Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.4% → 98.4%

Time: 9.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 97.4%

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

4. Applied egg-rr 97.4%

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

Alternative 2: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+19)
   (+ x y)
   (if (<= z -7e-282) x (if (<= z 2.4e-234) (* t (/ y a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+19) {
		tmp = x + y;
	} else if (z <= -7e-282) {
		tmp = x;
	} else if (z <= 2.4e-234) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.9d+19)) then
        tmp = x + y
    else if (z <= (-7d-282)) then
        tmp = x
    else if (z <= 2.4d-234) then
        tmp = t * (y / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+19) {
		tmp = x + y;
	} else if (z <= -7e-282) {
		tmp = x;
	} else if (z <= 2.4e-234) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+19:
		tmp = x + y
	elif z <= -7e-282:
		tmp = x
	elif z <= 2.4e-234:
		tmp = t * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+19)
		tmp = Float64(x + y);
	elseif (z <= -7e-282)
		tmp = x;
	elseif (z <= 2.4e-234)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+19)
		tmp = x + y;
	elseif (z <= -7e-282)
		tmp = x;
	elseif (z <= 2.4e-234)
		tmp = t * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+19], N[(x + y), $MachinePrecision], If[LessEqual[z, -7e-282], x, If[LessEqual[z, 2.4e-234], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e19 or 2.3999999999999999e-234 < z

   1. Initial program 81.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.9%

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

   5. Simplified 69.9%

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

   if -1.9e19 < z < -7.00000000000000013e-282

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 59.1%

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

   if -7.00000000000000013e-282 < z < 2.3999999999999999e-234

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 93.5%

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

   5. Simplified 93.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 93.6%

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

   7. Applied egg-rr 93.6%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot t}{a} \]

      2. associate-*l/ N/A

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

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

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

      4. /-lowering-/.f64 58.8%

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

   10. Simplified 58.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - z}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-54}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t z) a)))))
   (if (<= a -6.2e-25) t_1 (if (<= a 7.8e-54) (+ x (* (- z t) (/ y z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - z) / a));
	double tmp;
	if (a <= -6.2e-25) {
		tmp = t_1;
	} else if (a <= 7.8e-54) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((t - z) / a))
    if (a <= (-6.2d-25)) then
        tmp = t_1
    else if (a <= 7.8d-54) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - z) / a));
	double tmp;
	if (a <= -6.2e-25) {
		tmp = t_1;
	} else if (a <= 7.8e-54) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - z) / a))
	tmp = 0
	if a <= -6.2e-25:
		tmp = t_1
	elif a <= 7.8e-54:
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - z) / a)))
	tmp = 0.0
	if (a <= -6.2e-25)
		tmp = t_1;
	elseif (a <= 7.8e-54)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - z) / a));
	tmp = 0.0;
	if (a <= -6.2e-25)
		tmp = t_1;
	elseif (a <= 7.8e-54)
		tmp = x + ((z - t) * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e-25], t$95$1, If[LessEqual[a, 7.8e-54], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999989e-25 or 7.8e-54 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 87.9%

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

   5. Simplified 87.9%

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

   if -6.19999999999999989e-25 < a < 7.8e-54

   1. Initial program 87.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 86.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-54}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-54}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e-25)
   (+ x (* t (/ y a)))
   (if (<= a 4.9e-54) (+ x (* (- z t) (/ y z))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-25) {
		tmp = x + (t * (y / a));
	} else if (a <= 4.9e-54) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d-25)) then
        tmp = x + (t * (y / a))
    else if (a <= 4.9d-54) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-25) {
		tmp = x + (t * (y / a));
	} else if (a <= 4.9e-54) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e-25:
		tmp = x + (t * (y / a))
	elif a <= 4.9e-54:
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e-25)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 4.9e-54)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e-25)
		tmp = x + (t * (y / a));
	elseif (a <= 4.9e-54)
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e-25], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-54], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.79999999999999988e-25

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 80.8%

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

   5. Simplified 80.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 83.7%

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

   7. Applied egg-rr 83.7%

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

   if -2.79999999999999988e-25 < a < 4.90000000000000021e-54

   1. Initial program 87.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 86.5%

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

   if 4.90000000000000021e-54 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 79.9%

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

   5. Simplified 79.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 85.5%

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

   7. Applied egg-rr 85.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-54}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-55}:\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e-27)
   (+ x (* t (/ y a)))
   (if (<= a 3.3e-55) (- x (* y (+ (/ t z) -1.0))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-27) {
		tmp = x + (t * (y / a));
	} else if (a <= 3.3e-55) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.6d-27)) then
        tmp = x + (t * (y / a))
    else if (a <= 3.3d-55) then
        tmp = x - (y * ((t / z) + (-1.0d0)))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-27) {
		tmp = x + (t * (y / a));
	} else if (a <= 3.3e-55) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e-27:
		tmp = x + (t * (y / a))
	elif a <= 3.3e-55:
		tmp = x - (y * ((t / z) + -1.0))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e-27)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 3.3e-55)
		tmp = Float64(x - Float64(y * Float64(Float64(t / z) + -1.0)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e-27)
		tmp = x + (t * (y / a));
	elseif (a <= 3.3e-55)
		tmp = x - (y * ((t / z) + -1.0));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e-27], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-55], N[(x - N[(y * N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.5999999999999999e-27

