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

Percentage Accurate: 85.0% → 98.1%

Time: 11.2s

Alternatives: 14

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: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 82.6%

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

   1. +-commutative 82.6%

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

   2. associate-/l* 98.8%

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

   3. fma-define 98.8%

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

3. Simplified 98.8%

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

Alternative 2: 92.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+274}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 (- INFINITY))
     (+ x (* y (- 1.0 (/ t z))))
     (if (<= t_1 1e+274) (+ x t_1) (+ x (* t (/ y (- a z))))))))

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)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (t_1 <= 1e+274) {
		tmp = x + t_1;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	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) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (t_1 <= 1e+274) {
		tmp = x + t_1;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y * (1.0 - (t / z)))
	elif t_1 <= 1e+274:
		tmp = x + t_1
	else:
		tmp = x + (t * (y / (a - z)))
	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))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (t_1 <= 1e+274)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	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)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (t_1 <= 1e+274)
		tmp = x + t_1;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+274], N[(x + t$95$1), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 33.2%

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

   3. Taylor expanded in a around 0 23.3%

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

      1. associate-/l* 84.1%

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

      2. div-sub 84.1%

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

      3. *-inverses 84.1%

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

   5. Simplified 84.1%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.99999999999999921e273

   1. Initial program 99.9%

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

   if 9.99999999999999921e273 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 28.7%

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

      1. +-commutative 28.7%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

      1. fma-undefine 99.8%

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

      2. associate-/l* 28.7%

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

      3. div-inv 28.7%

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

      4. *-commutative 28.7%

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

      5. associate-*r* 99.5%

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

      6. div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 67.4%

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

      1. neg-mul-1 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in t around 0 33.2%

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

       1. mul-1-neg 33.2%

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

       2. associate-*r/ 67.4%

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

       3. sub-neg 67.4%

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

   12. Simplified 67.4%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 10^{+274}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+151}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -135000000000.0)
   (+ y x)
   (if (<= z 1.3e-47)
     (+ x (* t (/ y a)))
     (if (<= z 5.6e+151) (- x (* t (/ y z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = y + x;
	} else if (z <= 1.3e-47) {
		tmp = x + (t * (y / a));
	} else if (z <= 5.6e+151) {
		tmp = x - (t * (y / z));
	} 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 <= (-135000000000.0d0)) then
        tmp = y + x
    else if (z <= 1.3d-47) then
        tmp = x + (t * (y / a))
    else if (z <= 5.6d+151) then
        tmp = x - (t * (y / z))
    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 <= -135000000000.0) {
		tmp = y + x;
	} else if (z <= 1.3e-47) {
		tmp = x + (t * (y / a));
	} else if (z <= 5.6e+151) {
		tmp = x - (t * (y / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -135000000000.0:
		tmp = y + x
	elif z <= 1.3e-47:
		tmp = x + (t * (y / a))
	elif z <= 5.6e+151:
		tmp = x - (t * (y / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = Float64(y + x);
	elseif (z <= 1.3e-47)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 5.6e+151)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = y + x;
	elseif (z <= 1.3e-47)
		tmp = x + (t * (y / a));
	elseif (z <= 5.6e+151)
		tmp = x - (t * (y / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -135000000000.0], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.3e-47], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+151], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e11 or 5.59999999999999975e151 < z

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.1%

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

      1. +-commutative 85.1%

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

   7. Simplified 85.1%

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

   if -1.35e11 < z < 1.3e-47

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-/l* 97.1%

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

      3. fma-define 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. associate-/l* 76.3%

