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

Percentage Accurate: 98.2% → 98.2%

Time: 12.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

Alternative 2: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-35}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ (- t a) t)))))
   (if (<= t -2.9e+57)
     t_1
     (if (<= t -1.8e-35)
       (- x (* y (/ z t)))
       (if (<= t 9.6e+24) (+ x (* y (/ (- z t) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((t - a) / t));
	double tmp;
	if (t <= -2.9e+57) {
		tmp = t_1;
	} else if (t <= -1.8e-35) {
		tmp = x - (y * (z / t));
	} else if (t <= 9.6e+24) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / ((t - a) / t))
    if (t <= (-2.9d+57)) then
        tmp = t_1
    else if (t <= (-1.8d-35)) then
        tmp = x - (y * (z / t))
    else if (t <= 9.6d+24) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((t - a) / t));
	double tmp;
	if (t <= -2.9e+57) {
		tmp = t_1;
	} else if (t <= -1.8e-35) {
		tmp = x - (y * (z / t));
	} else if (t <= 9.6e+24) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / ((t - a) / t))
	tmp = 0
	if t <= -2.9e+57:
		tmp = t_1
	elif t <= -1.8e-35:
		tmp = x - (y * (z / t))
	elif t <= 9.6e+24:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(Float64(t - a) / t)))
	tmp = 0.0
	if (t <= -2.9e+57)
		tmp = t_1;
	elseif (t <= -1.8e-35)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 9.6e+24)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / ((t - a) / t));
	tmp = 0.0;
	if (t <= -2.9e+57)
		tmp = t_1;
	elseif (t <= -1.8e-35)
		tmp = x - (y * (z / t));
	elseif (t <= 9.6e+24)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+57], t$95$1, If[LessEqual[t, -1.8e-35], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+24], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000002e57 or 9.6000000000000003e24 < t

   1. Initial program 99.9%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 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 z around 0

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. unsub-neg N/A

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

      8. remove-double-neg N/A

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

      9. --lowering--.f64 82.4%

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

   7. Simplified 82.4%

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

   if -2.9000000000000002e57 < t < -1.80000000000000009e-35

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 86.3%

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

   8. Simplified 86.3%

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

   if -1.80000000000000009e-35 < t < 9.6000000000000003e24

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 79.7%

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

   5. Simplified 79.7%

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

Alternative 3: 55.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -240000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -240000000000.0)
   (+ x y)
   (if (<= x -1.7e-284)
     (* y (- 1.0 (/ z t)))
     (if (<= x 1.5e-180) (* y (/ (- z t) a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -240000000000.0) {
		tmp = x + y;
	} else if (x <= -1.7e-284) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 1.5e-180) {
		tmp = y * ((z - t) / a);
	} 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 <= (-240000000000.0d0)) then
        tmp = x + y
    else if (x <= (-1.7d-284)) then
        tmp = y * (1.0d0 - (z / t))
    else if (x <= 1.5d-180) then
        tmp = y * ((z - t) / a)
    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 <= -240000000000.0) {
		tmp = x + y;
	} else if (x <= -1.7e-284) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 1.5e-180) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -240000000000.0:
		tmp = x + y
	elif x <= -1.7e-284:
		tmp = y * (1.0 - (z / t))
	elif x <= 1.5e-180:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -240000000000.0)
		tmp = Float64(x + y);
	elseif (x <= -1.7e-284)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (x <= 1.5e-180)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -240000000000.0)
		tmp = x + y;
	elseif (x <= -1.7e-284)
		tmp = y * (1.0 - (z / t));
	elseif (x <= 1.5e-180)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -240000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[x, -1.7e-284], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-180], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e11

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 70.4%

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

   5. Simplified 70.4%

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

   if -2.4e11 < x < -1.69999999999999996e-284

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

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

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

      13. /-lowering-/.f64 48.0%

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

   8. Simplified 48.0%

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

   if -1.69999999999999996e-284 < x < 1.5e-180

   1. Initial program 98.8%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 69.4%

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

   5. Simplified 69.4%

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

   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. *-commutative N/A

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

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

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

      4. --lowering--.f64 56.1%

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

   8. Simplified 56.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. associate-*r/ N/A

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

      4. div-inv N/A

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

      5. times-frac N/A

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

      6. clear-num N/A

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

      7. /-rgt-identity N/A

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

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

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

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

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

      10. --lowering--.f64 59.2%

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

   10. Applied egg-rr 59.2%

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

   if 1.5e-180 < x

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 63.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -240000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+63}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{-144}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+63)
   (+ x y)
   (if (<= t 1.9e-301) x (if (<= t 3.95e-144) (/ (* y z) a) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+63) {
		tmp = x + y;
	} else if (t <= 1.9e-301) {
		tmp = x;
	} else if (t <= 3.95e-144) {
		tmp = (y * z) / a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d+63)) then
        tmp = x + y
    else if (t <= 1.9d-301) then
        tmp = x
    else if (t <= 3.95d-144) then
        tmp = (y * z) / a
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+63) {
		tmp = x + y;
	} else if (t <= 1.9e-301) {
		tmp = x;
	} else if (t <= 3.95e-144) {
		tmp = (y * z) / a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+63:
		tmp = x + y
	elif t <= 1.9e-301:
		tmp = x
	elif t <= 3.95e-144:
		tmp = (y * z) / a
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+63)
		tmp = Float64(x + y);
	elseif (t <= 1.9e-301)
		tmp = x;
	elseif (t <= 3.95e-144)
		tmp = Float64(Float64(y * z) / a);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+63)
		tmp = x + y;
	elseif (t <= 1.9e-301)
		tmp = x;
	elseif (t <= 3.95e-144)
		tmp = (y * z) / a;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+63], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.9e-301], x, If[LessEqual[t, 3.95e-144], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.14999999999999997e63 or 3.95000000000000026e-144 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 66.3%

