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

Percentage Accurate: 85.3% → 98.3%

Time: 11.2s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 99.1%

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

4. Applied egg-rr 99.1%

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

Alternative 2: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= t -1.05e-21)
     (+ x y)
     (if (<= t 3.3e-195)
       t_1
       (if (<= t 2.8e-153) x (if (<= t 3.2e-71) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -1.05e-21) {
		tmp = x + y;
	} else if (t <= 3.3e-195) {
		tmp = t_1;
	} else if (t <= 2.8e-153) {
		tmp = x;
	} else if (t <= 3.2e-71) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if (t <= (-1.05d-21)) then
        tmp = x + y
    else if (t <= 3.3d-195) then
        tmp = t_1
    else if (t <= 2.8d-153) then
        tmp = x
    else if (t <= 3.2d-71) then
        tmp = t_1
    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 t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -1.05e-21) {
		tmp = x + y;
	} else if (t <= 3.3e-195) {
		tmp = t_1;
	} else if (t <= 2.8e-153) {
		tmp = x;
	} else if (t <= 3.2e-71) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if t <= -1.05e-21:
		tmp = x + y
	elif t <= 3.3e-195:
		tmp = t_1
	elif t <= 2.8e-153:
		tmp = x
	elif t <= 3.2e-71:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.05e-21)
		tmp = Float64(x + y);
	elseif (t <= 3.3e-195)
		tmp = t_1;
	elseif (t <= 2.8e-153)
		tmp = x;
	elseif (t <= 3.2e-71)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -1.05e-21)
		tmp = x + y;
	elseif (t <= 3.3e-195)
		tmp = t_1;
	elseif (t <= 2.8e-153)
		tmp = x;
	elseif (t <= 3.2e-71)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-21], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.3e-195], t$95$1, If[LessEqual[t, 2.8e-153], x, If[LessEqual[t, 3.2e-71], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000006e-21 or 3.1999999999999999e-71 < t

   1. Initial program 80.5%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 74.6%

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

   5. Simplified 74.6%

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

   if -1.05000000000000006e-21 < t < 3.3e-195 or 2.8000000000000001e-153 < t < 3.1999999999999999e-71

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 61.5%

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

   5. Simplified 61.5%

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

   if 3.3e-195 < t < 2.8000000000000001e-153

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 85.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -2.5e-101)
     (+ x y)
     (if (<= t 4.8e-196)
       t_1
       (if (<= t 2.05e-120) x (if (<= t 3.2e-73) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -2.5e-101) {
		tmp = x + y;
	} else if (t <= 4.8e-196) {
		tmp = t_1;
	} else if (t <= 2.05e-120) {
		tmp = x;
	} else if (t <= 3.2e-73) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (t <= (-2.5d-101)) then
        tmp = x + y
    else if (t <= 4.8d-196) then
        tmp = t_1
    else if (t <= 2.05d-120) then
        tmp = x
    else if (t <= 3.2d-73) then
        tmp = t_1
    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 t_1 = y * (z / a);
	double tmp;
	if (t <= -2.5e-101) {
		tmp = x + y;
	} else if (t <= 4.8e-196) {
		tmp = t_1;
	} else if (t <= 2.05e-120) {
		tmp = x;
	} else if (t <= 3.2e-73) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -2.5e-101:
		tmp = x + y
	elif t <= 4.8e-196:
		tmp = t_1
	elif t <= 2.05e-120:
		tmp = x
	elif t <= 3.2e-73:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -2.5e-101)
		tmp = Float64(x + y);
	elseif (t <= 4.8e-196)
		tmp = t_1;
	elseif (t <= 2.05e-120)
		tmp = x;
	elseif (t <= 3.2e-73)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (t <= -2.5e-101)
		tmp = x + y;
	elseif (t <= 4.8e-196)
		tmp = t_1;
	elseif (t <= 2.05e-120)
		tmp = x;
	elseif (t <= 3.2e-73)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-101], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.8e-196], t$95$1, If[LessEqual[t, 2.05e-120], x, If[LessEqual[t, 3.2e-73], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e-101 or 3.19999999999999986e-73 < t

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 70.9%

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

   5. Simplified 70.9%

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

   if -2.5e-101 < t < 4.80000000000000041e-196 or 2.05000000000000017e-120 < t < 3.19999999999999986e-73