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

   7. Simplified 76.3%

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

   if 1.3e-47 < z < 5.59999999999999975e151

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 87.2%

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

      3. div-inv 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-*r* 99.9%

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

      6. div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 84.1%

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

      1. neg-mul-1 84.1%

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

   9. Simplified 84.1%

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

   10. Taylor expanded in z around inf 72.6%

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

       1. mul-1-neg 72.6%

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

       2. unsub-neg 72.6%

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

       3. associate-/l* 74.9%

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

   12. Simplified 74.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+151}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-10)
   (+ y x)
   (if (<= z 2.15e-294) x (if (<= z 7.6e-79) (* y (/ t a)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-10) {
		tmp = y + x;
	} else if (z <= 2.15e-294) {
		tmp = x;
	} else if (z <= 7.6e-79) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-10)) then
        tmp = y + x
    else if (z <= 2.15d-294) then
        tmp = x
    else if (z <= 7.6d-79) then
        tmp = y * (t / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-10) {
		tmp = y + x;
	} else if (z <= 2.15e-294) {
		tmp = x;
	} else if (z <= 7.6e-79) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-10:
		tmp = y + x
	elif z <= 2.15e-294:
		tmp = x
	elif z <= 7.6e-79:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-10)
		tmp = Float64(y + x);
	elseif (z <= 2.15e-294)
		tmp = x;
	elseif (z <= 7.6e-79)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-10)
		tmp = y + x;
	elseif (z <= 2.15e-294)
		tmp = x;
	elseif (z <= 7.6e-79)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-10], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.15e-294], x, If[LessEqual[z, 7.6e-79], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999996e-10 or 7.6000000000000002e-79 < z

   1. Initial program 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 74.9%

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

      1. +-commutative 74.9%

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

   7. Simplified 74.9%

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

   if -5.4999999999999996e-10 < z < 2.1500000000000001e-294

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-/l* 96.4%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 56.6%

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

   if 2.1500000000000001e-294 < z < 7.6000000000000002e-79

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-/l* 96.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 92.3%

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

      1. mul-1-neg 92.3%

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

      2. unsub-neg 92.3%

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

      3. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

      1. clear-num 89.3%

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

      2. un-div-inv 92.5%

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

   9. Applied egg-rr 92.5%

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

   10. Taylor expanded in x around 0 60.3%

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

       1. mul-1-neg 60.3%

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

       2. associate-/l* 60.4%

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

       3. distribute-rgt-neg-in 60.4%

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

       4. distribute-neg-frac2 60.4%

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

   12. Simplified 60.4%

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

   13. Taylor expanded in z around 0 59.6%

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

Alternative 5: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00385 \lor \neg \left(t \leq 96000000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.00385) (not (<= t 96000000000000.0)))
   (+ x (* t (/ y (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.00385) || !(t <= 96000000000000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (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 <= (-0.00385d0)) .or. (.not. (t <= 96000000000000.0d0))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * (z / (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 <= -0.00385) || !(t <= 96000000000000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.00385) or not (t <= 96000000000000.0):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.00385) || !(t <= 96000000000000.0))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.00385) || ~((t <= 96000000000000.0)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.00385], N[Not[LessEqual[t, 96000000000000.0]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0038500000000000001 or 9.6e13 < t

   1. Initial program 81.8%

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

      1. +-commutative 81.8%

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

      2. associate-/l* 97.6%

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

      3. fma-define 97.6%

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

   3. Simplified 97.6%

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

      1. fma-undefine 97.6%

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

      2. associate-/l* 81.8%

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

      3. div-inv 81.7%

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

      4. *-commutative 81.7%

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

      5. associate-*r* 99.0%

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

      6. div-inv 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in z around 0 90.5%

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

      1. neg-mul-1 90.5%

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

   9. Simplified 90.5%

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

   10. Taylor expanded in t around 0 80.9%

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

       1. mul-1-neg 80.9%

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

       2. associate-*r/ 90.5%

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

       3. sub-neg 90.5%

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

   12. Simplified 90.5%

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

   if -0.0038500000000000001 < t < 9.6e13

   1. Initial program 83.4%

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

   3. Taylor expanded in t around 0 75.2%

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

      1. associate-/l* 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00385 \lor \neg \left(t \leq 96000000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-104} \lor \neg \left(z \leq 9.5 \cdot 10^{+42}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e-104) (not (<= z 9.5e+42)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-104) || !(z <= 9.5e+42)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / 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 <= (-4.5d-104)) .or. (.not. (z <= 9.5d+42))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t * (y / 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 <= -4.5e-104) || !(z <= 9.5e+42)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e-104) or not (z <= 9.5e+42):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e-104) || !(z <= 9.5e+42))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e-104) || ~((z <= 9.5e+42)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e-104], N[Not[LessEqual[z, 9.5e+42]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999997e-104 or 9.50000000000000019e42 < z

