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

Percentage Accurate: 98.1% → 98.1%

Time: 11.6s

Alternatives: 13

Speedup: 0.5×

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: 98.1% 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: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 10^{+287}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 1e+287) (+ x t_1) (+ x (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 1e+287) {
		tmp = x + t_1;
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= 1d+287) then
        tmp = x + t_1
    else
        tmp = x + ((y / (a - t)) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 1e+287) {
		tmp = x + t_1;
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= 1e+287:
		tmp = x + t_1
	else:
		tmp = x + ((y / (a - t)) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= 1e+287)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - t)) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t_1 <= 1e+287)
		tmp = x + t_1;
	else
		tmp = x + ((y / (a - t)) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+287], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 1.0000000000000001e287

   1. Initial program 97.9%

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

   if 1.0000000000000001e287 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-/l* 76.8%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 10^{+287}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := x - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 480000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (- x (* y (/ z t)))))
   (if (<= t -9e+138)
     (+ x y)
     (if (<= t -2.55e-51)
       t_2
       (if (<= t -9.5e-56)
         (+ x y)
         (if (<= t 4.2e-100)
           (+ x (* z (/ y a)))
           (if (<= t 3.6e-59)
             t_2
             (if (<= t 480000000.0)
               t_1
               (if (<= t 5.1e+160)
                 t_2
                 (if (<= t 8.5e+160) t_1 (+ x y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -9e+138) {
		tmp = x + y;
	} else if (t <= -2.55e-51) {
		tmp = t_2;
	} else if (t <= -9.5e-56) {
		tmp = x + y;
	} else if (t <= 4.2e-100) {
		tmp = x + (z * (y / a));
	} else if (t <= 3.6e-59) {
		tmp = t_2;
	} else if (t <= 480000000.0) {
		tmp = t_1;
	} else if (t <= 5.1e+160) {
		tmp = t_2;
	} else if (t <= 8.5e+160) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = x - (y * (z / t))
    if (t <= (-9d+138)) then
        tmp = x + y
    else if (t <= (-2.55d-51)) then
        tmp = t_2
    else if (t <= (-9.5d-56)) then
        tmp = x + y
    else if (t <= 4.2d-100) then
        tmp = x + (z * (y / a))
    else if (t <= 3.6d-59) then
        tmp = t_2
    else if (t <= 480000000.0d0) then
        tmp = t_1
    else if (t <= 5.1d+160) then
        tmp = t_2
    else if (t <= 8.5d+160) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -9e+138) {
		tmp = x + y;
	} else if (t <= -2.55e-51) {
		tmp = t_2;
	} else if (t <= -9.5e-56) {
		tmp = x + y;
	} else if (t <= 4.2e-100) {
		tmp = x + (z * (y / a));
	} else if (t <= 3.6e-59) {
		tmp = t_2;
	} else if (t <= 480000000.0) {
		tmp = t_1;
	} else if (t <= 5.1e+160) {
		tmp = t_2;
	} else if (t <= 8.5e+160) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = x - (y * (z / t))
	tmp = 0
	if t <= -9e+138:
		tmp = x + y
	elif t <= -2.55e-51:
		tmp = t_2
	elif t <= -9.5e-56:
		tmp = x + y
	elif t <= 4.2e-100:
		tmp = x + (z * (y / a))
	elif t <= 3.6e-59:
		tmp = t_2
	elif t <= 480000000.0:
		tmp = t_1
	elif t <= 5.1e+160:
		tmp = t_2
	elif t <= 8.5e+160:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(x - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -9e+138)
		tmp = Float64(x + y);
	elseif (t <= -2.55e-51)
		tmp = t_2;
	elseif (t <= -9.5e-56)
		tmp = Float64(x + y);
	elseif (t <= 4.2e-100)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 3.6e-59)
		tmp = t_2;
	elseif (t <= 480000000.0)
		tmp = t_1;
	elseif (t <= 5.1e+160)
		tmp = t_2;
	elseif (t <= 8.5e+160)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = x - (y * (z / t));
	tmp = 0.0;
	if (t <= -9e+138)
		tmp = x + y;
	elseif (t <= -2.55e-51)
		tmp = t_2;
	elseif (t <= -9.5e-56)
		tmp = x + y;
	elseif (t <= 4.2e-100)
		tmp = x + (z * (y / a));
	elseif (t <= 3.6e-59)
		tmp = t_2;
	elseif (t <= 480000000.0)
		tmp = t_1;
	elseif (t <= 5.1e+160)
		tmp = t_2;
	elseif (t <= 8.5e+160)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+138], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.55e-51], t$95$2, If[LessEqual[t, -9.5e-56], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.2e-100], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-59], t$95$2, If[LessEqual[t, 480000000.0], t$95$1, If[LessEqual[t, 5.1e+160], t$95$2, If[LessEqual[t, 8.5e+160], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.99999999999999963e138 or -2.5499999999999999e-51 < t < -9.4999999999999991e-56 or 8.49999999999999982e160 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 85.9%

