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

Percentage Accurate: 85.6% → 98.3%

Time: 7.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

2. Taylor expanded in z around 0 83.3%

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

   1. fma-def 83.3%

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

   2. associate-*r/ 87.1%

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

   3. associate-*l/ 94.0%

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

   4. *-commutative 94.0%

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

   5. fma-def 94.0%

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

   6. neg-mul-1 94.0%

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

   7. +-commutative 94.0%

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

   8. sub-neg 94.0%

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

   9. distribute-rgt-out-- 94.1%

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

   10. associate-*l/ 83.8%

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

   11. associate-/l* 97.3%

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

4. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 2: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+15} \lor \neg \left(t \leq 3.4 \cdot 10^{+120}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+15) (not (<= t 3.4e+120)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+15) || !(t <= 3.4e+120)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (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 <= (-8d+15)) .or. (.not. (t <= 3.4d+120))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (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 <= -8e+15) || !(t <= 3.4e+120)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+15) or not (t <= 3.4e+120):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+15) || !(t <= 3.4e+120))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+15) || ~((t <= 3.4e+120)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+15], N[Not[LessEqual[t, 3.4e+120]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8e15 or 3.39999999999999999e120 < t

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 87.0%

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

      1. +-commutative 87.0%

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

   6. Simplified 87.0%

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

   if -8e15 < t < 3.39999999999999999e120

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.7%

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

      1. fma-def 92.7%

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

      2. associate-*r/ 87.3%

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

      3. associate-*l/ 92.4%

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

      4. *-commutative 92.4%

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

      5. fma-def 92.4%

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

      6. neg-mul-1 92.4%

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

      7. +-commutative 92.4%

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

      8. sub-neg 92.4%

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

      9. distribute-rgt-out-- 92.6%

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

      10. associate-*l/ 93.4%

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

      11. associate-/l* 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in z around inf 85.3%

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

      1. associate-*l/ 84.9%

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

      2. *-commutative 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+15} \lor \neg \left(t \leq 3.4 \cdot 10^{+120}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 3: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+14} \lor \neg \left(t \leq 7.2 \cdot 10^{+78}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.26e+14) (not (<= t 7.2e+78)))
   (+ x y)
   (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.26e+14) || !(t <= 7.2e+78)) {
		tmp = x + y;
	} 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 <= (-1.26d+14)) .or. (.not. (t <= 7.2d+78))) then
        tmp = x + y
    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 <= -1.26e+14) || !(t <= 7.2e+78)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.26e+14) or not (t <= 7.2e+78):
		tmp = x + y
	else:
		tmp = x + ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.26e+14) || !(t <= 7.2e+78))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.26e+14) || ~((t <= 7.2e+78)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.26e+14], N[Not[LessEqual[t, 7.2e+78]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.26e14 or 7.20000000000000039e78 < t

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-*l/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around inf 86.0%

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

      1. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   if -1.26e14 < t < 7.20000000000000039e78

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 86.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+14} \lor \neg \left(t \leq 7.2 \cdot 10^{+78}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 4: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+30} \lor \neg \left(t \leq 1.8 \cdot 10^{+120}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+30) (not (<= t 1.8e+120)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+30) || !(t <= 1.8e+120)) {
		tmp = x + y;
	} 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 <= (-1.05d+30)) .or. (.not. (t <= 1.8d+120))) then
        tmp = x + y
    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 <= -1.05e+30) || !(t <= 1.8e+120)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+30) or not (t <= 1.8e+120):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+30) || !(t <= 1.8e+120))
		tmp = Float64(x + y);
	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 <= -1.05e+30) || ~((t <= 1.8e+120)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+30], N[Not[LessEqual[t, 1.8e+120]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e30 or 1.80000000000000008e120 < t

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*l/ 96.2%

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

      3. fma-def 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 87.3%

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

      1. +-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -1.05e30 < t < 1.80000000000000008e120

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*l/ 92.9%

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

      3. fma-def 92.9%

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

   3. Simplified 92.9%

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

      1. fma-udef 92.9%

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

      2. associate-/r/ 95.8%

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

      3. div-inv 95.8%

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

      4. clear-num 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around inf 87.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+30} \lor \neg \left(t \leq 1.8 \cdot 10^{+120}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -580000000 \lor \neg \left(t \leq 5.7 \cdot 10^{+119}\right):\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -580000000.0) (not (<= t 5.7e+119)))
   (- x (/ t (/ (- a t) y)))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -580000000.0) || !(t <= 5.7e+119)) {
		tmp = x - (t / ((a - t) / y));
	} 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 <= (-580000000.0d0)) .or. (.not. (t <= 5.7d+119))) then
        tmp = x - (t / ((a - t) / y))
    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 <= -580000000.0) || !(t <= 5.7e+119)) {
		tmp = x - (t / ((a - t) / y));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -580000000.0) or not (t <= 5.7e+119):
		tmp = x - (t / ((a - t) / y))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -580000000.0) || !(t <= 5.7e+119))
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	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 <= -580000000.0) || ~((t <= 5.7e+119)))
		tmp = x - (t / ((a - t) / y));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -580000000.0], N[Not[LessEqual[t, 5.7e+119]], $MachinePrecision]], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8e8 or 5.7000000000000002e119 < t

