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

Percentage Accurate: 76.5% → 89.6%

Time: 11.2s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(\frac{z - t}{t - a} + 1\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (+ (/ (- z t) (- t a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((z - t) / (t - a)) + 1.0));
}

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) / (t - a)) + 1.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (((z - t) / (t - a)) + 1.0));
}

Python

def code(x, y, z, t, a):
	return x + (y * (((z - t) / (t - a)) + 1.0))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (((z - t) / (t - a)) + 1.0));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.8%

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

   1. associate--l+ N/A

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

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

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

   3. associate-*l/ N/A

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

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

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

   5. distribute-rgt1-in N/A

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

   6. *-commutative N/A

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

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

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

   8. metadata-eval N/A

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

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

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

   10. distribute-frac-neg2 N/A

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

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

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

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

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

   13. sub-neg N/A

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

   14. +-commutative N/A

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

   15. distribute-neg-in N/A

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

   16. unsub-neg N/A

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

   17. remove-double-neg N/A

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

   18. --lowering--.f64 N/A

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

   19. metadata-eval 92.4%

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

3. Simplified 92.4%

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

Alternative 2: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-59}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-59)
   (- (+ x y) (/ y (/ a z)))
   (if (<= a 2.8e-34) (+ x (* (/ y t) (- z a))) (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-59) {
		tmp = (x + y) - (y / (a / z));
	} else if (a <= 2.8e-34) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-59)) then
        tmp = (x + y) - (y / (a / z))
    else if (a <= 2.8d-34) then
        tmp = x + ((y / t) * (z - a))
    else
        tmp = (x + y) - (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-59) {
		tmp = (x + y) - (y / (a / z));
	} else if (a <= 2.8e-34) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-59:
		tmp = (x + y) - (y / (a / z))
	elif a <= 2.8e-34:
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-59)
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	elseif (a <= 2.8e-34)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-59)
		tmp = (x + y) - (y / (a / z));
	elseif (a <= 2.8e-34)
		tmp = x + ((y / t) * (z - a));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-59], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-34], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6e-59

   1. Initial program 86.6%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 88.5%

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

   5. Simplified 88.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 88.5%

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

   7. Applied egg-rr 88.5%

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

   if -1.6e-59 < a < 2.79999999999999997e-34

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 84.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 84.6%

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

   7. Applied egg-rr 84.6%

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

   if 2.79999999999999997e-34 < a

   1. Initial program 84.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 90.1%

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

   5. Simplified 90.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-59}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))))
   (if (<= a -3.1e-61) t_1 (if (<= a 2.2e-33) (+ x (* (/ y t) (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -3.1e-61) {
		tmp = t_1;
	} else if (a <= 2.2e-33) {
		tmp = x + ((y / t) * (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 = (x + y) - (y * (z / a))
    if (a <= (-3.1d-61)) then
        tmp = t_1
    else if (a <= 2.2d-33) then
        tmp = x + ((y / t) * (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 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -3.1e-61) {
		tmp = t_1;
	} else if (a <= 2.2e-33) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / a))
	tmp = 0
	if a <= -3.1e-61:
		tmp = t_1
	elif a <= 2.2e-33:
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -3.1e-61)
		tmp = t_1;
	elseif (a <= 2.2e-33)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / a));
	tmp = 0.0;
	if (a <= -3.1e-61)
		tmp = t_1;
	elseif (a <= 2.2e-33)
		tmp = x + ((y / t) * (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e-61], t$95$1, If[LessEqual[a, 2.2e-33], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.09999999999999995e-61 or 2.20000000000000005e-33 < a

   1. Initial program 85.6%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 89.2%

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

   5. Simplified 89.2%

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

   if -3.09999999999999995e-61 < a < 2.20000000000000005e-33

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 84.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 84.6%

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

   7. Applied egg-rr 84.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-61}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e+29)
   (+ x y)
   (if (<= a 4.3e-17) (+ x (* (/ y t) (- z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+29) {
		tmp = x + y;
	} else if (a <= 4.3e-17) {
		tmp = x + ((y / t) * (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 (a <= (-3.1d+29)) then
        tmp = x + y
    else if (a <= 4.3d-17) then
        tmp = x + ((y / t) * (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 (a <= -3.1e+29) {
		tmp = x + y;
	} else if (a <= 4.3e-17) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e+29:
		tmp = x + y
	elif a <= 4.3e-17:
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e+29)
		tmp = Float64(x + y);
	elseif (a <= 4.3e-17)
		tmp = Float64(x + Float64(Float64(y / t) * 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 (a <= -3.1e+29)
		tmp = x + y;
	elseif (a <= 4.3e-17)
		tmp = x + ((y / t) * (z - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e+29], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.3e-17], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0999999999999999e29 or 4.30000000000000023e-17 < a