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

      1. +-commutative 85.9%

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

   5. Simplified 85.9%

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

   if -8.99999999999999963e138 < t < -2.5499999999999999e-51 or 4.20000000000000019e-100 < t < 3.6e-59 or 4.8e8 < t < 5.1000000000000001e160

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.5%

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

   4. Taylor expanded in a around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-*r/ 69.3%

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

      3. mul-1-neg 69.3%

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

      4. distribute-rgt-neg-out 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in y around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. associate-*r/ 72.9%

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

      3. distribute-lft-neg-in 72.9%

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

      4. cancel-sign-sub-inv 72.9%

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

   9. Simplified 72.9%

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

   if -9.4999999999999991e-56 < t < 4.20000000000000019e-100

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 83.9%

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

      3. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 3.6e-59 < t < 4.8e8 or 5.1000000000000001e160 < t < 8.49999999999999982e160

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 74.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-59}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 480000000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+160}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{t}{z}}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 850000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ t z)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -3.2e+138)
     (+ x y)
     (if (<= t -1e-51)
       (- x (* y (/ z t)))
       (if (<= t -4.7e-54)
         (+ x y)
         (if (<= t 1.8e-100)
           (+ x (* z (/ y a)))
           (if (<= t 5.2e-60)
             t_1
             (if (<= t 850000000.0)
               t_2
               (if (<= t 8.4e+160)
                 t_1
                 (if (<= t 8.5e+160) t_2 (+ x y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / z));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -3.2e+138) {
		tmp = x + y;
	} else if (t <= -1e-51) {
		tmp = x - (y * (z / t));
	} else if (t <= -4.7e-54) {
		tmp = x + y;
	} else if (t <= 1.8e-100) {
		tmp = x + (z * (y / a));
	} else if (t <= 5.2e-60) {
		tmp = t_1;
	} else if (t <= 850000000.0) {
		tmp = t_2;
	} else if (t <= 8.4e+160) {
		tmp = t_1;
	} else if (t <= 8.5e+160) {
		tmp = t_2;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y / (t / z))
    t_2 = x + (y * (z / a))
    if (t <= (-3.2d+138)) then
        tmp = x + y
    else if (t <= (-1d-51)) then
        tmp = x - (y * (z / t))
    else if (t <= (-4.7d-54)) then
        tmp = x + y
    else if (t <= 1.8d-100) then
        tmp = x + (z * (y / a))
    else if (t <= 5.2d-60) then
        tmp = t_1
    else if (t <= 850000000.0d0) then
        tmp = t_2
    else if (t <= 8.4d+160) then
        tmp = t_1
    else if (t <= 8.5d+160) then
        tmp = t_2
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / z));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -3.2e+138) {
		tmp = x + y;
	} else if (t <= -1e-51) {
		tmp = x - (y * (z / t));
	} else if (t <= -4.7e-54) {
		tmp = x + y;
	} else if (t <= 1.8e-100) {
		tmp = x + (z * (y / a));
	} else if (t <= 5.2e-60) {
		tmp = t_1;
	} else if (t <= 850000000.0) {
		tmp = t_2;
	} else if (t <= 8.4e+160) {
		tmp = t_1;
	} else if (t <= 8.5e+160) {
		tmp = t_2;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (t / z))
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -3.2e+138:
		tmp = x + y
	elif t <= -1e-51:
		tmp = x - (y * (z / t))
	elif t <= -4.7e-54:
		tmp = x + y
	elif t <= 1.8e-100:
		tmp = x + (z * (y / a))
	elif t <= 5.2e-60:
		tmp = t_1
	elif t <= 850000000.0:
		tmp = t_2
	elif t <= 8.4e+160:
		tmp = t_1
	elif t <= 8.5e+160:
		tmp = t_2
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(t / z)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -3.2e+138)
		tmp = Float64(x + y);
	elseif (t <= -1e-51)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= -4.7e-54)
		tmp = Float64(x + y);
	elseif (t <= 1.8e-100)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 5.2e-60)
		tmp = t_1;
	elseif (t <= 850000000.0)
		tmp = t_2;
	elseif (t <= 8.4e+160)
		tmp = t_1;
	elseif (t <= 8.5e+160)
		tmp = t_2;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (t / z));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -3.2e+138)
		tmp = x + y;
	elseif (t <= -1e-51)
		tmp = x - (y * (z / t));
	elseif (t <= -4.7e-54)
		tmp = x + y;
	elseif (t <= 1.8e-100)
		tmp = x + (z * (y / a));
	elseif (t <= 5.2e-60)
		tmp = t_1;
	elseif (t <= 850000000.0)
		tmp = t_2;
	elseif (t <= 8.4e+160)
		tmp = t_1;
	elseif (t <= 8.5e+160)
		tmp = t_2;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+138], N[(x + y), $MachinePrecision], If[LessEqual[t, -1e-51], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-54], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.8e-100], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-60], t$95$1, If[LessEqual[t, 850000000.0], t$95$2, If[LessEqual[t, 8.4e+160], t$95$1, If[LessEqual[t, 8.5e+160], t$95$2, N[(x + y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2000000000000001e138 or -1e-51 < t < -4.7e-54 or 8.49999999999999982e160 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 85.9%