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 55.5%

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

   if 4.80000000000000041e-196 < t < 2.05000000000000017e-120

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 66.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1060000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+202)
   (* z (/ y a))
   (if (<= z 1060000000.0) (+ x y) (if (<= z 3.4e+102) x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+202) {
		tmp = z * (y / a);
	} else if (z <= 1060000000.0) {
		tmp = x + y;
	} else if (z <= 3.4e+102) {
		tmp = x;
	} else {
		tmp = y / (a / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.7d+202)) then
        tmp = z * (y / a)
    else if (z <= 1060000000.0d0) then
        tmp = x + y
    else if (z <= 3.4d+102) then
        tmp = x
    else
        tmp = y / (a / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+202) {
		tmp = z * (y / a);
	} else if (z <= 1060000000.0) {
		tmp = x + y;
	} else if (z <= 3.4e+102) {
		tmp = x;
	} else {
		tmp = y / (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+202:
		tmp = z * (y / a)
	elif z <= 1060000000.0:
		tmp = x + y
	elif z <= 3.4e+102:
		tmp = x
	else:
		tmp = y / (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+202)
		tmp = Float64(z * Float64(y / a));
	elseif (z <= 1060000000.0)
		tmp = Float64(x + y);
	elseif (z <= 3.4e+102)
		tmp = x;
	else
		tmp = Float64(y / Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+202)
		tmp = z * (y / a);
	elseif (z <= 1060000000.0)
		tmp = x + y;
	elseif (z <= 3.4e+102)
		tmp = x;
	else
		tmp = y / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+202], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1060000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.4e+102], x, N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7e202

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. --lowering--.f64 57.9%

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

   8. Simplified 57.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 67.9%

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

   10. Applied egg-rr 67.9%

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

   11. Taylor expanded in z around inf

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

   13. Simplified 67.9%

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

   if -1.7e202 < z < 1.06e9

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.5%

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

   5. Simplified 67.5%

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

   if 1.06e9 < z < 3.4e102

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.3%

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

   if 3.4e102 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 70.0%

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

   5. Simplified 70.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

      5. --lowering--.f64 70.0%

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

   7. Applied egg-rr 70.0%

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

   8. Taylor expanded in a around inf

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

   10. Simplified 51.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1060000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+201}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1080000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+201)
   (* z (/ y a))
   (if (<= z 1080000000.0) (+ x y) (if (<= z 1.85e+102) x (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+201) {
		tmp = z * (y / a);
	} else if (z <= 1080000000.0) {
		tmp = x + y;
	} else if (z <= 1.85e+102) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-4.2d+201)) then
        tmp = z * (y / a)
    else if (z <= 1080000000.0d0) then
        tmp = x + y
    else if (z <= 1.85d+102) then
        tmp = x
    else
        tmp = 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 (z <= -4.2e+201) {
		tmp = z * (y / a);
	} else if (z <= 1080000000.0) {
		tmp = x + y;
	} else if (z <= 1.85e+102) {
		tmp = x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+201:
		tmp = z * (y / a)
	elif z <= 1080000000.0:
		tmp = x + y
	elif z <= 1.85e+102:
		tmp = x
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+201)
		tmp = Float64(z * Float64(y / a));
	elseif (z <= 1080000000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.85e+102)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+201)
		tmp = z * (y / a);
	elseif (z <= 1080000000.0)
		tmp = x + y;
	elseif (z <= 1.85e+102)
		tmp = x;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+201], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1080000000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.85e+102], x, N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1999999999999998e201

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. --lowering--.f64 57.9%

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

   8. Simplified 57.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 67.9%

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

   10. Applied egg-rr 67.9%

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

   11. Taylor expanded in z around inf

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

   13. Simplified 67.9%

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

   if -4.1999999999999998e201 < z < 1.08e9

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.5%

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

   5. Simplified 67.5%

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

   if 1.08e9 < z < 1.85000000000000011e102

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.3%

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

   if 1.85000000000000011e102 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 51.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+201}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1080000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+190)
   (+ x (* y (/ t (- t a))))
   (if (<= t 9.2e-49) (+ x (* z (/ y (- a t)))) (+ x (- y (/ y (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+190) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 9.2e-49) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y - (y / (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.3d+190)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 9.2d-49) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y - (y / (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+190) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 9.2e-49) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y - (y / (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+190:
		tmp = x + (y * (t / (t - a)))
	elif t <= 9.2e-49:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y - (y / (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+190)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 9.2e-49)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e+190)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 9.2e-49)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y - (y / (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+190], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-49], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e190

   1. Initial program 64.3%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. --lowering--.f64 97.1%

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

   5. Simplified 97.1%

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

   if -3.3e190 < t < 9.1999999999999996e-49

   1. Initial program 92.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

      1. +-commutative N/A

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

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

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. --lowering--.f64 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around inf

