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

Percentage Accurate: 98.1% → 98.9%

Time: 12.2s

Alternatives: 12

Speedup: 0.5×

• could not determine a ground truth

  1. x = -5.979294665592788e-283
  2. y = 1.7424396974686487e-283
  3. z = -7.043716734362677e-196
  4. t = -1.1971704947040996e+133
  5. a = -2.2044808644925774e-97

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: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

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

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 <= -((double) INFINITY)) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (z / ((a - t) / y))
	else:
		tmp = t_1 + x
	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 <= Float64(-Inf))
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(t_1 + x);
	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 <= -Inf)
		tmp = x + (z / ((a - t) / y));
	else
		tmp = t_1 + x;
	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, (-Infinity)], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < -inf.0

   1. Initial program 59.1%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      3. associate-/r/ 59.1%

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

   5. Simplified 59.1%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 78.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+18} \lor \neg \left(t \leq 8 \cdot 10^{+81}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+18) (not (<= t 8e+81)))
   (+ y x)
   (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+18) || !(t <= 8e+81)) {
		tmp = y + x;
	} else {
		tmp = x + (y * ((z - 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 ((t <= (-1.3d+18)) .or. (.not. (t <= 8d+81))) then
        tmp = y + x
    else
        tmp = x + (y * ((z - 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 ((t <= -1.3e+18) || !(t <= 8e+81)) {
		tmp = y + x;
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+18) or not (t <= 8e+81):
		tmp = y + x
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+18) || !(t <= 8e+81))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e+18) || ~((t <= 8e+81)))
		tmp = y + x;
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+18], N[Not[LessEqual[t, 8e+81]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e18 or 7.99999999999999937e81 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 81.2%

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

      1. +-commutative 81.2%

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

   5. Simplified 81.2%

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

   if -1.3e18 < t < 7.99999999999999937e81

   1. Initial program 95.7%

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

   3. Taylor expanded in a around inf 78.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+18} \lor \neg \left(t \leq 8 \cdot 10^{+81}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+50} \lor \neg \left(t \leq 3.6 \cdot 10^{+237}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+50) (not (<= t 3.6e+237)))
   (+ y x)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+50) || !(t <= 3.6e+237)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / (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 ((t <= (-3.2d+50)) .or. (.not. (t <= 3.6d+237))) then
        tmp = y + x
    else
        tmp = x + (y * (z / (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 ((t <= -3.2e+50) || !(t <= 3.6e+237)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+50) or not (t <= 3.6e+237):
		tmp = y + x
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+50) || !(t <= 3.6e+237))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e+50) || ~((t <= 3.6e+237)))
		tmp = y + x;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e+50], N[Not[LessEqual[t, 3.6e+237]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999983e50 or 3.60000000000000015e237 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 85.3%

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

      1. +-commutative 85.3%

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

   5. Simplified 85.3%

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

   if -3.19999999999999983e50 < t < 3.60000000000000015e237

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 80.4%

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

      1. *-commutative 80.4%

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

      2. associate-/l* 82.3%

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

      3. associate-/r/ 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+50} \lor \neg \left(t \leq 3.6 \cdot 10^{+237}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+50} \lor \neg \left(t \leq 3.6 \cdot 10^{+237}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+50) (not (<= t 3.6e+237)))
   (+ y x)
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+50) || !(t <= 3.6e+237)) {
		tmp = y + x;
	} 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 <= (-2.3d+50)) .or. (.not. (t <= 3.6d+237))) then
        tmp = y + x
    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 <= -2.3e+50) || !(t <= 3.6e+237)) {
		tmp = y + x;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+50) or not (t <= 3.6e+237):
		tmp = y + x
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+50) || !(t <= 3.6e+237))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+50) || ~((t <= 3.6e+237)))
		tmp = y + x;
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+50], N[Not[LessEqual[t, 3.6e+237]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.29999999999999997e50 or 3.60000000000000015e237 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 85.3%

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

      1. +-commutative 85.3%

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

   5. Simplified 85.3%

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

   if -2.29999999999999997e50 < t < 3.60000000000000015e237

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 80.4%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+50} \lor \neg \left(t \leq 3.6 \cdot 10^{+237}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.25e+50)
   (+ y x)
   (if (<= t 2.6e+140) (+ x (/ z (/ (- a t) y))) (+ x (/ 1.0 (/ 1.0 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.25e+50) {
		tmp = y + x;
	} else if (t <= 2.6e+140) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (1.0 / (1.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.25d+50)) then
        tmp = y + x
    else if (t <= 2.6d+140) then
        tmp = x + (z / ((a - t) / y))
    else
        tmp = x + (1.0d0 / (1.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.25e+50) {
		tmp = y + x;
	} else if (t <= 2.6e+140) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (1.0 / (1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.25e+50:
		tmp = y + x
	elif t <= 2.6e+140:
		tmp = x + (z / ((a - t) / y))
	else:
		tmp = x + (1.0 / (1.0 / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.25e+50)
		tmp = Float64(y + x);
	elseif (t <= 2.6e+140)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.25e+50)
		tmp = y + x;
	elseif (t <= 2.6e+140)
		tmp = x + (z / ((a - t) / y));
	else
		tmp = x + (1.0 / (1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.25e+50], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.6e+140], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2500000000000001e50

