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

Percentage Accurate: 85.5% → 98.0%

Time: 10.6s

Alternatives: 13

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. +-commutative 91.5%

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

   2. associate-/l* 99.0%

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

   3. fma-define 99.0%

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

3. Simplified 99.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing

5. Final simplification 99.0%

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

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+306}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -4e+306)
     (* (- z t) (/ y (- z a)))
     (if (<= t_1 5e+292) (+ x t_1) (/ (- z t) (/ (- z a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -4e+306) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 5e+292) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) / ((z - a) / 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 - t)) / (z - a)
    if (t_1 <= (-4d+306)) then
        tmp = (z - t) * (y / (z - a))
    else if (t_1 <= 5d+292) then
        tmp = x + t_1
    else
        tmp = (z - t) / ((z - a) / 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 - t)) / (z - a);
	double tmp;
	if (t_1 <= -4e+306) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 5e+292) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) / ((z - a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -4e+306:
		tmp = (z - t) * (y / (z - a))
	elif t_1 <= 5e+292:
		tmp = x + t_1
	else:
		tmp = (z - t) / ((z - a) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -4e+306)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (t_1 <= 5e+292)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(z - t) / Float64(Float64(z - a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_1 <= -4e+306)
		tmp = (z - t) * (y / (z - a));
	elseif (t_1 <= 5e+292)
		tmp = x + t_1;
	else
		tmp = (z - t) / ((z - a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+306], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+292], N[(x + t$95$1), $MachinePrecision], N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -4.00000000000000007e306

   1. Initial program 64.2%

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

      1. +-commutative 64.2%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 95.6%

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

      1. div-sub 95.6%

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

      2. associate-*r/ 64.2%

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

      3. associate-*l/ 95.7%

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

   7. Simplified 95.7%

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

   if -4.00000000000000007e306 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999996e292

   1. Initial program 99.5%

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

   if 4.9999999999999996e292 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 51.1%

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

      1. +-commutative 51.1%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.9%

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

      1. div-sub 78.9%

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

      2. associate-*r/ 51.1%

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

      3. associate-*l/ 78.7%

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

   7. Simplified 78.7%

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

      1. *-commutative 78.7%

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

      2. clear-num 78.8%

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

      3. un-div-inv 78.9%

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

   9. Applied egg-rr 78.9%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -4 \cdot 10^{+306}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 6000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -9e+17)
     t_1
     (if (<= z 6e-125)
       (+ x (* y (/ t a)))
       (if (<= z 1.85e-103)
         (* (- z t) (/ y (- z a)))
         (if (<= z 6000000000.0) (+ x (/ (* y t) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -9e+17) {
		tmp = t_1;
	} else if (z <= 6e-125) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.85e-103) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 6000000000.0) {
		tmp = x + ((y * 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 * (z / (z - a)))
    if (z <= (-9d+17)) then
        tmp = t_1
    else if (z <= 6d-125) then
        tmp = x + (y * (t / a))
    else if (z <= 1.85d-103) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 6000000000.0d0) then
        tmp = x + ((y * 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 * (z / (z - a)));
	double tmp;
	if (z <= -9e+17) {
		tmp = t_1;
	} else if (z <= 6e-125) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.85e-103) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 6000000000.0) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -9e+17:
		tmp = t_1
	elif z <= 6e-125:
		tmp = x + (y * (t / a))
	elif z <= 1.85e-103:
		tmp = (z - t) * (y / (z - a))
	elif z <= 6000000000.0:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -9e+17)
		tmp = t_1;
	elseif (z <= 6e-125)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.85e-103)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 6000000000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -9e+17)
		tmp = t_1;
	elseif (z <= 6e-125)
		tmp = x + (y * (t / a));
	elseif (z <= 1.85e-103)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 6000000000.0)
		tmp = x + ((y * 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[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+17], t$95$1, If[LessEqual[z, 6e-125], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-103], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6000000000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9e17 or 6e9 < z

