Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.9% → 89.1%

Time: 16.2s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+76} \lor \neg \left(z \leq 1.7 \cdot 10^{+26}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e+76) (not (<= z 1.7e+26)))
   (+
    (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
    (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+76) || !(z <= 1.7e+26)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e+76) || !(z <= 1.7e+26))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e+76], N[Not[LessEqual[z, 1.7e+26]], $MachinePrecision]], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e76 or 1.7000000000000001e26 < z

   1. Initial program 38.1%

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

      1. fma-define 38.2%

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

      2. +-commutative 38.2%

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

      3. fma-define 38.2%

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

   3. Simplified 38.2%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. associate--r+ 75.2%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 75.2%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 75.2%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. *-commutative 75.2%

         \[\leadsto \left(\frac{\color{blue}{y \cdot x}}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. times-frac 78.4%

         \[\leadsto \left(\color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. div-sub 78.4%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      7. associate-/l* 94.4%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   if -3.5e76 < z < 1.7000000000000001e26

   1. Initial program 91.2%

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

      1. fma-define 91.2%

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

      2. +-commutative 91.2%

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

      3. fma-define 91.2%

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

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+76} \lor \neg \left(z \leq 1.7 \cdot 10^{+26}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+76} \lor \neg \left(z \leq 4.3 \cdot 10^{+21}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e+76) (not (<= z 4.3e+21)))
   (+
    (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
    (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+76) || !(z <= 4.3e+21)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.5d+76)) .or. (.not. (z <= 4.3d+21))) then
        tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+76) || !(z <= 4.3e+21)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e+76) or not (z <= 4.3e+21):
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e+76) || !(z <= 4.3e+21))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.5e+76) || ~((z <= 4.3e+21)))
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e+76], N[Not[LessEqual[z, 4.3e+21]], $MachinePrecision]], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e76 or 4.3e21 < z

   1. Initial program 38.1%

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

      1. fma-define 38.2%

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

      2. +-commutative 38.2%

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

      3. fma-define 38.2%

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

   3. Simplified 38.2%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. associate--r+ 75.2%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 75.2%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 75.2%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. *-commutative 75.2%

         \[\leadsto \left(\frac{\color{blue}{y \cdot x}}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. times-frac 78.4%

         \[\leadsto \left(\color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. div-sub 78.4%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      7. associate-/l* 94.4%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   if -3.5e76 < z < 4.3e21

   1. Initial program 91.2%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+76} \lor \neg \left(z \leq 4.3 \cdot 10^{+21}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-90}:\\ \;\;\;\;\frac{x + t \cdot \frac{z}{y}}{\left(-z\right) - -1}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z (- b y))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -4e+30)
     t_2
     (if (<= z -1.45e-149)
       t_1
       (if (<= z 1.85e-90)
         (/ (+ x (* t (/ z y))) (- (- z) -1.0))
         (if (<= z 1.15e-5) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e+30) {
		tmp = t_2;
	} else if (z <= -1.45e-149) {
		tmp = t_1;
	} else if (z <= 1.85e-90) {
		tmp = (x + (t * (z / y))) / (-z - -1.0);
	} else if (z <= 1.15e-5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-4d+30)) then
        tmp = t_2
    else if (z <= (-1.45d-149)) then
        tmp = t_1
    else if (z <= 1.85d-90) then
        tmp = (x + (t * (z / y))) / (-z - (-1.0d0))
    else if (z <= 1.15d-5) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e+30) {
		tmp = t_2;
	} else if (z <= -1.45e-149) {
		tmp = t_1;
	} else if (z <= 1.85e-90) {
		tmp = (x + (t * (z / y))) / (-z - -1.0);
	} else if (z <= 1.15e-5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4e+30:
		tmp = t_2
	elif z <= -1.45e-149:
		tmp = t_1
	elif z <= 1.85e-90:
		tmp = (x + (t * (z / y))) / (-z - -1.0)
	elif z <= 1.15e-5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4e+30)
		tmp = t_2;
	elseif (z <= -1.45e-149)
		tmp = t_1;
	elseif (z <= 1.85e-90)
		tmp = Float64(Float64(x + Float64(t * Float64(z / y))) / Float64(Float64(-z) - -1.0));
	elseif (z <= 1.15e-5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4e+30)
		tmp = t_2;
	elseif (z <= -1.45e-149)
		tmp = t_1;
	elseif (z <= 1.85e-90)
		tmp = (x + (t * (z / y))) / (-z - -1.0);
	elseif (z <= 1.15e-5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+30], t$95$2, If[LessEqual[z, -1.45e-149], t$95$1, If[LessEqual[z, 1.85e-90], N[(N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[((-z) - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-5], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000001e30 or 1.15e-5 < z