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 81.8%

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

      1. +-commutative 81.8%

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

   5. Simplified 81.8%

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

   if -3.2500000000000001e50 < t < 2.6000000000000001e140

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-/l* 83.2%

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

      3. associate-/r/ 81.6%

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

   5. Simplified 81.6%

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

      1. associate-*l/ 81.1%

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

      2. associate-/l* 83.2%

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

   7. Applied egg-rr 83.2%

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

   if 2.6000000000000001e140 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 75.4%

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

      2. clear-num 75.6%

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

      3. associate-/r* 85.8%

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

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in t around inf 86.4%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+135}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e-16)
   (+ x (* (/ y t) (- t z)))
   (if (<= t 7.5e+135) (+ x (/ z (/ (- a t) y))) (+ x (/ 1.0 (/ 1.0 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e-16) {
		tmp = x + ((y / t) * (t - z));
	} else if (t <= 7.5e+135) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (1.0 / (1.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d-16)) then
        tmp = x + ((y / t) * (t - z))
    else if (t <= 7.5d+135) then
        tmp = x + (z / ((a - t) / y))
    else
        tmp = x + (1.0d0 / (1.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e-16) {
		tmp = x + ((y / t) * (t - z));
	} else if (t <= 7.5e+135) {
		tmp = x + (z / ((a - t) / y));
	} else {
		tmp = x + (1.0 / (1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e-16:
		tmp = x + ((y / t) * (t - z))
	elif t <= 7.5e+135:
		tmp = x + (z / ((a - t) / y))
	else:
		tmp = x + (1.0 / (1.0 / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e-16)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	elseif (t <= 7.5e+135)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e-16)
		tmp = x + ((y / t) * (t - z));
	elseif (t <= 7.5e+135)
		tmp = x + (z / ((a - t) / y));
	else
		tmp = x + (1.0 / (1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e-16], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+135], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e-16

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 88.8%

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

      4. associate-/r/ 80.6%

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

   5. Simplified 80.6%

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

   if -2.1000000000000001e-16 < t < 7.49999999999999947e135

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 83.9%

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

      3. associate-/r/ 82.2%

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

   5. Simplified 82.2%

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

      1. associate-*l/ 81.6%

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

      2. associate-/l* 83.9%

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

   7. Applied egg-rr 83.9%

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

   if 7.49999999999999947e135 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 75.4%

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

      2. clear-num 75.6%

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

      3. associate-/r* 85.8%

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

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in t around inf 86.4%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+135}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 0.00086:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+23)
   (+ x (/ z (/ (- a t) y)))
   (if (<= z 0.00086) (- x (* t (/ y (- a t)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+23) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 0.00086) {
		tmp = x - (t * (y / (a - t)));
	} 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 (z <= (-3.5d+23)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 0.00086d0) then
        tmp = x - (t * (y / (a - t)))
    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 (z <= -3.5e+23) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 0.00086) {
		tmp = x - (t * (y / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+23:
		tmp = x + (z / ((a - t) / y))
	elif z <= 0.00086:
		tmp = x - (t * (y / (a - t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+23)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 0.00086)
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+23)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 0.00086)
		tmp = x - (t * (y / (a - t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+23], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00086], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e23

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 86.7%

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

      3. associate-/r/ 84.7%

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

   5. Simplified 84.7%

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

      1. associate-*l/ 82.7%

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

      2. associate-/l* 86.7%

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

   7. Applied egg-rr 86.7%

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

   if -3.5000000000000002e23 < z < 8.59999999999999979e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