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. associate-/l* 87.4%

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

   5. Simplified 87.4%

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

   if -9e17 < z < 5.99999999999999981e-125

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/l* 85.5%

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

   5. Applied egg-rr 85.5%

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

   if 5.99999999999999981e-125 < z < 1.85e-103

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 95.6%

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

      1. div-sub 95.6%

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

      2. associate-*r/ 95.3%

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

      3. associate-*l/ 95.6%

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

   7. Simplified 95.6%

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

   if 1.85e-103 < z < 6e9

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 6000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -13000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 5600000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (- 1.0 (/ a z))))))
   (if (<= z -13000000.0)
     t_1
     (if (<= z 7.2e-125)
       (+ x (* y (/ t a)))
       (if (<= z 1.92e-103)
         (* (- z t) (/ y (- z a)))
         (if (<= z 5600000000.0) (+ x (/ (* y t) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -13000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-125) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.92e-103) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 5600000000.0) {
		tmp = x + ((y * 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 / (1.0d0 - (a / z)))
    if (z <= (-13000000.0d0)) then
        tmp = t_1
    else if (z <= 7.2d-125) then
        tmp = x + (y * (t / a))
    else if (z <= 1.92d-103) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 5600000000.0d0) then
        tmp = x + ((y * 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 / (1.0 - (a / z)));
	double tmp;
	if (z <= -13000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-125) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.92e-103) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 5600000000.0) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (1.0 - (a / z)))
	tmp = 0
	if z <= -13000000.0:
		tmp = t_1
	elif z <= 7.2e-125:
		tmp = x + (y * (t / a))
	elif z <= 1.92e-103:
		tmp = (z - t) * (y / (z - a))
	elif z <= 5600000000.0:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))))
	tmp = 0.0
	if (z <= -13000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-125)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.92e-103)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 5600000000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (1.0 - (a / z)));
	tmp = 0.0;
	if (z <= -13000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-125)
		tmp = x + (y * (t / a));
	elseif (z <= 1.92e-103)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 5600000000.0)
		tmp = x + ((y * 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[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -13000000.0], t$95$1, If[LessEqual[z, 7.2e-125], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.92e-103], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5600000000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e7 or 5.6e9 < z

   1. Initial program 83.5%

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

      1. clear-num 83.5%

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

      2. inv-pow 83.5%

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

   4. Applied egg-rr 83.5%

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

      1. unpow-1 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. div-sub 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in t around 0 87.5%

      \[\leadsto x + \color{blue}{\frac{y}{1 - \frac{a}{z}}} \]

   if -1.3e7 < z < 7.2000000000000004e-125

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/l* 85.5%

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

   5. Applied egg-rr 85.5%

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

   if 7.2000000000000004e-125 < z < 1.9200000000000001e-103

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 95.6%

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

      1. div-sub 95.6%

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

      2. associate-*r/ 95.3%

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

      3. associate-*l/ 95.6%

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

   7. Simplified 95.6%

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

   if 1.9200000000000001e-103 < z < 5.6e9

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13000000:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 5600000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -3200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-147}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 5600000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (- 1.0 (/ a z))))))
   (if (<= z -3200000000000.0)
     t_1
     (if (<= z 4.35e-147)
       (+ x (* y (/ t a)))
       (if (<= z 2.1e-84)
         (+ x (/ (* y (- z t)) z))
         (if (<= z 5600000000.0) (+ x (/ (* y t) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -3200000000000.0) {
		tmp = t_1;
	} else if (z <= 4.35e-147) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.1e-84) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 5600000000.0) {
		tmp = x + ((y * 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 / (1.0d0 - (a / z)))
    if (z <= (-3200000000000.0d0)) then
        tmp = t_1
    else if (z <= 4.35d-147) then
        tmp = x + (y * (t / a))
    else if (z <= 2.1d-84) then
        tmp = x + ((y * (z - t)) / z)
    else if (z <= 5600000000.0d0) then
        tmp = x + ((y * 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 / (1.0 - (a / z)));
	double tmp;
	if (z <= -3200000000000.0) {
		tmp = t_1;
	} else if (z <= 4.35e-147) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.1e-84) {
		tmp = x + ((y * (z - t)) / z);
	} else if (z <= 5600000000.0) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (1.0 - (a / z)))
	tmp = 0
	if z <= -3200000000000.0:
		tmp = t_1
	elif z <= 4.35e-147:
		tmp = x + (y * (t / a))
	elif z <= 2.1e-84:
		tmp = x + ((y * (z - t)) / z)
	elif z <= 5600000000.0:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))))
	tmp = 0.0
	if (z <= -3200000000000.0)
		tmp = t_1;
	elseif (z <= 4.35e-147)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.1e-84)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	elseif (z <= 5600000000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (1.0 - (a / z)));
	tmp = 0.0;
	if (z <= -3200000000000.0)
		tmp = t_1;
	elseif (z <= 4.35e-147)
		tmp = x + (y * (t / a));
	elseif (z <= 2.1e-84)
		tmp = x + ((y * (z - t)) / z);
	elseif (z <= 5600000000.0)
		tmp = x + ((y * 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[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3200000000000.0], t$95$1, If[LessEqual[z, 4.35e-147], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-84], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5600000000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2e12 or 5.6e9 < z