   1. Initial program 76.8%

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

   3. Taylor expanded in a around 0 66.9%

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

      1. associate-/l* 85.4%

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

      2. div-sub 85.4%

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

      3. *-inverses 85.4%

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

   5. Simplified 85.4%

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

   if -4.4999999999999997e-104 < z < 9.50000000000000019e42

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-/l* 96.7%

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

      3. fma-define 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. associate-/l* 81.4%

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

   7. Simplified 81.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-104} \lor \neg \left(z \leq 9.5 \cdot 10^{+42}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+189}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+189)
   (* t (/ y (- a z)))
   (if (<= t 9.5e+27) (+ x (* y (/ z (- z a)))) (+ x (* (- z t) (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+189) {
		tmp = t * (y / (a - z));
	} else if (t <= 9.5e+27) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((z - t) * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.3d+189)) then
        tmp = t * (y / (a - z))
    else if (t <= 9.5d+27) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + ((z - t) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+189) {
		tmp = t * (y / (a - z));
	} else if (t <= 9.5e+27) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((z - t) * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+189:
		tmp = t * (y / (a - z))
	elif t <= 9.5e+27:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((z - t) * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+189)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (t <= 9.5e+27)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e+189)
		tmp = t * (y / (a - z));
	elseif (t <= 9.5e+27)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((z - t) * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+189], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+27], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3000000000000002e189

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-/l* 95.7%

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

      3. fma-define 95.7%

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

   3. Simplified 95.7%

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

      1. fma-undefine 95.7%

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

      2. associate-/l* 75.2%

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

      3. div-inv 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-*r* 95.6%

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

      6. div-inv 95.7%

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

   6. Applied egg-rr 95.7%

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

   7. Taylor expanded in z around 0 91.4%

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

      1. neg-mul-1 91.4%

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

   9. Simplified 91.4%

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

   10. Taylor expanded in t around 0 75.0%

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

       1. mul-1-neg 75.0%

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

       2. associate-*r/ 91.4%

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

       3. sub-neg 91.4%

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

   12. Simplified 91.4%

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

   13. Taylor expanded in x around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-/l* 74.4%

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

       3. distribute-rgt-neg-in 74.4%

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

       4. distribute-frac-neg 74.4%

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

   15. Simplified 74.4%

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

   if -3.3000000000000002e189 < t < 9.4999999999999997e27

   1. Initial program 83.1%

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

   3. Taylor expanded in t around 0 72.6%

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

      1. associate-/l* 88.8%

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

   5. Simplified 88.8%

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

   if 9.4999999999999997e27 < t

   1. Initial program 84.0%

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

      1. +-commutative 84.0%

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

      2. associate-/l* 97.0%

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

      3. fma-define 97.0%

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

   3. Simplified 97.0%

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

      1. fma-undefine 97.0%

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

      2. associate-/l* 84.0%

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

      3. div-inv 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-*r* 99.6%

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

      6. div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 75.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+189}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -215000000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -215000000000.0)
   (+ x (* y (/ z (- z a))))
   (if (<= a 3.5e+53) (+ x (* y (- 1.0 (/ t z)))) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -215000000000.0) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 3.5e+53) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-215000000000.0d0)) then
        tmp = x + (y * (z / (z - a)))
    else if (a <= 3.5d+53) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -215000000000.0) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= 3.5e+53) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -215000000000.0:
		tmp = x + (y * (z / (z - a)))
	elif a <= 3.5e+53:
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -215000000000.0)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (a <= 3.5e+53)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -215000000000.0)
		tmp = x + (y * (z / (z - a)));
	elseif (a <= 3.5e+53)
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -215000000000.0], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+53], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.15e11

   1. Initial program 77.2%

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

   3. Taylor expanded in t around 0 66.7%

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

      1. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

   if -2.15e11 < a < 3.50000000000000019e53

   1. Initial program 84.0%

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

   3. Taylor expanded in a around 0 70.4%

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

      1. associate-/l* 85.5%

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

      2. div-sub 85.5%

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

      3. *-inverses 85.5%

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

   5. Simplified 85.5%

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

   if 3.50000000000000019e53 < a

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

      1. clear-num 82.8%

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

      2. un-div-inv 82.8%

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

   9. Applied egg-rr 82.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -215000000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -70000000000 \lor \neg \left(z \leq 3.1 \cdot 10^{+141}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -70000000000.0) (not (<= z 3.1e+141)))
   (+ y x)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -70000000000.0) || !(z <= 3.1e+141)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / 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 <= (-70000000000.0d0)) .or. (.not. (z <= 3.1d+141))) then
        tmp = y + x
    else
        tmp = x + (t * (y / 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 <= -70000000000.0) || !(z <= 3.1e+141)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -70000000000.0) or not (z <= 3.1e+141):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -70000000000.0) || !(z <= 3.1e+141))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -70000000000.0) || ~((z <= 3.1e+141)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -70000000000.0], N[Not[LessEqual[z, 3.1e+141]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e10 or 3.10000000000000004e141 < z