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

   9. Simplified 91.3%

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

   if 9.1999999999999996e-49 < t

   1. Initial program 82.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

      11. /-lowering-/.f64 93.2%

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

   7. Simplified 93.2%

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

      1. distribute-rgt-in N/A

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

      2. fma-define N/A

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

      3. neg-mul-1 N/A

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

      4. fmm-undef N/A

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

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

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

      6. *-commutative N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

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

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

      10. /-lowering-/.f64 93.2%

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

   9. Applied egg-rr 93.2%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+190)
   (+ x (* y (/ t (- t a))))
   (if (<= t 9.2e-49) (+ x (* z (/ y (- a t)))) (- x (* y (+ -1.0 (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+190) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 9.2e-49) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (-1.0 + (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.3d+190)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 9.2d-49) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y * ((-1.0d0) + (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+190) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 9.2e-49) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (-1.0 + (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+190:
		tmp = x + (y * (t / (t - a)))
	elif t <= 9.2e-49:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y * (-1.0 + (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+190)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 9.2e-49)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y * Float64(-1.0 + Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e+190)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 9.2e-49)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y * (-1.0 + (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+190], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-49], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(-1.0 + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e190

   1. Initial program 64.3%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. --lowering--.f64 97.1%

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

   5. Simplified 97.1%

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

   if -3.3e190 < t < 9.1999999999999996e-49

   1. Initial program 92.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

      1. +-commutative N/A

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

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

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. --lowering--.f64 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around inf

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

   9. Simplified 91.3%

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

   if 9.1999999999999996e-49 < t

   1. Initial program 82.5%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (+ -1.0 (/ z t))))))
   (if (<= t -3.3e+190)
     t_1
     (if (<= t 4.6e-49) (+ x (* z (/ y (- a t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (-1.0 + (z / t)));
	double tmp;
	if (t <= -3.3e+190) {
		tmp = t_1;
	} else if (t <= 4.6e-49) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((-1.0d0) + (z / t)))
    if (t <= (-3.3d+190)) then
        tmp = t_1
    else if (t <= 4.6d-49) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (-1.0 + (z / t)));
	double tmp;
	if (t <= -3.3e+190) {
		tmp = t_1;
	} else if (t <= 4.6e-49) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (-1.0 + (z / t)))
	tmp = 0
	if t <= -3.3e+190:
		tmp = t_1
	elif t <= 4.6e-49:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(-1.0 + Float64(z / t))))
	tmp = 0.0
	if (t <= -3.3e+190)
		tmp = t_1;
	elseif (t <= 4.6e-49)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (-1.0 + (z / t)));
	tmp = 0.0;
	if (t <= -3.3e+190)
		tmp = t_1;
	elseif (t <= 4.6e-49)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(-1.0 + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+190], t$95$1, If[LessEqual[t, 4.6e-49], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3e190 or 4.5999999999999998e-49 < t

   1. Initial program 77.6%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 93.7%

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

   5. Simplified 93.7%

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

   if -3.3e190 < t < 4.5999999999999998e-49

   1. Initial program 92.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

      1. +-commutative N/A

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

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

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. --lowering--.f64 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around inf

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

   9. Simplified 91.3%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+236}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+190)
   (+ x y)
   (if (<= t 3.45e+236) (+ x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+190) {
		tmp = x + y;
	} else if (t <= 3.45e+236) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.2d+190)) then
        tmp = x + y
    else if (t <= 3.45d+236) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+190) {
		tmp = x + y;
	} else if (t <= 3.45e+236) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+190:
		tmp = x + y
	elif t <= 3.45e+236:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+190)
		tmp = Float64(x + y);
	elseif (t <= 3.45e+236)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e+190)
		tmp = x + y;
	elseif (t <= 3.45e+236)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+190], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.45e+236], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000022e190 or 3.4499999999999999e236 < t

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 95.0%

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

   5. Simplified 95.0%

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

   if -5.20000000000000022e190 < t < 3.4499999999999999e236

   1. Initial program 90.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.0%

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

   4. Applied egg-rr 99.0%

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

      1. +-commutative N/A

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

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

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. --lowering--.f64 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in z around inf