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

      1. +-commutative 85.9%

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

   5. Simplified 85.9%

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

   if -3.2000000000000001e138 < t < -1e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 70.2%

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

   4. Taylor expanded in a around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. associate-*r/ 67.8%

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

      3. mul-1-neg 67.8%

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

      4. distribute-rgt-neg-out 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*r/ 70.1%

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

      3. distribute-lft-neg-in 70.1%

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

      4. cancel-sign-sub-inv 70.1%

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

   9. Simplified 70.1%

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

   if -4.7e-54 < t < 1.7999999999999999e-100

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 83.9%

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

      3. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1.7999999999999999e-100 < t < 5.1999999999999995e-60 or 8.5e8 < t < 8.39999999999999987e160

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.3%

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

   4. Taylor expanded in a around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

      3. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

   if 5.1999999999999995e-60 < t < 8.5e8 or 8.39999999999999987e160 < t < 8.49999999999999982e160

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 74.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 850000000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+160}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) a)))))
   (if (<= a -1.45e-33)
     t_1
     (if (<= a -1.9e-117)
       (+ x y)
       (if (<= a -2.4e-122)
         (+ x (* y (/ z a)))
         (if (<= a 3.35e-40) (- x (/ (* y 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 <= -1.45e-33) {
		tmp = t_1;
	} else if (a <= -1.9e-117) {
		tmp = x + y;
	} else if (a <= -2.4e-122) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.35e-40) {
		tmp = x - ((y * 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 <= (-1.45d-33)) then
        tmp = t_1
    else if (a <= (-1.9d-117)) then
        tmp = x + y
    else if (a <= (-2.4d-122)) then
        tmp = x + (y * (z / a))
    else if (a <= 3.35d-40) then
        tmp = x - ((y * 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 <= -1.45e-33) {
		tmp = t_1;
	} else if (a <= -1.9e-117) {
		tmp = x + y;
	} else if (a <= -2.4e-122) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.35e-40) {
		tmp = x - ((y * 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 <= -1.45e-33:
		tmp = t_1
	elif a <= -1.9e-117:
		tmp = x + y
	elif a <= -2.4e-122:
		tmp = x + (y * (z / a))
	elif a <= 3.35e-40:
		tmp = x - ((y * 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 <= -1.45e-33)
		tmp = t_1;
	elseif (a <= -1.9e-117)
		tmp = Float64(x + y);
	elseif (a <= -2.4e-122)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 3.35e-40)
		tmp = Float64(x - Float64(Float64(y * 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 <= -1.45e-33)
		tmp = t_1;
	elseif (a <= -1.9e-117)
		tmp = x + y;
	elseif (a <= -2.4e-122)
		tmp = x + (y * (z / a));
	elseif (a <= 3.35e-40)
		tmp = x - ((y * 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, -1.45e-33], t$95$1, If[LessEqual[a, -1.9e-117], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.4e-122], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.35e-40], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45000000000000001e-33 or 3.3499999999999999e-40 < a