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. +-commutative 84.6%

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

   7. Simplified 84.6%

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

   if -7e10 < z < 3.10000000000000004e141

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70000000000 \lor \neg \left(z \leq 3.1 \cdot 10^{+141}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-10} \lor \neg \left(z \leq 1.15 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.1e-10) (not (<= z 1.15e-17))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.1e-10) || !(z <= 1.15e-17)) {
		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 <= (-4.1d-10)) .or. (.not. (z <= 1.15d-17))) 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 <= -4.1e-10) || !(z <= 1.15e-17)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.1e-10) or not (z <= 1.15e-17):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.1e-10) || !(z <= 1.15e-17))
		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 <= -4.1e-10) || ~((z <= 1.15e-17)))
		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, -4.1e-10], N[Not[LessEqual[z, 1.15e-17]], $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 < -4.0999999999999998e-10 or 1.15000000000000004e-17 < z

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -4.0999999999999998e-10 < z < 1.15000000000000004e-17

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 72.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-10} \lor \neg \left(z \leq 1.15 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+230}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e+226) x (if (<= a 3.4e+230) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+226) {
		tmp = x;
	} else if (a <= 3.4e+230) {
		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 <= (-1.8d+226)) then
        tmp = x
    else if (a <= 3.4d+230) 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 <= -1.8e+226) {
		tmp = x;
	} else if (a <= 3.4e+230) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e+226:
		tmp = x
	elif a <= 3.4e+230:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e+226)
		tmp = x;
	elseif (a <= 3.4e+230)
		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 <= -1.8e+226)
		tmp = x;
	elseif (a <= 3.4e+230)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e+226], x, If[LessEqual[a, 3.4e+230], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7999999999999999e226 or 3.39999999999999986e230 < a

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 79.1%

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

   if -1.7999999999999999e226 < a < 3.39999999999999986e230

   1. Initial program 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 98.6%

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

      3. fma-define 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around inf 65.4%

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

      1. +-commutative 65.4%

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

   7. Simplified 65.4%

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

Alternative 12: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-38}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.2e-128) x (if (<= x 8.8e-38) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.2e-128) {
		tmp = x;
	} else if (x <= 8.8e-38) {
		tmp = 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 (x <= (-1.2d-128)) then
        tmp = x
    else if (x <= 8.8d-38) then
        tmp = 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 (x <= -1.2e-128) {
		tmp = x;
	} else if (x <= 8.8e-38) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.2e-128:
		tmp = x
	elif x <= 8.8e-38:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.2e-128)
		tmp = x;
	elseif (x <= 8.8e-38)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.2e-128)
		tmp = x;
	elseif (x <= 8.8e-38)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.2e-128], x, If[LessEqual[x, 8.8e-38], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1999999999999999e-128 or 8.80000000000000029e-38 < x

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 71.4%

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

   if -1.1999999999999999e-128 < x < 8.80000000000000029e-38

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-/l* 96.7%

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

      3. fma-define 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 46.3%

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

      1. +-commutative 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in y around inf 35.4%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

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

   1. +-commutative 82.6%

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

   2. associate-/l* 98.8%

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

   3. fma-define 98.8%

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

3. Simplified 98.8%

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

   1. fma-undefine 98.8%

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

   2. associate-/l* 82.6%

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

   3. div-inv 82.6%

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

   4. *-commutative 82.6%

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

   5. associate-*r* 97.5%

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

   6. div-inv 97.5%

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

6. Applied egg-rr 97.5%

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

7. Final simplification 97.5%

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

Alternative 14: 51.2% 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 82.6%

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

   1. +-commutative 82.6%

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

   2. associate-/l* 98.8%

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

   3. fma-define 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in y around 0 52.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 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 2024139 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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