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

Percentage Accurate: 84.5% → 99.5%

Time: 11.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+287)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+287)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+287)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+287):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+287))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+287)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+287]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 2.0000000000000002e287 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 45.6%

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

      1. *-commutative 45.6%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.0000000000000002e287

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+25}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-73}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+25)
   (+ y x)
   (if (<= z -4.7e-73)
     (- x (* t (/ y z)))
     (if (<= z 3.15e+38) (+ x (/ y (/ a t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+25) {
		tmp = y + x;
	} else if (z <= -4.7e-73) {
		tmp = x - (t * (y / z));
	} else if (z <= 3.15e+38) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.35d+25)) then
        tmp = y + x
    else if (z <= (-4.7d-73)) then
        tmp = x - (t * (y / z))
    else if (z <= 3.15d+38) then
        tmp = x + (y / (a / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+25) {
		tmp = y + x;
	} else if (z <= -4.7e-73) {
		tmp = x - (t * (y / z));
	} else if (z <= 3.15e+38) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+25:
		tmp = y + x
	elif z <= -4.7e-73:
		tmp = x - (t * (y / z))
	elif z <= 3.15e+38:
		tmp = x + (y / (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+25)
		tmp = Float64(y + x);
	elseif (z <= -4.7e-73)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 3.15e+38)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+25)
		tmp = y + x;
	elseif (z <= -4.7e-73)
		tmp = x - (t * (y / z));
	elseif (z <= 3.15e+38)
		tmp = x + (y / (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+25], N[(y + x), $MachinePrecision], If[LessEqual[z, -4.7e-73], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e+38], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3499999999999999e25 or 3.15000000000000001e38 < z

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-*l/ 91.1%

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

      3. fma-def 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -2.3499999999999999e25 < z < -4.69999999999999994e-73

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-/l* 86.2%

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

      3. associate-/r/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-*r/ 81.5%

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

      3. distribute-lft-neg-in 81.5%

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

   10. Simplified 81.5%

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

   11. Taylor expanded in t around 0 81.4%

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

       1. mul-1-neg 81.4%

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

       2. associate-*r/ 81.5%

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

       3. sub-neg 81.5%

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

   13. Simplified 81.5%

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

   if -4.69999999999999994e-73 < z < 3.15000000000000001e38

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-*l/ 93.6%

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

      3. fma-def 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/l* 82.9%

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

   7. Simplified 82.9%

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

      1. clear-num 82.9%

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

      2. associate-/r/ 82.8%

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

      3. clear-num 83.1%

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

   9. Applied egg-rr 83.1%

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

       1. associate-*l/ 85.1%

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

       2. associate-/l* 85.3%

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

   11. Applied egg-rr 85.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+25}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-73}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+33} \lor \neg \left(z \leq 2.2 \cdot 10^{+116}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+33) (not (<= z 2.2e+116)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ (* y (- z t)) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+33) || !(z <= 2.2e+116)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (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 ((z <= (-8.2d+33)) .or. (.not. (z <= 2.2d+116))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + ((y * (z - t)) / (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 ((z <= -8.2e+33) || !(z <= 2.2e+116)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+33) or not (z <= 2.2e+116):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+33) || !(z <= 2.2e+116))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.2e+33) || ~((z <= 2.2e+116)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+33], N[Not[LessEqual[z, 2.2e+116]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999999e33 or 2.2e116 < z

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-*l/ 90.0%

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

      3. fma-def 90.0%

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

   3. Simplified 90.0%

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

      1. fma-udef 90.0%

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

      2. associate-/r/ 99.9%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 89.9%

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

   if -8.1999999999999999e33 < z < 2.2e116

   1. Initial program 98.2%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+33} \lor \neg \left(z \leq 2.2 \cdot 10^{+116}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+33} \lor \neg \left(z \leq 3.2 \cdot 10^{+117}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e+33) (not (<= z 3.2e+117)))
   (+ y x)
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+33) || !(z <= 3.2e+117)) {
		tmp = y + x;
	} else {
		tmp = x + (y / ((a - 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 ((z <= (-7.5d+33)) .or. (.not. (z <= 3.2d+117))) then
        tmp = y + x
    else
        tmp = x + (y / ((a - 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 ((z <= -7.5e+33) || !(z <= 3.2e+117)) {
		tmp = y + x;
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e+33) or not (z <= 3.2e+117):
		tmp = y + x
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e+33) || !(z <= 3.2e+117))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e+33) || ~((z <= 3.2e+117)))
		tmp = y + x;
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e+33], N[Not[LessEqual[z, 3.2e+117]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000046e33 or 3.20000000000000005e117 < z