   1. Initial program 83.5%

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

      1. clear-num 83.5%

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

      2. inv-pow 83.5%

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

   4. Applied egg-rr 83.5%

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

      1. unpow-1 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. div-sub 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in t around 0 87.5%

      \[\leadsto x + \color{blue}{\frac{y}{1 - \frac{a}{z}}} \]

   if -3.2e12 < z < 4.3500000000000002e-147

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/l* 85.5%

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

   5. Applied egg-rr 85.5%

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

   if 4.3500000000000002e-147 < z < 2.09999999999999998e-84

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 80.2%

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

   if 2.09999999999999998e-84 < z < 5.6e9

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 88.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200000000000:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-147}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;z \leq 5600000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+28)
   (+ y x)
   (if (<= z 4.8e-125)
     (+ x (* y (/ t a)))
     (if (<= z 4e-103)
       (* (- z t) (/ y (- z a)))
       (if (<= z 9.5e+75) (+ x (/ (* y t) a)) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+28) {
		tmp = y + x;
	} else if (z <= 4.8e-125) {
		tmp = x + (y * (t / a));
	} else if (z <= 4e-103) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 9.5e+75) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y + 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 (z <= (-5.4d+28)) then
        tmp = y + x
    else if (z <= 4.8d-125) then
        tmp = x + (y * (t / a))
    else if (z <= 4d-103) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 9.5d+75) then
        tmp = x + ((y * t) / a)
    else
        tmp = y + 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 (z <= -5.4e+28) {
		tmp = y + x;
	} else if (z <= 4.8e-125) {
		tmp = x + (y * (t / a));
	} else if (z <= 4e-103) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 9.5e+75) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+28:
		tmp = y + x
	elif z <= 4.8e-125:
		tmp = x + (y * (t / a))
	elif z <= 4e-103:
		tmp = (z - t) * (y / (z - a))
	elif z <= 9.5e+75:
		tmp = x + ((y * t) / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+28)
		tmp = Float64(y + x);
	elseif (z <= 4.8e-125)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 4e-103)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 9.5e+75)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+28)
		tmp = y + x;
	elseif (z <= 4.8e-125)
		tmp = x + (y * (t / a));
	elseif (z <= 4e-103)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 9.5e+75)
		tmp = x + ((y * t) / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+28], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.8e-125], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-103], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+75], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4000000000000003e28 or 9.50000000000000061e75 < z

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 77.5%

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

      1. +-commutative 77.5%

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

   7. Simplified 77.5%

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

   if -5.4000000000000003e28 < z < 4.8000000000000003e-125

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/l* 85.5%

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

   5. Applied egg-rr 85.5%

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

   if 4.8000000000000003e-125 < z < 3.99999999999999983e-103

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 95.6%

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

      1. div-sub 95.6%

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

      2. associate-*r/ 95.3%

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

      3. associate-*l/ 95.6%

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

   7. Simplified 95.6%

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

   if 3.99999999999999983e-103 < z < 9.50000000000000061e75

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.95 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 245:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+264}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.95e-28)
   (+ x (* y (/ t a)))
   (if (<= a 245.0)
     (- x (* y (/ (- t z) z)))
     (if (<= a 5e+185)
       (+ x (/ y (- 1.0 (/ a z))))
       (if (<= a 9.6e+264) (+ x (* t (/ y a))) (- x (/ (* y z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.95e-28) {
		tmp = x + (y * (t / a));
	} else if (a <= 245.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (a <= 5e+185) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (a <= 9.6e+264) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.95d-28)) then
        tmp = x + (y * (t / a))
    else if (a <= 245.0d0) then
        tmp = x - (y * ((t - z) / z))
    else if (a <= 5d+185) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else if (a <= 9.6d+264) then
        tmp = x + (t * (y / a))
    else
        tmp = x - ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.95e-28) {
		tmp = x + (y * (t / a));
	} else if (a <= 245.0) {
		tmp = x - (y * ((t - z) / z));
	} else if (a <= 5e+185) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (a <= 9.6e+264) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.95e-28:
		tmp = x + (y * (t / a))
	elif a <= 245.0:
		tmp = x - (y * ((t - z) / z))
	elif a <= 5e+185:
		tmp = x + (y / (1.0 - (a / z)))
	elif a <= 9.6e+264:
		tmp = x + (t * (y / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.95e-28)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= 245.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (a <= 5e+185)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	elseif (a <= 9.6e+264)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.95e-28)
		tmp = x + (y * (t / a));
	elseif (a <= 245.0)
		tmp = x - (y * ((t - z) / z));
	elseif (a <= 5e+185)
		tmp = x + (y / (1.0 - (a / z)));
	elseif (a <= 9.6e+264)
		tmp = x + (t * (y / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.95e-28], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 245.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+185], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+264], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.9499999999999999e-28

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-/l* 92.1%

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

   5. Applied egg-rr 92.1%

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

   if -3.9499999999999999e-28 < a < 245

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-/l* 98.4%

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

      3. fma-define 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   if 245 < a < 4.9999999999999999e185