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 83.0%

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

   if -1.45000000000000001e-33 < a < -1.89999999999999986e-117

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. +-commutative 63.6%

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

   5. Simplified 63.6%

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

   if -1.89999999999999986e-117 < a < -2.39999999999999987e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   if -2.39999999999999987e-122 < a < 3.3499999999999999e-40

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf 80.8%

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

   4. Taylor expanded in a around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-*r/ 72.6%

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

      3. mul-1-neg 72.6%

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

      4. distribute-rgt-neg-out 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. associate-*r/ 69.8%

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

      3. distribute-lft-neg-in 69.8%

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

      4. cancel-sign-sub-inv 69.8%

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

   9. Simplified 69.8%

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

   10. Taylor expanded in y around 0 72.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-33}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-27} \lor \neg \left(t \leq 8.5 \cdot 10^{+160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.4e-56)
   (+ x y)
   (if (<= t 4.4e-100)
     (+ x (* z (/ y a)))
     (if (or (<= t 1.28e-27) (not (<= t 8.5e+160)))
       (+ x y)
       (+ x (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e-56) {
		tmp = x + y;
	} else if (t <= 4.4e-100) {
		tmp = x + (z * (y / a));
	} else if ((t <= 1.28e-27) || !(t <= 8.5e+160)) {
		tmp = x + y;
	} 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 (t <= (-5.4d-56)) then
        tmp = x + y
    else if (t <= 4.4d-100) then
        tmp = x + (z * (y / a))
    else if ((t <= 1.28d-27) .or. (.not. (t <= 8.5d+160))) then
        tmp = x + y
    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 (t <= -5.4e-56) {
		tmp = x + y;
	} else if (t <= 4.4e-100) {
		tmp = x + (z * (y / a));
	} else if ((t <= 1.28e-27) || !(t <= 8.5e+160)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.4e-56:
		tmp = x + y
	elif t <= 4.4e-100:
		tmp = x + (z * (y / a))
	elif (t <= 1.28e-27) or not (t <= 8.5e+160):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.4e-56)
		tmp = Float64(x + y);
	elseif (t <= 4.4e-100)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif ((t <= 1.28e-27) || !(t <= 8.5e+160))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.4e-56)
		tmp = x + y;
	elseif (t <= 4.4e-100)
		tmp = x + (z * (y / a));
	elseif ((t <= 1.28e-27) || ~((t <= 8.5e+160)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.4e-56], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.4e-100], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.28e-27], N[Not[LessEqual[t, 8.5e+160]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.3999999999999999e-56 or 4.39999999999999978e-100 < t < 1.27999999999999993e-27 or 8.49999999999999982e160 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. +-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -5.3999999999999999e-56 < t < 4.39999999999999978e-100

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 83.9%

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

      3. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1.27999999999999993e-27 < t < 8.49999999999999982e160

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 64.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-27} \lor \neg \left(t \leq 8.5 \cdot 10^{+160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 10^{-27} \lor \neg \left(t \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e-56)
   (+ x y)
   (if (<= t 4.4e-100)
     (+ x (* z (/ y a)))
     (if (or (<= t 1e-27) (not (<= t 7.5e+122)))
       (+ x y)
       (+ x (/ z (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-56) {
		tmp = x + y;
	} else if (t <= 4.4e-100) {
		tmp = x + (z * (y / a));
	} else if ((t <= 1e-27) || !(t <= 7.5e+122)) {
		tmp = x + y;
	} else {
		tmp = x + (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) :: tmp
    if (t <= (-9.5d-56)) then
        tmp = x + y
    else if (t <= 4.4d-100) then
        tmp = x + (z * (y / a))
    else if ((t <= 1d-27) .or. (.not. (t <= 7.5d+122))) then
        tmp = x + y
    else
        tmp = x + (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 tmp;
	if (t <= -9.5e-56) {
		tmp = x + y;
	} else if (t <= 4.4e-100) {
		tmp = x + (z * (y / a));
	} else if ((t <= 1e-27) || !(t <= 7.5e+122)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e-56:
		tmp = x + y
	elif t <= 4.4e-100:
		tmp = x + (z * (y / a))
	elif (t <= 1e-27) or not (t <= 7.5e+122):
		tmp = x + y
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e-56)
		tmp = Float64(x + y);
	elseif (t <= 4.4e-100)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif ((t <= 1e-27) || !(t <= 7.5e+122))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e-56)
		tmp = x + y;
	elseif (t <= 4.4e-100)
		tmp = x + (z * (y / a));
	elseif ((t <= 1e-27) || ~((t <= 7.5e+122)))
		tmp = x + y;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e-56], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.4e-100], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1e-27], N[Not[LessEqual[t, 7.5e+122]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999991e-56 or 4.39999999999999978e-100 < t < 1e-27 or 7.5000000000000002e122 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. +-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -9.4999999999999991e-56 < t < 4.39999999999999978e-100