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-*l/ 90.0%

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

      3. fma-def 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

   7. Simplified 78.5%

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

   if -7.50000000000000046e33 < z < 3.20000000000000005e117

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 91.7%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

      3. *-commutative 90.1%

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

      4. distribute-rgt-neg-out 90.1%

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

   5. Simplified 90.1%

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

      1. associate-*l/ 91.7%

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

      2. frac-2neg 91.7%

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

      3. add-sqr-sqrt 43.4%

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

      4. sqrt-unprod 66.6%

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

      5. sqr-neg 66.6%

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

      6. sqrt-unprod 30.2%

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

      7. add-sqr-sqrt 50.5%

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

      8. distribute-rgt-neg-out 50.5%

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

      9. add-sqr-sqrt 20.3%

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

      10. sqrt-unprod 61.1%

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

      11. sqr-neg 61.1%

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

      12. sqrt-unprod 48.2%

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

      13. add-sqr-sqrt 91.7%

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

   7. Applied egg-rr 91.7%

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

      1. associate-/l* 90.2%

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

   9. Simplified 90.2%

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

   10. Taylor expanded in z around 0 88.9%

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

       1. +-commutative 88.9%

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

       2. mul-1-neg 88.9%

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

       3. sub-neg 88.9%

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

       4. div-sub 90.2%

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

   12. Simplified 90.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+33} \lor \neg \left(z \leq 3.2 \cdot 10^{+117}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+30} \lor \neg \left(z \leq 1.5 \cdot 10^{+112}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+30) (not (<= z 1.5e+112)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+30) || !(z <= 1.5e+112)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y / ((a - 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 ((z <= (-3d+30)) .or. (.not. (z <= 1.5d+112))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y / ((a - 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 ((z <= -3e+30) || !(z <= 1.5e+112)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+30) or not (z <= 1.5e+112):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+30) || !(z <= 1.5e+112))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+30) || ~((z <= 1.5e+112)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+30], N[Not[LessEqual[z, 1.5e+112]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999978e30 or 1.4999999999999999e112 < z

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-*l/ 90.0%

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

      3. fma-def 90.0%

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

   3. Simplified 90.0%

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

      1. fma-udef 90.0%

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

      2. associate-/r/ 99.9%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 89.9%

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

   if -2.99999999999999978e30 < z < 1.4999999999999999e112

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 91.7%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

      3. *-commutative 90.1%

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

      4. distribute-rgt-neg-out 90.1%

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

   5. Simplified 90.1%

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

      1. associate-*l/ 91.7%

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

      2. frac-2neg 91.7%

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

      3. add-sqr-sqrt 43.4%

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

      4. sqrt-unprod 66.6%

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

      5. sqr-neg 66.6%

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

      6. sqrt-unprod 30.2%

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

      7. add-sqr-sqrt 50.5%

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

      8. distribute-rgt-neg-out 50.5%

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

      9. add-sqr-sqrt 20.3%

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

      10. sqrt-unprod 61.1%

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

      11. sqr-neg 61.1%

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

      12. sqrt-unprod 48.2%

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

      13. add-sqr-sqrt 91.7%

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

   7. Applied egg-rr 91.7%

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

      1. associate-/l* 90.2%

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

   9. Simplified 90.2%

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

   10. Taylor expanded in z around 0 88.9%

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

       1. +-commutative 88.9%

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

       2. mul-1-neg 88.9%

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

       3. sub-neg 88.9%

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

       4. div-sub 90.2%

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

   12. Simplified 90.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+30} \lor \neg \left(z \leq 1.5 \cdot 10^{+112}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.95e+31)
   (+ x (* y (/ z (- z a))))
   (if (<= z 3e+38) (+ x (/ y (/ (- a z) t))) (+ x (/ y (/ z (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.95e+31) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 3e+38) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / (z / (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 (z <= (-2.95d+31)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 3d+38) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y / (z / (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 (z <= -2.95e+31) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 3e+38) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.95e+31:
		tmp = x + (y * (z / (z - a)))
	elif z <= 3e+38:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.95e+31)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 3e+38)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.95e+31)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 3e+38)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.95e+31], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+38], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9500000000000002e31