      1. clear-num 86.3%

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

      2. associate-/r/ 86.1%

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

      3. clear-num 86.2%

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

   7. Applied egg-rr 86.2%

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

   if 8.59999999999999979e-4 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 0.00086:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z}{t\_1}\\ \mathbf{elif}\;z \leq 0.0065:\\ \;\;\;\;x - \frac{t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)))
   (if (<= z -4.2e+23)
     (+ x (/ z t_1))
     (if (<= z 0.0065) (- x (/ t t_1)) (+ x (/ y (/ (- a t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -4.2e+23) {
		tmp = x + (z / t_1);
	} else if (z <= 0.0065) {
		tmp = x - (t / 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 = (a - t) / y
    if (z <= (-4.2d+23)) then
        tmp = x + (z / t_1)
    else if (z <= 0.0065d0) then
        tmp = x - (t / 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 = (a - t) / y;
	double tmp;
	if (z <= -4.2e+23) {
		tmp = x + (z / t_1);
	} else if (z <= 0.0065) {
		tmp = x - (t / t_1);
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a - t) / y
	tmp = 0
	if z <= -4.2e+23:
		tmp = x + (z / t_1)
	elif z <= 0.0065:
		tmp = x - (t / t_1)
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - t) / y)
	tmp = 0.0
	if (z <= -4.2e+23)
		tmp = Float64(x + Float64(z / t_1));
	elseif (z <= 0.0065)
		tmp = Float64(x - Float64(t / t_1));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a - t) / y;
	tmp = 0.0;
	if (z <= -4.2e+23)
		tmp = x + (z / t_1);
	elseif (z <= 0.0065)
		tmp = x - (t / 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[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -4.2e+23], N[(x + N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0065], N[(x - N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000003e23

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 86.7%

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

      3. associate-/r/ 84.7%

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

   5. Simplified 84.7%

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

      1. associate-*l/ 82.7%

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

      2. associate-/l* 86.7%

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

   7. Applied egg-rr 86.7%

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

   if -4.2000000000000003e23 < z < 0.0064999999999999997

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   if 0.0064999999999999997 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 0.0065:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 0.155:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+23)
   (+ x (/ z (/ (- a t) y)))
   (if (<= z 0.155) (- x (* y (/ t (- a t)))) (+ x (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+23) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 0.155) {
		tmp = x - (y * (t / (a - t)));
	} 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 (z <= (-3d+23)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 0.155d0) then
        tmp = x - (y * (t / (a - t)))
    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 (z <= -3e+23) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 0.155) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+23:
		tmp = x + (z / ((a - t) / y))
	elif z <= 0.155:
		tmp = x - (y * (t / (a - t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+23)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 0.155)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+23)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 0.155)
		tmp = x - (y * (t / (a - t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+23], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.155], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e23

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 86.7%

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

      3. associate-/r/ 84.7%

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

   5. Simplified 84.7%

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

      1. associate-*l/ 82.7%

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

      2. associate-/l* 86.7%

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

   7. Applied egg-rr 86.7%

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

   if -3.0000000000000001e23 < z < 0.154999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 91.3%

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

      1. neg-mul-1 91.3%

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

      2. distribute-neg-frac 91.3%

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

   5. Simplified 91.3%

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

   if 0.154999999999999999 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 75.0%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 0.155:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21} \lor \neg \left(a \leq 1.2 \cdot 10^{-73}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e+21) (not (<= a 1.2e-73))) (+ x (* y (/ z a))) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e+21) || !(a <= 1.2e-73)) {
		tmp = x + (y * (z / 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 ((a <= (-2d+21)) .or. (.not. (a <= 1.2d-73))) then
        tmp = x + (y * (z / 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 ((a <= -2e+21) || !(a <= 1.2e-73)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2e+21) or not (a <= 1.2e-73):
		tmp = x + (y * (z / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e+21) || !(a <= 1.2e-73))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2e+21) || ~((a <= 1.2e-73)))
		tmp = x + (y * (z / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e+21], N[Not[LessEqual[a, 1.2e-73]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2e21 or 1.20000000000000003e-73 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 79.9%

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

   if -2e21 < a < 1.20000000000000003e-73

   1. Initial program 94.3%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. +-commutative 65.3%

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

   5. Simplified 65.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21} \lor \neg \left(a \leq 1.2 \cdot 10^{-73}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+175}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+21) x (if (<= a 9e+175) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+21) {
		tmp = x;
	} else if (a <= 9e+175) {
		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 <= (-2.05d+21)) then
        tmp = x
    else if (a <= 9d+175) 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 <= -2.05e+21) {
		tmp = x;
	} else if (a <= 9e+175) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+21:
		tmp = x
	elif a <= 9e+175:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+21)
		tmp = x;
	elseif (a <= 9e+175)
		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 <= -2.05e+21)
		tmp = x;
	elseif (a <= 9e+175)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+21], x, If[LessEqual[a, 9e+175], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.05e21 or 8.99999999999999979e175 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 65.8%

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

   if -2.05e21 < a < 8.99999999999999979e175

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 63.7%

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

      1. +-commutative 63.7%

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

   5. Simplified 63.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+175}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 97.3%

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

3. Taylor expanded in x around inf 49.4%

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

4. Final simplification 49.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(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)))))