   1. Initial program 44.6%

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

      1. fma-define 44.6%

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

      2. +-commutative 44.6%

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

      3. fma-define 44.6%

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

   3. Simplified 44.6%

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

   5. Taylor expanded in z around inf 85.3%

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

   if -4.0000000000000001e30 < z < -1.45e-149 or 1.85000000000000009e-90 < z < 1.15e-5

   1. Initial program 93.0%

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

      1. fma-define 93.0%

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

      2. +-commutative 93.0%

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

      3. fma-define 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in x around 0 71.9%

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

   if -1.45e-149 < z < 1.85000000000000009e-90

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around inf 89.5%

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

      1. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in y around -inf 57.8%

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

      1. associate-*r* 57.8%

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

      2. neg-mul-1 57.8%

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

      3. sub-neg 57.8%

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

      4. metadata-eval 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in a around 0 69.7%

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

       1. mul-1-neg 69.7%

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

       2. associate-/l* 69.9%

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

       3. sub-neg 69.9%

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

       4. metadata-eval 69.9%

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

       5. +-commutative 69.9%

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

   13. Simplified 69.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+30}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-149}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-90}:\\ \;\;\;\;\frac{x + t \cdot \frac{z}{y}}{\left(-z\right) - -1}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 9000:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4e+30)
     t_1
     (if (<= z -1.5e-149)
       (/ (* z (- t a)) (+ y (* z (- b y))))
       (if (<= z 9000.0)
         (/ (* y (+ x (* z (/ (- t a) y)))) (+ y (* z b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e+30) {
		tmp = t_1;
	} else if (z <= -1.5e-149) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 9000.0) {
		tmp = (y * (x + (z * ((t - a) / y)))) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-4d+30)) then
        tmp = t_1
    else if (z <= (-1.5d-149)) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= 9000.0d0) then
        tmp = (y * (x + (z * ((t - a) / y)))) / (y + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e+30) {
		tmp = t_1;
	} else if (z <= -1.5e-149) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 9000.0) {
		tmp = (y * (x + (z * ((t - a) / y)))) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -4e+30:
		tmp = t_1
	elif z <= -1.5e-149:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= 9000.0:
		tmp = (y * (x + (z * ((t - a) / y)))) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4e+30)
		tmp = t_1;
	elseif (z <= -1.5e-149)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 9000.0)
		tmp = Float64(Float64(y * Float64(x + Float64(z * Float64(Float64(t - a) / y)))) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4e+30)
		tmp = t_1;
	elseif (z <= -1.5e-149)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= 9000.0)
		tmp = (y * (x + (z * ((t - a) / y)))) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+30], t$95$1, If[LessEqual[z, -1.5e-149], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9000.0], N[(N[(y * N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000001e30 or 9e3 < z

   1. Initial program 44.4%

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

      1. fma-define 44.5%

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

      2. +-commutative 44.5%

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

      3. fma-define 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in z around inf 86.6%

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

   if -4.0000000000000001e30 < z < -1.5000000000000001e-149

   1. Initial program 91.5%

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

      1. fma-define 91.5%

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

      2. +-commutative 91.5%

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

      3. fma-define 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in x around 0 74.8%

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

   if -1.5000000000000001e-149 < z < 9e3

   1. Initial program 90.0%

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

      1. fma-define 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in y around inf 89.0%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in b around inf 77.5%