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-*l/ 92.0%

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

      3. fma-def 92.0%

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

   3. Simplified 92.0%

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

      1. fma-udef 92.0%

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

      2. associate-/r/ 99.9%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 90.5%

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

   if -2.9500000000000002e31 < z < 3.0000000000000001e38

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf 91.7%

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

      1. associate-*r/ 90.0%

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

      2. neg-mul-1 90.0%

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

      3. *-commutative 90.0%

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

      4. distribute-rgt-neg-out 90.0%

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

   5. Simplified 90.0%

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

      1. associate-*l/ 91.7%

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

      2. frac-2neg 91.7%

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

      3. add-sqr-sqrt 42.8%

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

      4. sqrt-unprod 66.5%

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

      5. sqr-neg 66.5%

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

      6. sqrt-unprod 29.9%

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

      7. add-sqr-sqrt 49.2%

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

      8. distribute-rgt-neg-out 49.2%

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

      9. add-sqr-sqrt 19.3%

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

      10. sqrt-unprod 59.9%

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

      11. sqr-neg 59.9%

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

      12. sqrt-unprod 48.7%

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

      13. add-sqr-sqrt 91.7%

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

   7. Applied egg-rr 91.7%

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

      1. associate-/l* 90.1%

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

   9. Simplified 90.1%

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

   10. Taylor expanded in z around 0 88.7%

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

       1. +-commutative 88.7%

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

       2. mul-1-neg 88.7%

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

       3. sub-neg 88.7%

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

       4. div-sub 90.1%

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

   12. Simplified 90.1%

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

   if 3.0000000000000001e38 < z

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. associate-*l/ 90.4%

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

      3. fma-def 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in a around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-/l* 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+28)
   (+ x (* y (/ z (- z a))))
   (if (<= z 6.6e+36) (- x (/ (* y t) (- z a))) (+ x (/ y (/ z (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+28) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 6.6e+36) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y / (z / (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 (z <= (-2.7d+28)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 6.6d+36) then
        tmp = x - ((y * t) / (z - a))
    else
        tmp = x + (y / (z / (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 (z <= -2.7e+28) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 6.6e+36) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+28:
		tmp = x + (y * (z / (z - a)))
	elif z <= 6.6e+36:
		tmp = x - ((y * t) / (z - a))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+28)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 6.6e+36)
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+28)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 6.6e+36)
		tmp = x - ((y * t) / (z - a));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+28], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+36], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000002e28

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-*l/ 92.0%

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

      3. fma-def 92.0%

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

   3. Simplified 92.0%

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

      1. fma-udef 92.0%

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

      2. associate-/r/ 99.9%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 90.5%

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

   if -2.7000000000000002e28 < z < 6.5999999999999997e36

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-lft-neg-out 91.7%

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

      3. *-commutative 91.7%

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

   5. Simplified 91.7%

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

   if 6.5999999999999997e36 < z

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. associate-*l/ 90.4%

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

      3. fma-def 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in a around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-/l* 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+21} \lor \neg \left(z \leq 4.4 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+21) (not (<= z 4.4e+37))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+21) || !(z <= 4.4e+37)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7d+21)) .or. (.not. (z <= 4.4d+37))) then
        tmp = y + x
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+21) || !(z <= 4.4e+37)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e+21) or not (z <= 4.4e+37):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+21) || !(z <= 4.4e+37))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7e+21) || ~((z <= 4.4e+37)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e+21], N[Not[LessEqual[z, 4.4e+37]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e21 or 4.4000000000000001e37 < z

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-*l/ 91.3%

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

      3. fma-def 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   7. Simplified 77.6%