   1. Initial program 84.5%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.8%

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

   7. Simplified 82.8%

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

   if -3.0999999999999999e29 < a < 4.30000000000000023e-17

   1. Initial program 81.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 79.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 80.0%

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

   7. Applied egg-rr 80.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e+29)
   (+ x y)
   (if (<= a 4.5e-16) (+ x (* y (/ (- z a) t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e+29) {
		tmp = x + y;
	} else if (a <= 4.5e-16) {
		tmp = x + (y * ((z - 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 (a <= (-2.7d+29)) then
        tmp = x + y
    else if (a <= 4.5d-16) then
        tmp = x + (y * ((z - 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 (a <= -2.7e+29) {
		tmp = x + y;
	} else if (a <= 4.5e-16) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.7e+29:
		tmp = x + y
	elif a <= 4.5e-16:
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e+29)
		tmp = Float64(x + y);
	elseif (a <= 4.5e-16)
		tmp = Float64(x + Float64(y * Float64(Float64(z - 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 (a <= -2.7e+29)
		tmp = x + y;
	elseif (a <= 4.5e-16)
		tmp = x + (y * ((z - a) / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e+29], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.5e-16], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7e29 or 4.5000000000000002e-16 < a

   1. Initial program 84.5%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.8%

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

   7. Simplified 82.8%

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

   if -2.7e29 < a < 4.5000000000000002e-16

   1. Initial program 81.3%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

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

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

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

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

      7. --lowering--.f64 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e+29) (+ x y) (if (<= a 1.18e-70) (+ x (* z (/ y t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+29) {
		tmp = x + y;
	} else if (a <= 1.18e-70) {
		tmp = x + (z * (y / 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 (a <= (-3.1d+29)) then
        tmp = x + y
    else if (a <= 1.18d-70) then
        tmp = x + (z * (y / 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 (a <= -3.1e+29) {
		tmp = x + y;
	} else if (a <= 1.18e-70) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e+29:
		tmp = x + y
	elif a <= 1.18e-70:
		tmp = x + (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e+29)
		tmp = Float64(x + y);
	elseif (a <= 1.18e-70)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e+29)
		tmp = x + y;
	elseif (a <= 1.18e-70)
		tmp = x + (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e+29], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.18e-70], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0999999999999999e29 or 1.18e-70 < a

   1. Initial program 84.1%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 79.7%

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

   7. Simplified 79.7%

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

   if -3.0999999999999999e29 < a < 1.18e-70

   1. Initial program 81.4%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

      3. *-lowering-*.f64 78.4%

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

   7. Simplified 78.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 79.2%

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

   9. Applied egg-rr 79.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+29) (+ x y) (if (<= a 4.5e-71) (+ x (* y (/ z t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+29) {
		tmp = x + y;
	} else if (a <= 4.5e-71) {
		tmp = x + (y * (z / 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 (a <= (-3.2d+29)) then
        tmp = x + y
    else if (a <= 4.5d-71) then
        tmp = x + (y * (z / 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 (a <= -3.2e+29) {
		tmp = x + y;
	} else if (a <= 4.5e-71) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+29:
		tmp = x + y
	elif a <= 4.5e-71:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+29)
		tmp = Float64(x + y);
	elseif (a <= 4.5e-71)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+29)
		tmp = x + y;
	elseif (a <= 4.5e-71)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+29], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.5e-71], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999987e29 or 4.5000000000000002e-71 < a

   1. Initial program 84.1%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 79.7%

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

   7. Simplified 79.7%

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

   if -3.19999999999999987e29 < a < 4.5000000000000002e-71

   1. Initial program 81.4%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 77.0%

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

   7. Simplified 77.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= z -5.5e+118) t_1 (if (<= z 2.3e+179) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -5.5e+118) {
		tmp = t_1;
	} else if (z <= 2.3e+179) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (z <= (-5.5d+118)) then
        tmp = t_1
    else if (z <= 2.3d+179) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -5.5e+118) {
		tmp = t_1;
	} else if (z <= 2.3e+179) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if z <= -5.5e+118:
		tmp = t_1
	elif z <= 2.3e+179:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (z <= -5.5e+118)
		tmp = t_1;
	elseif (z <= 2.3e+179)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (z <= -5.5e+118)
		tmp = t_1;
	elseif (z <= 2.3e+179)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+118], t$95$1, If[LessEqual[z, 2.3e+179], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000003e118 or 2.29999999999999994e179 < z