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

   9. Simplified 88.5%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+236}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e+61)
   (+ x y)
   (if (<= t 1.9e-27) (+ x (* y (/ (- z t) a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+61) {
		tmp = x + y;
	} else if (t <= 1.9e-27) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.35d+61)) then
        tmp = x + y
    else if (t <= 1.9d-27) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+61) {
		tmp = x + y;
	} else if (t <= 1.9e-27) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e+61:
		tmp = x + y
	elif t <= 1.9e-27:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e+61)
		tmp = Float64(x + y);
	elseif (t <= 1.9e-27)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.35e+61)
		tmp = x + y;
	elseif (t <= 1.9e-27)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e+61], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.9e-27], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3500000000000001e61 or 1.9e-27 < t

   1. Initial program 76.3%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 79.7%

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

   5. Simplified 79.7%

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

   if -1.3500000000000001e61 < t < 1.9e-27

   1. Initial program 95.1%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 82.9%

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

   5. Simplified 82.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+157}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e+157) (+ x y) (if (<= t 5.6e-30) (+ x (/ y (/ a z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+157) {
		tmp = x + y;
	} else if (t <= 5.6e-30) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.8d+157)) then
        tmp = x + y
    else if (t <= 5.6d-30) then
        tmp = x + (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+157) {
		tmp = x + y;
	} else if (t <= 5.6e-30) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e+157:
		tmp = x + y
	elif t <= 5.6e-30:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e+157)
		tmp = Float64(x + y);
	elseif (t <= 5.6e-30)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e+157)
		tmp = x + y;
	elseif (t <= 5.6e-30)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e+157], N[(x + y), $MachinePrecision], If[LessEqual[t, 5.6e-30], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.79999999999999941e157 or 5.59999999999999977e-30 < t

   1. Initial program 75.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.8%

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

   5. Simplified 81.8%

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

   if -7.79999999999999941e157 < t < 5.59999999999999977e-30

   1. Initial program 93.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+157}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+190) (+ x y) (if (<= t 5.6e-27) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+190) {
		tmp = x + y;
	} else if (t <= 5.6e-27) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.3d+190)) then
        tmp = x + y
    else if (t <= 5.6d-27) then
        tmp = x + (y * (z / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+190) {
		tmp = x + y;
	} else if (t <= 5.6e-27) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+190:
		tmp = x + y
	elif t <= 5.6e-27:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+190)
		tmp = Float64(x + y);
	elseif (t <= 5.6e-27)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e+190)
		tmp = x + y;
	elseif (t <= 5.6e-27)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+190], N[(x + y), $MachinePrecision], If[LessEqual[t, 5.6e-27], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3e190 or 5.5999999999999999e-27 < t

   1. Initial program 76.1%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.5%

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

   5. Simplified 82.5%

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

   if -3.3e190 < t < 5.5999999999999999e-27

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 79.5%

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

   8. Simplified 79.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-37) (+ x y) (if (<= t 6.1e-49) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-37) {
		tmp = x + y;
	} else if (t <= 6.1e-49) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d-37)) then
        tmp = x + y
    else if (t <= 6.1d-49) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-37) {
		tmp = x + y;
	} else if (t <= 6.1e-49) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-37:
		tmp = x + y
	elif t <= 6.1e-49:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-37)
		tmp = Float64(x + y);
	elseif (t <= 6.1e-49)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-37)
		tmp = x + y;
	elseif (t <= 6.1e-49)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-37], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.1e-49], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999995e-37 or 6.09999999999999963e-49 < t

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 75.2%

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

   5. Simplified 75.2%

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

   if -1.19999999999999995e-37 < t < 6.09999999999999963e-49

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 43.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-232}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-213}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.52e-232) x (if (<= x 1.05e-213) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.52e-232) {
		tmp = x;
	} else if (x <= 1.05e-213) {
		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 (x <= (-1.52d-232)) then
        tmp = x
    else if (x <= 1.05d-213) 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 (x <= -1.52e-232) {
		tmp = x;
	} else if (x <= 1.05e-213) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.52e-232:
		tmp = x
	elif x <= 1.05e-213:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.52e-232)
		tmp = x;
	elseif (x <= 1.05e-213)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.52e-232)
		tmp = x;
	elseif (x <= 1.05e-213)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.52e-232], x, If[LessEqual[x, 1.05e-213], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52e-232 or 1.0499999999999999e-213 < x

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 55.6%

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

   if -1.52e-232 < x < 1.0499999999999999e-213

   1. Initial program 86.3%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 38.5%

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

   5. Simplified 38.5%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 37.4%

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

Alternative 15: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 94.9%

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

4. Applied egg-rr 94.9%

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

5. Final simplification 94.9%

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

Alternative 16: 50.7% 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 86.7%

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

3. Taylor expanded in x around inf

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

5. Simplified 49.0%

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

Developer Target 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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