp = 0.0;
	if (t <= -1.3e+212)
		tmp = t_1;
	elseif (t <= -2.45e-47)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 3e+73)
		tmp = x + (z * (y / (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[(y * N[(-1.0 + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+212], t$95$1, If[LessEqual[t, -2.45e-47], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+73], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2999999999999999e212 or 3.00000000000000011e73 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 100.0%

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

   5. Simplified 100.0%

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

   if -1.2999999999999999e212 < t < -2.4500000000000002e-47

   1. Initial program 98.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 94.6%

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

   7. Simplified 94.6%

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

   if -2.4500000000000002e-47 < t < 3.00000000000000011e73

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 88.9%

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

   5. Simplified 88.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 91.0%

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

   7. Applied egg-rr 91.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+212}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+73}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-90}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+151)
   (+ x y)
   (if (<= t -6.4e-90)
     (- x (* t (/ y a)))
     (if (<= t 4.2e+72) (+ x (* y (/ z a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+151) {
		tmp = x + y;
	} else if (t <= -6.4e-90) {
		tmp = x - (t * (y / a));
	} else if (t <= 4.2e+72) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + 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 <= (-2.7d+151)) then
        tmp = x + y
    else if (t <= (-6.4d-90)) then
        tmp = x - (t * (y / a))
    else if (t <= 4.2d+72) then
        tmp = x + (y * (z / a))
    else
        tmp = x + 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 <= -2.7e+151) {
		tmp = x + y;
	} else if (t <= -6.4e-90) {
		tmp = x - (t * (y / a));
	} else if (t <= 4.2e+72) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+151:
		tmp = x + y
	elif t <= -6.4e-90:
		tmp = x - (t * (y / a))
	elif t <= 4.2e+72:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+151)
		tmp = Float64(x + y);
	elseif (t <= -6.4e-90)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 4.2e+72)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+151)
		tmp = x + y;
	elseif (t <= -6.4e-90)
		tmp = x - (t * (y / a));
	elseif (t <= 4.2e+72)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+151], N[(x + y), $MachinePrecision], If[LessEqual[t, -6.4e-90], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+72], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e151 or 4.2000000000000003e72 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 94.3%

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

   5. Simplified 94.3%

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

   if -2.7000000000000001e151 < t < -6.40000000000000014e-90

   1. Initial program 96.3%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 80.7%

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

   10. Simplified 80.7%

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

   if -6.40000000000000014e-90 < t < 4.2000000000000003e72

   1. Initial program 95.3%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-90}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e-47)
   (+ x (* y (/ t (- t a))))
   (if (<= t 1.45e+84)
     (+ x (* z (/ y (- a t))))
     (- x (* y (+ -1.0 (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e-47) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 1.45e+84) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (-1.0 + (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 <= (-1.95d-47)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 1.45d+84) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y * ((-1.0d0) + (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 <= -1.95e-47) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 1.45e+84) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (-1.0 + (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e-47:
		tmp = x + (y * (t / (t - a)))
	elif t <= 1.45e+84:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y * (-1.0 + (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e-47)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 1.45e+84)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y * Float64(-1.0 + Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e-47)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 1.45e+84)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y * (-1.0 + (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e-47], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+84], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(-1.0 + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999989e-47

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. --lowering--.f64 94.5%

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

   5. Simplified 94.5%

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

   if -1.94999999999999989e-47 < t < 1.44999999999999994e84

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 88.9%

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

   5. Simplified 88.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 91.0%

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

   7. Applied egg-rr 91.0%

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

   if 1.44999999999999994e84 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{x - y \cdot \left(-1 + \frac{z}{t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{+81}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.15e-47)
   (+ x (* t (/ y (- t a))))
   (if (<= t 1.72e+81) (+ x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e-47) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 1.72e+81) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + 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 <= (-2.15d-47)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 1.72d+81) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + 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 <= -2.15e-47) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 1.72e+81) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.15e-47:
		tmp = x + (t * (y / (t - a)))
	elif t <= 1.72e+81:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.15e-47)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 1.72e+81)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.15e-47)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 1.72e+81)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.15e-47], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e+81], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1499999999999999e-47

   1. Initial program 99.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 89.9%

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

   7. Simplified 89.9%

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

   if -2.1499999999999999e-47 < t < 1.72000000000000002e81

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 88.9%

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

   5. Simplified 88.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 91.0%

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

   7. Applied egg-rr 91.0%

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

   if 1.72000000000000002e81 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 94.3%

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

   5. Simplified 94.3%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{+81}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+80}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.7e+135)
   (+ x y)
   (if (<= t 3.4e+80) (+ x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.7e+135) {
		tmp = x + y;
	} else if (t <= 3.4e+80) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + 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 <= (-5.7d+135)) then
        tmp = x + y
    else if (t <= 3.4d+80) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + 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 <= -5.7e+135) {
		tmp = x + y;
	} else if (t <= 3.4e+80) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.7e+135:
		tmp = x + y
	elif t <= 3.4e+80:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.7e+135)
		tmp = Float64(x + y);
	elseif (t <= 3.4e+80)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.7e+135)
		tmp = x + y;
	elseif (t <= 3.4e+80)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.7e+135], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.4e+80], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7000000000000002e135 or 3.39999999999999992e80 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 92.4%