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

   5. Simplified 66.3%

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

   if -1.14999999999999997e63 < t < 1.89999999999999998e-301

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 46.5%

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

   if 1.89999999999999998e-301 < t < 3.95000000000000026e-144

   1. Initial program 93.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. /-lowering-/.f64 N/A

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

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

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

      3. --lowering--.f64 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 65.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+63}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{-144}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-24}:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) a)))))
   (if (<= a -1.2e-121)
     t_1
     (if (<= a 4.7e-24) (- x (* y (+ -1.0 (/ z t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -1.2e-121) {
		tmp = t_1;
	} else if (a <= 4.7e-24) {
		tmp = x - (y * (-1.0 + (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / a))
    if (a <= (-1.2d-121)) then
        tmp = t_1
    else if (a <= 4.7d-24) then
        tmp = x - (y * ((-1.0d0) + (z / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -1.2e-121) {
		tmp = t_1;
	} else if (a <= 4.7e-24) {
		tmp = x - (y * (-1.0 + (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / a))
	tmp = 0
	if a <= -1.2e-121:
		tmp = t_1
	elif a <= 4.7e-24:
		tmp = x - (y * (-1.0 + (z / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -1.2e-121)
		tmp = t_1;
	elseif (a <= 4.7e-24)
		tmp = Float64(x - Float64(y * Float64(-1.0 + Float64(z / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (a <= -1.2e-121)
		tmp = t_1;
	elseif (a <= 4.7e-24)
		tmp = x - (y * (-1.0 + (z / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-121], t$95$1, If[LessEqual[a, 4.7e-24], N[(x - N[(y * N[(-1.0 + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.20000000000000002e-121 or 4.69999999999999992e-24 < a

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 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%

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

   if -1.20000000000000002e-121 < a < 4.69999999999999992e-24

   1. Initial program 97.1%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 88.9%

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

   5. Simplified 88.9%

      \[\leadsto \color{blue}{x - y \cdot \left(-1 + \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-35}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e-35)
   (- x (* y (/ z t)))
   (if (<= t 3.8e+126) (+ x (* y (/ (- z t) a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e-35) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.8e+126) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d-35)) then
        tmp = x - (y * (z / t))
    else if (t <= 3.8d+126) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e-35) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.8e+126) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e-35:
		tmp = x - (y * (z / t))
	elif t <= 3.8e+126:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e-35)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 3.8e+126)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e-35)
		tmp = x - (y * (z / t));
	elseif (t <= 3.8e+126)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e-35], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+126], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e-35

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 76.7%

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

   8. Simplified 76.7%

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

   if -2.1e-35 < t < 3.80000000000000017e126

   1. Initial program 97.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 77.1%

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

   5. Simplified 77.1%

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

   if 3.80000000000000017e126 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-35}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e-27)
   (- x (* y (/ z t)))
   (if (<= t 3.8e+126) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e-27) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.8e+126) {
		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 <= (-7.5d-27)) then
        tmp = x - (y * (z / t))
    else if (t <= 3.8d+126) 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 <= -7.5e-27) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.8e+126) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e-27:
		tmp = x - (y * (z / t))
	elif t <= 3.8e+126:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e-27)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 3.8e+126)
		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 <= -7.5e-27)
		tmp = x - (y * (z / t));
	elseif (t <= 3.8e+126)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e-27], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+126], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.50000000000000029e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. *-inverses N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

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

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

      12. /-lowering-/.f64 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 76.7%

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

   8. Simplified 76.7%

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

   if -7.50000000000000029e-27 < t < 3.80000000000000017e126

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 73.2%

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

   5. Simplified 73.2%

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

   if 3.80000000000000017e126 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+82) (+ x y) (if (<= t 3.8e+126) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+82) {
		tmp = x + y;
	} else if (t <= 3.8e+126) {
		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 <= (-3d+82)) then
        tmp = x + y
    else if (t <= 3.8d+126) 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 <= -3e+82) {
		tmp = x + y;
	} else if (t <= 3.8e+126) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+82:
		tmp = x + y
	elif t <= 3.8e+126:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+82)
		tmp = Float64(x + y);
	elseif (t <= 3.8e+126)
		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 <= -3e+82)
		tmp = x + y;
	elseif (t <= 3.8e+126)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+82], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.8e+126], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999989e82 or 3.80000000000000017e126 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 84.5%

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

   5. Simplified 84.5%

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

   if -2.99999999999999989e82 < t < 3.80000000000000017e126

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 71.2%

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

   5. Simplified 71.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+79) x (if (<= a 2.3e+33) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+79) {
		tmp = x;
	} else if (a <= 2.3e+33) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+79)) then
        tmp = x
    else if (a <= 2.3d+33) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+79) {
		tmp = x;
	} else if (a <= 2.3e+33) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+79:
		tmp = x
	elif a <= 2.3e+33:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+79)
		tmp = x;
	elseif (a <= 2.3e+33)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+79)
		tmp = x;
	elseif (a <= 2.3e+33)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+79], x, If[LessEqual[a, 2.3e+33], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.99999999999999967e78 or 2.30000000000000011e33 < a

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.1%

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

   if -9.99999999999999967e78 < a < 2.30000000000000011e33

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 51.2%

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

   5. Simplified 51.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 98.3%

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

3. Taylor expanded in x around inf

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

5. Simplified 45.7%

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

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024191 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

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

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