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 83.9%

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

      3. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1e-27 < t < 7.5000000000000002e122

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 61.0%

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

      1. +-commutative 61.0%

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

      2. associate-/l* 64.0%

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

      3. associate-/r/ 67.4%

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

   5. Simplified 67.4%

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

      1. *-commutative 67.4%

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

      2. clear-num 67.3%

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

      3. un-div-inv 67.4%

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

   7. Applied egg-rr 67.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 10^{-27} \lor \neg \left(t \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 0.0225:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e-33)
   (+ x (/ z (/ a y)))
   (if (<= a -7.8e-115)
     (+ x y)
     (if (<= a 4.4e-140)
       (- x (/ (* y z) t))
       (if (<= a 0.0225) (+ x y) (+ x (* y (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-33) {
		tmp = x + (z / (a / y));
	} else if (a <= -7.8e-115) {
		tmp = x + y;
	} else if (a <= 4.4e-140) {
		tmp = x - ((y * z) / t);
	} else if (a <= 0.0225) {
		tmp = x + y;
	} 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 <= (-3.1d-33)) then
        tmp = x + (z / (a / y))
    else if (a <= (-7.8d-115)) then
        tmp = x + y
    else if (a <= 4.4d-140) then
        tmp = x - ((y * z) / t)
    else if (a <= 0.0225d0) then
        tmp = x + y
    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 <= -3.1e-33) {
		tmp = x + (z / (a / y));
	} else if (a <= -7.8e-115) {
		tmp = x + y;
	} else if (a <= 4.4e-140) {
		tmp = x - ((y * z) / t);
	} else if (a <= 0.0225) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e-33:
		tmp = x + (z / (a / y))
	elif a <= -7.8e-115:
		tmp = x + y
	elif a <= 4.4e-140:
		tmp = x - ((y * z) / t)
	elif a <= 0.0225:
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e-33)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (a <= -7.8e-115)
		tmp = Float64(x + y);
	elseif (a <= 4.4e-140)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	elseif (a <= 0.0225)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e-33)
		tmp = x + (z / (a / y));
	elseif (a <= -7.8e-115)
		tmp = x + y;
	elseif (a <= 4.4e-140)
		tmp = x - ((y * z) / t);
	elseif (a <= 0.0225)
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e-33], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.8e-115], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.4e-140], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0225], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.09999999999999997e-33

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 64.7%

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

      1. +-commutative 64.7%

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

      2. associate-/l* 70.1%

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

      3. associate-/r/ 71.7%

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

   5. Simplified 71.7%

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

      1. *-commutative 71.7%

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

      2. clear-num 71.7%

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

      3. un-div-inv 71.8%

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

   7. Applied egg-rr 71.8%

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

   if -3.09999999999999997e-33 < a < -7.7999999999999997e-115 or 4.3999999999999998e-140 < a < 0.022499999999999999

   1. Initial program 96.3%

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

   3. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -7.7999999999999997e-115 < a < 4.3999999999999998e-140

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 85.8%

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

   4. Taylor expanded in a around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-*r/ 75.4%

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

      3. mul-1-neg 75.4%

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

      4. distribute-rgt-neg-out 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. associate-*r/ 70.9%

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

      3. distribute-lft-neg-in 70.9%

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

      4. cancel-sign-sub-inv 70.9%

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

   9. Simplified 70.9%

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

   10. Taylor expanded in y around 0 75.4%

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

   if 0.022499999999999999 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 78.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 0.0225:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+138} \lor \neg \left(t \leq 5.2 \cdot 10^{+192}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+138) (not (<= t 5.2e+192)))
   (+ x y)
   (+ x (* (/ y (- a t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+138) || !(t <= 5.2e+192)) {
		tmp = x + y;
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.2d+138)) .or. (.not. (t <= 5.2d+192))) then
        tmp = x + y
    else
        tmp = x + ((y / (a - t)) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+138) || !(t <= 5.2e+192)) {
		tmp = x + y;
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+138) or not (t <= 5.2e+192):
		tmp = x + y
	else:
		tmp = x + ((y / (a - t)) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+138) || !(t <= 5.2e+192))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - t)) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e+138) || ~((t <= 5.2e+192)))
		tmp = x + y;
	else
		tmp = x + ((y / (a - t)) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e+138], N[Not[LessEqual[t, 5.2e+192]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000001e138 or 5.20000000000000006e192 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.1%