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-*l/ 96.5%

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

      3. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 67.7%

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

      1. associate-*r/ 90.0%

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

      2. neg-mul-1 90.0%

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

      3. unsub-neg 90.0%

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

      4. associate-*r/ 67.7%

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

      5. associate-/l* 90.0%

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

   6. Simplified 90.0%

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

   if -5.8e8 < t < 5.7000000000000002e119

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-*l/ 92.5%

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

      3. fma-def 92.5%

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

   3. Simplified 92.5%

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

      1. fma-udef 92.5%

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

      2. associate-/r/ 95.6%

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

      3. div-inv 95.6%

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

      4. clear-num 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in z around inf 87.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -580000000 \lor \neg \left(t \leq 5.7 \cdot 10^{+119}\right):\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2200000000:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2200000000.0)
   (- x (/ t (/ (- a t) y)))
   (if (<= t 3.2e+91) (+ x (* y (/ z (- a t)))) (- x (/ y (/ t (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2200000000.0) {
		tmp = x - (t / ((a - t) / y));
	} else if (t <= 3.2e+91) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x - (y / (t / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2200000000.0d0)) then
        tmp = x - (t / ((a - t) / y))
    else if (t <= 3.2d+91) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x - (y / (t / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2200000000.0) {
		tmp = x - (t / ((a - t) / y));
	} else if (t <= 3.2e+91) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x - (y / (t / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2200000000.0:
		tmp = x - (t / ((a - t) / y))
	elif t <= 3.2e+91:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x - (y / (t / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2200000000.0)
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	elseif (t <= 3.2e+91)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2200000000.0)
		tmp = x - (t / ((a - t) / y));
	elseif (t <= 3.2e+91)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x - (y / (t / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2200000000.0], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+91], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e9

   1. Initial program 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-*l/ 95.7%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 65.9%

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

      1. associate-*r/ 88.9%

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

      2. neg-mul-1 88.9%

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

      3. unsub-neg 88.9%

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

      4. associate-*r/ 65.9%

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

      5. associate-/l* 89.0%

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

   6. Simplified 89.0%

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

   if -2.2e9 < t < 3.19999999999999989e91

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

      1. fma-udef 92.4%

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

      2. associate-/r/ 95.5%

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

      3. div-inv 95.5%

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

      4. clear-num 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in z around inf 88.4%

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

   if 3.19999999999999989e91 < t

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-*l/ 98.2%

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

      3. fma-def 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in a around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

      3. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2200000000:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3800000 \lor \neg \left(t \leq 1.22 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3800000.0) (not (<= t 1.22e+67))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3800000.0) || !(t <= 1.22e+67)) {
		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 <= (-3800000.0d0)) .or. (.not. (t <= 1.22d+67))) 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 <= -3800000.0) || !(t <= 1.22e+67)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3800000.0) or not (t <= 1.22e+67):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3800000.0) || !(t <= 1.22e+67))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3800000.0) || ~((t <= 1.22e+67)))
		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, -3800000.0], N[Not[LessEqual[t, 1.22e+67]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e6 or 1.22000000000000004e67 < t

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-*l/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around inf 85.4%

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

      1. +-commutative 85.4%

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

   6. Simplified 85.4%

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

   if -3.8e6 < t < 1.22000000000000004e67

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 71.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3800000 \lor \neg \left(t \leq 1.22 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 8: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -45000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -45000000.0)
   (+ x y)
   (if (<= t 7.2e+68) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -45000000.0) {
		tmp = x + y;
	} else if (t <= 7.2e+68) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-45000000.0d0)) then
        tmp = x + y
    else if (t <= 7.2d+68) then
        tmp = x + (y * (z / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -45000000.0) {
		tmp = x + y;
	} else if (t <= 7.2e+68) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -45000000.0:
		tmp = x + y
	elif t <= 7.2e+68:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -45000000.0)
		tmp = Float64(x + y);
	elseif (t <= 7.2e+68)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -45000000.0)
		tmp = x + y;
	elseif (t <= 7.2e+68)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -45000000.0], N[(x + y), $MachinePrecision], If[LessEqual[t, 7.2e+68], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e7 or 7.1999999999999998e68 < t

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-*l/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around inf 85.4%

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

      1. +-commutative 85.4%

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

   6. Simplified 85.4%

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

   if -4.5e7 < t < 7.1999999999999998e68

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-*l/ 92.3%

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

      3. fma-def 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

      1. clear-num 75.5%

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

      2. associate-/r/ 75.5%

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

      3. clear-num 75.5%

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

   8. Applied egg-rr 75.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -45000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 63.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+148}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.8e+182) x (if (<= a 2.7e+148) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e+182) {
		tmp = x;
	} else if (a <= 2.7e+148) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.8d+182)) then
        tmp = x
    else if (a <= 2.7d+148) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e+182) {
		tmp = x;
	} else if (a <= 2.7e+148) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.8e+182:
		tmp = x
	elif a <= 2.7e+148:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.8e+182)
		tmp = x;
	elseif (a <= 2.7e+148)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.8e+182)
		tmp = x;
	elseif (a <= 2.7e+148)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.8e+182], x, If[LessEqual[a, 2.7e+148], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.7999999999999998e182 or 2.70000000000000019e148 < a

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-*l/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 63.4%

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

   if -7.7999999999999998e182 < a < 2.70000000000000019e148

   1. Initial program 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-*l/ 93.1%

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

      3. fma-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 67.1%

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

      1. +-commutative 67.1%

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

   6. Simplified 67.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+148}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 50.9% 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 83.8%

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

   1. +-commutative 83.8%

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

   2. associate-*l/ 94.1%

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

   3. fma-def 94.1%

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

3. Simplified 94.1%

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

4. Taylor expanded in y around 0 50.2%

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

5. Final simplification 50.2%

   \[\leadsto x \]

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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