   1. Initial program 90.0%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

   4. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-/r* 99.9%

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

   6. Simplified 99.9%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in t around 0 86.9%

      \[\leadsto x + \color{blue}{\frac{y}{1 - \frac{a}{z}}} \]

   if 4.9999999999999999e185 < a < 9.59999999999999971e264

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 97.3%

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

      3. fma-define 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   if 9.59999999999999971e264 < a

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0 89.8%

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

      1. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

   8. Simplified 89.8%

      \[\leadsto \color{blue}{x - \frac{y \cdot z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.95 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 245:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+264}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-28} \lor \neg \left(a \leq 1.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4e-28) (not (<= a 1.1e+31)))
   (+ x (* y (/ (- t z) a)))
   (- x (* y (/ (- t z) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e-28) || !(a <= 1.1e+31)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - (y * ((t - z) / 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 ((a <= (-4d-28)) .or. (.not. (a <= 1.1d+31))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x - (y * ((t - z) / 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 ((a <= -4e-28) || !(a <= 1.1e+31)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - (y * ((t - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4e-28) or not (a <= 1.1e+31):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x - (y * ((t - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4e-28) || !(a <= 1.1e+31))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4e-28) || ~((a <= 1.1e+31)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x - (y * ((t - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4e-28], N[Not[LessEqual[a, 1.1e+31]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.99999999999999988e-28 or 1.10000000000000005e31 < a

   1. Initial program 90.1%

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

      1. +-commutative 90.1%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

      3. associate-/l* 91.4%

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

   7. Simplified 91.4%

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

   if -3.99999999999999988e-28 < a < 1.10000000000000005e31

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-/l* 98.5%

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

      3. fma-define 98.5%

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

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-28} \lor \neg \left(a \leq 1.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+18} \lor \neg \left(z \leq 9.5 \cdot 10^{+75}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+18) (not (<= z 9.5e+75))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+18) || !(z <= 9.5e+75)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.8d+18)) .or. (.not. (z <= 9.5d+75))) then
        tmp = y + x
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+18) || !(z <= 9.5e+75)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+18) or not (z <= 9.5e+75):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+18) || !(z <= 9.5e+75))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+18) || ~((z <= 9.5e+75)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+18], N[Not[LessEqual[z, 9.5e+75]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8e18 or 9.50000000000000061e75 < z

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 77.5%

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

      1. +-commutative 77.5%

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

   7. Simplified 77.5%

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

   if -8.8e18 < z < 9.50000000000000061e75

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-/l* 80.2%

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

   5. Applied egg-rr 80.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+18} \lor \neg \left(z \leq 9.5 \cdot 10^{+75}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. clear-num 91.4%

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

   2. inv-pow 91.4%

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

4. Applied egg-rr 91.4%

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

   1. unpow-1 91.4%

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

   2. *-commutative 91.4%

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

   3. associate-/r* 98.7%

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

6. Simplified 98.7%

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

   1. div-sub 98.7%

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

8. Applied egg-rr 98.7%

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

9. Taylor expanded in y around 0 98.8%

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

10. Final simplification 98.8%

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

Alternative 11: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.1 \cdot 10^{+93}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+144) x (if (<= a 8.1e+93) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+144) {
		tmp = x;
	} else if (a <= 8.1e+93) {
		tmp = y + x;
	} 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 <= (-5.8d+144)) then
        tmp = x
    else if (a <= 8.1d+93) then
        tmp = y + x
    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 <= -5.8e+144) {
		tmp = x;
	} else if (a <= 8.1e+93) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+144:
		tmp = x
	elif a <= 8.1e+93:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+144)
		tmp = x;
	elseif (a <= 8.1e+93)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+144)
		tmp = x;
	elseif (a <= 8.1e+93)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+144], x, If[LessEqual[a, 8.1e+93], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.79999999999999996e144 or 8.09999999999999983e93 < a

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 99.4%

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

      3. fma-define 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.4%

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

   if -5.79999999999999996e144 < a < 8.09999999999999983e93

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-/l* 98.8%

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

      3. fma-define 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 65.0%

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

      1. +-commutative 65.0%

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

   7. Simplified 65.0%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.1 \cdot 10^{+93}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{-1}{\frac{\frac{z - a}{t - z}}{y}} \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. clear-num 91.4%

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

   2. inv-pow 91.4%

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

4. Applied egg-rr 91.4%

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

   1. unpow-1 91.4%

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

   2. *-commutative 91.4%

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

   3. associate-/r* 98.7%

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

6. Simplified 98.7%

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

7. Final simplification 98.7%

   \[\leadsto x + \frac{-1}{\frac{\frac{z - a}{t - z}}{y}} \]
8. Add Preprocessing

Alternative 13: 49.6% 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 91.5%

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

   1. +-commutative 91.5%

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

   2. associate-/l* 99.0%

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

   3. fma-define 99.0%

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

3. Simplified 99.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 56.6%

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

6. Final simplification 56.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024054 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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