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

   if -7e21 < z < 4.4000000000000001e37

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 81.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+21} \lor \neg \left(z \leq 4.4 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+17} \lor \neg \left(z \leq 2 \cdot 10^{+39}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+17) (not (<= z 2e+39))) (+ y x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+17) || !(z <= 2e+39)) {
		tmp = y + x;
	} else {
		tmp = x + (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 ((z <= (-1.45d+17)) .or. (.not. (z <= 2d+39))) then
        tmp = y + x
    else
        tmp = x + (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 ((z <= -1.45e+17) || !(z <= 2e+39)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+17) or not (z <= 2e+39):
		tmp = y + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+17) || !(z <= 2e+39))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+17) || ~((z <= 2e+39)))
		tmp = y + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+17], N[Not[LessEqual[z, 2e+39]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e17 or 1.99999999999999988e39 < z

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-*l/ 91.3%

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

      3. fma-def 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   7. Simplified 77.6%

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

   if -1.45e17 < z < 1.99999999999999988e39

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. associate-*l/ 94.4%

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

      3. fma-def 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

      1. clear-num 79.2%

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

      2. associate-/r/ 79.2%

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

      3. clear-num 79.4%

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

   9. Applied egg-rr 79.4%

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

       1. associate-*l/ 81.1%

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

       2. associate-/l* 81.3%

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

   11. Applied egg-rr 81.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+17} \lor \neg \left(z \leq 2 \cdot 10^{+39}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+28) x (if (<= a 4.4e+201) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+28) {
		tmp = x;
	} else if (a <= 4.4e+201) {
		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 <= (-9.5d+28)) then
        tmp = x
    else if (a <= 4.4d+201) 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 <= -9.5e+28) {
		tmp = x;
	} else if (a <= 4.4e+201) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+28:
		tmp = x
	elif a <= 4.4e+201:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+28)
		tmp = x;
	elseif (a <= 4.4e+201)
		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 <= -9.5e+28)
		tmp = x;
	elseif (a <= 4.4e+201)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+28], x, If[LessEqual[a, 4.4e+201], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.49999999999999927e28 or 4.4e201 < a

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. associate-*l/ 96.9%

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

      3. fma-def 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 74.0%

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

   if -9.49999999999999927e28 < a < 4.4e201

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*l/ 91.5%

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

      3. fma-def 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around inf 58.0%

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

      1. +-commutative 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.1e+176) y (if (<= y 3.4e+63) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e+176) {
		tmp = y;
	} else if (y <= 3.4e+63) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-3.1d+176)) then
        tmp = y
    else if (y <= 3.4d+63) then
        tmp = x
    else
        tmp = 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 (y <= -3.1e+176) {
		tmp = y;
	} else if (y <= 3.4e+63) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.1e+176:
		tmp = y
	elif y <= 3.4e+63:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.1e+176)
		tmp = y;
	elseif (y <= 3.4e+63)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.1e+176)
		tmp = y;
	elseif (y <= 3.4e+63)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.1e+176], y, If[LessEqual[y, 3.4e+63], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e176 or 3.3999999999999999e63 < y

   1. Initial program 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-*l/ 92.2%

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

      3. fma-def 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in a around 0 30.1%

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

      1. +-commutative 30.1%

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

      2. associate-/l* 51.2%

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

      3. associate-/r/ 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in y around inf 49.9%

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

   9. Taylor expanded in t around 0 32.7%

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

   if -3.0999999999999999e176 < y < 3.3999999999999999e63

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. associate-*l/ 93.5%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in y around 0 63.2%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

   1. +-commutative 89.3%

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

   2. associate-*l/ 93.1%

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

   3. fma-def 93.1%

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

3. Simplified 93.1%

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

   1. fma-udef 93.1%

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

   2. associate-/r/ 97.8%

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

   3. div-inv 97.6%

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

   4. clear-num 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 13: 49.8% 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 89.3%

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

   1. +-commutative 89.3%

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

   2. associate-*l/ 93.1%

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

   3. fma-def 93.1%

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

3. Simplified 93.1%

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

5. Taylor expanded in y around 0 49.1%

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

6. Final simplification 49.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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