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 80.8%

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

   5. Simplified 80.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 83.7%

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

   7. Applied egg-rr 83.7%

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

   if -5.5999999999999999e-27 < a < 3.2999999999999999e-55

   1. Initial program 87.9%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 86.0%

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

   5. Simplified 86.0%

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

   if 3.2999999999999999e-55 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 79.9%

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

   5. Simplified 79.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 85.5%

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

   7. Applied egg-rr 85.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-55}:\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-14) (+ x y) (if (<= z 2.9e+21) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-14) {
		tmp = x + y;
	} else if (z <= 2.9e+21) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d-14)) then
        tmp = x + y
    else if (z <= 2.9d+21) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-14) {
		tmp = x + y;
	} else if (z <= 2.9e+21) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-14:
		tmp = x + y
	elif z <= 2.9e+21:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-14)
		tmp = Float64(x + y);
	elseif (z <= 2.9e+21)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e-14)
		tmp = x + y;
	elseif (z <= 2.9e+21)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-14], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.9e+21], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-14 or 2.9e21 < z

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 79.2%

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

   5. Simplified 79.2%

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

   if -1.6000000000000001e-14 < z < 2.9e21

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 77.1%

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

   5. Simplified 77.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 79.6%

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

   7. Applied egg-rr 79.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+19) (+ x y) (if (<= z 6.2e+18) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+19) {
		tmp = x + y;
	} else if (z <= 6.2e+18) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+19)) then
        tmp = x + y
    else if (z <= 6.2d+18) then
        tmp = x + (t * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+19) {
		tmp = x + y;
	} else if (z <= 6.2e+18) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+19:
		tmp = x + y
	elif z <= 6.2e+18:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+19)
		tmp = Float64(x + y);
	elseif (z <= 6.2e+18)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+19)
		tmp = x + y;
	elseif (z <= 6.2e+18)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+19], N[(x + y), $MachinePrecision], If[LessEqual[z, 6.2e+18], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e19 or 6.2e18 < z

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 78.9%

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

   5. Simplified 78.9%

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

   if -1.05e19 < z < 6.2e18

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 77.3%

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

   5. Simplified 77.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 76.0%

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

   7. Applied egg-rr 76.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.25e+135)
   (* y (- 1.0 (/ t z)))
   (if (<= y 4.7e+226) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.25e+135) {
		tmp = y * (1.0 - (t / z));
	} else if (y <= 4.7e+226) {
		tmp = x;
	} else {
		tmp = t * (y / 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 (y <= (-2.25d+135)) then
        tmp = y * (1.0d0 - (t / z))
    else if (y <= 4.7d+226) then
        tmp = x
    else
        tmp = t * (y / 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 (y <= -2.25e+135) {
		tmp = y * (1.0 - (t / z));
	} else if (y <= 4.7e+226) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.25e+135:
		tmp = y * (1.0 - (t / z))
	elif y <= 4.7e+226:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.25e+135)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (y <= 4.7e+226)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.25e+135)
		tmp = y * (1.0 - (t / z));
	elseif (y <= 4.7e+226)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.25e+135], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+226], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25000000000000004e135

   1. Initial program 52.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 70.5%

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

   8. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

      4. *-inverses N/A

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

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

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

      6. /-lowering-/.f64 65.7%

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

   10. Simplified 65.7%

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

   if -2.25000000000000004e135 < y < 4.69999999999999991e226

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.1%

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

   if 4.69999999999999991e226 < y

   1. Initial program 76.9%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 65.9%

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

   5. Simplified 65.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 66.1%

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

   7. Applied egg-rr 66.1%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot t}{a} \]

      2. associate-*l/ N/A

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

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

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

      4. /-lowering-/.f64 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+18) (+ x y) (if (<= z 2e-217) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+18) {
		tmp = x + y;
	} else if (z <= 2e-217) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6d+18)) then
        tmp = x + y
    else if (z <= 2d-217) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+18) {
		tmp = x + y;
	} else if (z <= 2e-217) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+18:
		tmp = x + y
	elif z <= 2e-217:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+18)
		tmp = Float64(x + y);
	elseif (z <= 2e-217)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+18)
		tmp = x + y;
	elseif (z <= 2e-217)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+18], N[(x + y), $MachinePrecision], If[LessEqual[z, 2e-217], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6e18 or 2.00000000000000016e-217 < z

   1. Initial program 82.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 70.5%

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

   5. Simplified 70.5%

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

   if -6e18 < z < 2.00000000000000016e-217

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - t) * (y / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 97.0%

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

4. Applied egg-rr 97.0%

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

5. Final simplification 97.0%

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

Alternative 11: 60.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+243}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.1e+243) (+ x y) (* y (/ t a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.1e+243) {
		tmp = x + y;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 4.1d+243) then
        tmp = x + y
    else
        tmp = y * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.1e+243) {
		tmp = x + y;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.1e+243:
		tmp = x + y
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.1e+243)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.1e+243)
		tmp = x + y;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.1e+243], N[(x + y), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.10000000000000008e243

   1. Initial program 87.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 61.1%

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

   5. Simplified 61.1%

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

   if 4.10000000000000008e243 < y

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 80.5%

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

   8. Simplified 80.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 74.2%

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

   10. Applied egg-rr 74.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+243}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+154}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y -1.05e+154) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+154) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.05d+154)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+154) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+154:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+154)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+154)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+154], y, x]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999997e154

   1. Initial program 52.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 48.0%

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

   if -1.04999999999999997e154 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.0%

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

Alternative 13: 50.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 87.5%

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

3. Taylor expanded in x around inf

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

5. Simplified 53.1%

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

Developer Target 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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