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

      1. +-commutative 88.1%

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

   5. Simplified 88.1%

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

   if -3.2000000000000001e138 < t < 5.20000000000000006e192

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 82.6%

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

      2. associate-/r/ 83.7%

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

   5. Applied egg-rr 83.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+138} \lor \neg \left(t \leq 5.2 \cdot 10^{+192}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.098 \lor \neg \left(z \leq 7.5 \cdot 10^{-74}\right):\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.098) (not (<= z 7.5e-74)))
   (+ x (* (/ y (- a t)) z))
   (- x (* y (/ t (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.098) || !(z <= 7.5e-74)) {
		tmp = x + ((y / (a - t)) * z);
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.098d0)) .or. (.not. (z <= 7.5d-74))) then
        tmp = x + ((y / (a - t)) * z)
    else
        tmp = x - (y * (t / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.098) || !(z <= 7.5e-74)) {
		tmp = x + ((y / (a - t)) * z);
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.098) or not (z <= 7.5e-74):
		tmp = x + ((y / (a - t)) * z)
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.098) || !(z <= 7.5e-74))
		tmp = Float64(x + Float64(Float64(y / Float64(a - t)) * z));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.098) || ~((z <= 7.5e-74)))
		tmp = x + ((y / (a - t)) * z);
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.098], N[Not[LessEqual[z, 7.5e-74]], $MachinePrecision]], N[(x + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.098000000000000004 or 7.5e-74 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 87.3%

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

      2. associate-/r/ 88.8%

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

   5. Applied egg-rr 88.8%

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

   if -0.098000000000000004 < z < 7.5e-74

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

      1. associate-/r/ 93.7%

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

   7. Applied egg-rr 93.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.098 \lor \neg \left(z \leq 7.5 \cdot 10^{-74}\right):\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-54} \lor \neg \left(t \leq 8.5 \cdot 10^{+160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.6e-54) (not (<= t 8.5e+160))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e-54) || !(t <= 8.5e+160)) {
		tmp = x + y;
	} 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 ((t <= (-3.6d-54)) .or. (.not. (t <= 8.5d+160))) then
        tmp = x + y
    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 ((t <= -3.6e-54) || !(t <= 8.5e+160)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.6e-54) or not (t <= 8.5e+160):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.6e-54) || !(t <= 8.5e+160))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.6e-54) || ~((t <= 8.5e+160)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.6e-54], N[Not[LessEqual[t, 8.5e+160]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.59999999999999976e-54 or 8.49999999999999982e160 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -3.59999999999999976e-54 < t < 8.49999999999999982e160

   1. Initial program 94.0%

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

   3. Taylor expanded in t around 0 75.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-54} \lor \neg \left(t \leq 8.5 \cdot 10^{+160}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-94} \lor \neg \left(t \leq 9.5 \cdot 10^{-90}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e-94) (not (<= t 9.5e-90))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-94) || !(t <= 9.5e-90)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3d-94)) .or. (.not. (t <= 9.5d-90))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-94) || !(t <= 9.5e-90)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e-94) or not (t <= 9.5e-90):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e-94) || !(t <= 9.5e-90))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e-94) || ~((t <= 9.5e-90)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e-94], N[Not[LessEqual[t, 9.5e-90]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.0000000000000001e-94 or 9.5000000000000003e-90 < t

   1. Initial program 98.7%

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

   3. Taylor expanded in t around inf 66.6%

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

      1. +-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -3.0000000000000001e-94 < t < 9.5000000000000003e-90

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 57.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-94} \lor \neg \left(t \leq 9.5 \cdot 10^{-90}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-*r/ 86.3%

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

3. Simplified 86.3%

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

   1. associate-/l* 96.5%

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

   2. associate-/r/ 97.2%

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

6. Applied egg-rr 97.2%

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

7. Final simplification 97.2%

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

Alternative 13: 51.6% 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 96.2%

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

3. Taylor expanded in x around inf 52.2%

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

4. Final simplification 52.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.4% 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 2024018 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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