   1. Initial program 89.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

      1. clear-num N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t - a}} \]
   8. 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

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

      4. --lowering--.f64 70.4%

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

   9. Simplified 70.4%

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

   if -5.5000000000000003e118 < z < 2.29999999999999994e179

   1. Initial program 80.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+178}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)))
   (if (<= z -4.8e+119) t_1 (if (<= z 6e+178) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / t;
	double tmp;
	if (z <= -4.8e+119) {
		tmp = t_1;
	} else if (z <= 6e+178) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / t
    if (z <= (-4.8d+119)) then
        tmp = t_1
    else if (z <= 6d+178) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / t;
	double tmp;
	if (z <= -4.8e+119) {
		tmp = t_1;
	} else if (z <= 6e+178) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / t
	tmp = 0
	if z <= -4.8e+119:
		tmp = t_1
	elif z <= 6e+178:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / t)
	tmp = 0.0
	if (z <= -4.8e+119)
		tmp = t_1;
	elseif (z <= 6e+178)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / t;
	tmp = 0.0;
	if (z <= -4.8e+119)
		tmp = t_1;
	elseif (z <= 6e+178)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -4.8e+119], t$95$1, If[LessEqual[z, 6e+178], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e119 or 6.00000000000000031e178 < z

   1. Initial program 89.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

      3. *-lowering-*.f64 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in x around 0

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

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

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

      2. *-lowering-*.f64 54.9%

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

   10. Simplified 54.9%

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

   if -4.8e119 < z < 6.00000000000000031e178

   1. Initial program 80.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+178}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+204}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+120}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+204) x (if (<= t 2.05e+120) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+204) {
		tmp = x;
	} else if (t <= 2.05e+120) {
		tmp = x + 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 (t <= (-2.1d+204)) then
        tmp = x
    else if (t <= 2.05d+120) then
        tmp = x + 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 (t <= -2.1e+204) {
		tmp = x;
	} else if (t <= 2.05e+120) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+204:
		tmp = x
	elif t <= 2.05e+120:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+204)
		tmp = x;
	elseif (t <= 2.05e+120)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+204)
		tmp = x;
	elseif (t <= 2.05e+120)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+204], x, If[LessEqual[t, 2.05e+120], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e204 or 2.05e120 < t

   1. Initial program 61.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 74.3%

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

   if -2.1e204 < t < 2.05e120

   1. Initial program 89.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 63.1%

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

   7. Simplified 63.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+204}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+120}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+165}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6e+165) y (if (<= y 8.8e+119) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e+165) {
		tmp = y;
	} else if (y <= 8.8e+119) {
		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 <= (-6d+165)) then
        tmp = y
    else if (y <= 8.8d+119) 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 <= -6e+165) {
		tmp = y;
	} else if (y <= 8.8e+119) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6e+165:
		tmp = y
	elif y <= 8.8e+119:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6e+165)
		tmp = y;
	elseif (y <= 8.8e+119)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6e+165)
		tmp = y;
	elseif (y <= 8.8e+119)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6e+165], y, If[LessEqual[y, 8.8e+119], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999981e165 or 8.8000000000000005e119 < y

   1. Initial program 67.2%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in y around inf

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

   10. Simplified 47.2%

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

   if -5.99999999999999981e165 < y < 8.8000000000000005e119

   1. Initial program 87.2%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. unsub-neg N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 N/A

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

      19. metadata-eval 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 61.7%

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

Alternative 12: 50.8% 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 82.8%

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

   1. associate--l+ N/A

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

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

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

   3. associate-*l/ N/A

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

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

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

   5. distribute-rgt1-in N/A

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

   6. *-commutative N/A

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

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

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

   8. metadata-eval N/A

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

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

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

   10. distribute-frac-neg2 N/A

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

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

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

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

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

   13. sub-neg N/A

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

   14. +-commutative N/A

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

   15. distribute-neg-in N/A

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

   16. unsub-neg N/A

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

   17. remove-double-neg N/A

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

   18. --lowering--.f64 N/A

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

   19. metadata-eval 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in x around inf

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

7. Simplified 50.4%

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

Developer Target 1: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * 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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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