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

   5. Simplified 92.4%

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

   if -5.7000000000000002e135 < t < 3.39999999999999992e80

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 86.8%

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

   5. Simplified 86.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 89.0%

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

   7. Applied egg-rr 89.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+80}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+151)
   (+ x y)
   (if (<= t 4.8e+52) (+ x (* y (/ (- z t) a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+151) {
		tmp = x + y;
	} else if (t <= 4.8e+52) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + 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 <= (-2.8d+151)) then
        tmp = x + y
    else if (t <= 4.8d+52) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + 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 <= -2.8e+151) {
		tmp = x + y;
	} else if (t <= 4.8e+52) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+151:
		tmp = x + y
	elif t <= 4.8e+52:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+151)
		tmp = Float64(x + y);
	elseif (t <= 4.8e+52)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+151)
		tmp = x + y;
	elseif (t <= 4.8e+52)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+151], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.8e+52], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999987e151 or 4.8e52 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 91.6%

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

   5. Simplified 91.6%

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

   if -2.79999999999999987e151 < t < 4.8e52

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.36e+114)
   (+ x y)
   (if (<= t 1.02e+74) (+ x (/ y (/ a z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.36e+114) {
		tmp = x + y;
	} else if (t <= 1.02e+74) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + 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 <= (-1.36d+114)) then
        tmp = x + y
    else if (t <= 1.02d+74) then
        tmp = x + (y / (a / z))
    else
        tmp = x + 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 <= -1.36e+114) {
		tmp = x + y;
	} else if (t <= 1.02e+74) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.36e+114:
		tmp = x + y
	elif t <= 1.02e+74:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.36e+114)
		tmp = Float64(x + y);
	elseif (t <= 1.02e+74)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.36e+114)
		tmp = x + y;
	elseif (t <= 1.02e+74)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.36e+114], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.02e+74], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.36000000000000008e114 or 1.02000000000000005e74 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 90.5%

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

   5. Simplified 90.5%

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

   if -1.36000000000000008e114 < t < 1.02000000000000005e74

   1. Initial program 95.4%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+74}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.4e+114)
   (+ x y)
   (if (<= t 1.95e+74) (+ x (* z (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+114) {
		tmp = x + y;
	} else if (t <= 1.95e+74) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + 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 <= (-1.4d+114)) then
        tmp = x + y
    else if (t <= 1.95d+74) then
        tmp = x + (z * (y / a))
    else
        tmp = x + 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 <= -1.4e+114) {
		tmp = x + y;
	} else if (t <= 1.95e+74) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.4e+114:
		tmp = x + y
	elif t <= 1.95e+74:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.4e+114)
		tmp = Float64(x + y);
	elseif (t <= 1.95e+74)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.4e+114)
		tmp = x + y;
	elseif (t <= 1.95e+74)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.4e+114], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.95e+74], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e114 or 1.95000000000000004e74 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 90.5%

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

   5. Simplified 90.5%

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

   if -1.4e114 < t < 1.95000000000000004e74

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0

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

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

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

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

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

      3. *-lowering-*.f64 77.3%

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

   5. Simplified 77.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 79.5%

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

   7. Applied egg-rr 79.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+74}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.36e+114)
   (+ x y)
   (if (<= t 2.55e+72) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.36e+114) {
		tmp = x + y;
	} else if (t <= 2.55e+72) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + 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 <= (-1.36d+114)) then
        tmp = x + y
    else if (t <= 2.55d+72) then
        tmp = x + (y * (z / a))
    else
        tmp = x + 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 <= -1.36e+114) {
		tmp = x + y;
	} else if (t <= 2.55e+72) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.36e+114:
		tmp = x + y
	elif t <= 2.55e+72:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.36e+114)
		tmp = Float64(x + y);
	elseif (t <= 2.55e+72)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.36e+114)
		tmp = x + y;
	elseif (t <= 2.55e+72)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.36e+114], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.55e+72], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.36000000000000008e114 or 2.54999999999999989e72 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 90.5%

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

   5. Simplified 90.5%

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

   if -1.36000000000000008e114 < t < 2.54999999999999989e72

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+135) (+ x y) (if (<= t 1.75e+53) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+135) {
		tmp = x + y;
	} else if (t <= 1.75e+53) {
		tmp = x;
	} else {
		tmp = x + 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 <= (-1.8d+135)) then
        tmp = x + y
    else if (t <= 1.75d+53) then
        tmp = x
    else
        tmp = x + 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 <= -1.8e+135) {
		tmp = x + y;
	} else if (t <= 1.75e+53) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+135:
		tmp = x + y
	elif t <= 1.75e+53:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+135)
		tmp = Float64(x + y);
	elseif (t <= 1.75e+53)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+135)
		tmp = x + y;
	elseif (t <= 1.75e+53)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+135], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.75e+53], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7999999999999999e135 or 1.75000000000000009e53 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 90.0%

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

   5. Simplified 90.0%

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

   if -1.7999999999999999e135 < t < 1.75000000000000009e53

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+197}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+200}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e+197) y (if (<= y 1.85e+200) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+197) {
		tmp = y;
	} else if (y <= 1.85e+200) {
		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 (y <= (-1.2d+197)) then
        tmp = y
    else if (y <= 1.85d+200) 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 (y <= -1.2e+197) {
		tmp = y;
	} else if (y <= 1.85e+200) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e+197:
		tmp = y
	elif y <= 1.85e+200:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e+197)
		tmp = y;
	elseif (y <= 1.85e+200)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.2e+197)
		tmp = y;
	elseif (y <= 1.85e+200)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e+197], y, If[LessEqual[y, 1.85e+200], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1999999999999999e197 or 1.8500000000000001e200 < y

   1. Initial program 95.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 31.6%

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

   5. Simplified 31.6%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 29.8%

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

   if -1.1999999999999999e197 < y < 1.8500000000000001e200

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 14: 50.2% accurate, 11.0× 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 97.0%

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

3. Taylor expanded in x around inf

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

5. Simplified 57.8%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (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 + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (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 + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

  (+ x (* y (/ (- z t) (- a t)))))