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

Alternative 5: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-146}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq 126000000:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1e+31)
     t_2
     (if (<= z -3.8e-146)
       (/ (* z (- t a)) t_1)
       (if (<= z 126000000.0) (/ (+ (* y x) (* z t)) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1e+31) {
		tmp = t_2;
	} else if (z <= -3.8e-146) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 126000000.0) {
		tmp = ((y * x) + (z * t)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-1d+31)) then
        tmp = t_2
    else if (z <= (-3.8d-146)) then
        tmp = (z * (t - a)) / t_1
    else if (z <= 126000000.0d0) then
        tmp = ((y * x) + (z * t)) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1e+31) {
		tmp = t_2;
	} else if (z <= -3.8e-146) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 126000000.0) {
		tmp = ((y * x) + (z * t)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1e+31:
		tmp = t_2
	elif z <= -3.8e-146:
		tmp = (z * (t - a)) / t_1
	elif z <= 126000000.0:
		tmp = ((y * x) + (z * t)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1e+31)
		tmp = t_2;
	elseif (z <= -3.8e-146)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= 126000000.0)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1e+31)
		tmp = t_2;
	elseif (z <= -3.8e-146)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= 126000000.0)
		tmp = ((y * x) + (z * t)) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+31], t$95$2, If[LessEqual[z, -3.8e-146], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 126000000.0], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999996e30 or 1.26e8 < z

   1. Initial program 44.4%

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

      1. fma-define 44.5%

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

      2. +-commutative 44.5%

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

      3. fma-define 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in z around inf 86.6%

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

   if -9.9999999999999996e30 < z < -3.79999999999999994e-146

   1. Initial program 91.3%

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

      1. fma-define 91.3%

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

      2. +-commutative 91.3%

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

      3. fma-define 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around 0 74.2%

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

   if -3.79999999999999994e-146 < z < 1.26e8

   1. Initial program 90.1%

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

   3. Taylor expanded in t around inf 73.5%

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

      1. *-commutative 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-146}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 126000000:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+77} \lor \neg \left(z \leq 1.45 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e+77) (not (<= z 1.45e+64)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e+77) || !(z <= 1.45e+64)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.2d+77)) .or. (.not. (z <= 1.45d+64))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e+77) || !(z <= 1.45e+64)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e+77) or not (z <= 1.45e+64):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e+77) || !(z <= 1.45e+64))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.2e+77) || ~((z <= 1.45e+64)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e+77], N[Not[LessEqual[z, 1.45e+64]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e77 or 1.44999999999999997e64 < z

   1. Initial program 35.5%

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

      1. fma-define 35.6%

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

      2. +-commutative 35.6%

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

      3. fma-define 35.6%

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

   3. Simplified 35.6%

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

   5. Taylor expanded in z around inf 90.9%

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

   if -3.2000000000000002e77 < z < 1.44999999999999997e64

   1. Initial program 88.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+77} \lor \neg \left(z \leq 1.45 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.64:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.64)
     t_1
     (if (<= z -1.5e-149)
       (/ (* z (- t a)) (+ y (* z b)))
       (if (<= z 1.3e-5) (+ x (* z (+ x (/ (- t a) y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.64) {
		tmp = t_1;
	} else if (z <= -1.5e-149) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else if (z <= 1.3e-5) {
		tmp = x + (z * (x + ((t - a) / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.64d0)) then
        tmp = t_1
    else if (z <= (-1.5d-149)) then
        tmp = (z * (t - a)) / (y + (z * b))
    else if (z <= 1.3d-5) then
        tmp = x + (z * (x + ((t - a) / y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.64) {
		tmp = t_1;
	} else if (z <= -1.5e-149) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else if (z <= 1.3e-5) {
		tmp = x + (z * (x + ((t - a) / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.64:
		tmp = t_1
	elif z <= -1.5e-149:
		tmp = (z * (t - a)) / (y + (z * b))
	elif z <= 1.3e-5:
		tmp = x + (z * (x + ((t - a) / y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.64)
		tmp = t_1;
	elseif (z <= -1.5e-149)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	elseif (z <= 1.3e-5)
		tmp = Float64(x + Float64(z * Float64(x + Float64(Float64(t - a) / y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.64)
		tmp = t_1;
	elseif (z <= -1.5e-149)
		tmp = (z * (t - a)) / (y + (z * b));
	elseif (z <= 1.3e-5)
		tmp = x + (z * (x + ((t - a) / y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.64], t$95$1, If[LessEqual[z, -1.5e-149], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-5], N[(x + N[(z * N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.640000000000000013 or 1.29999999999999992e-5 < z

   1. Initial program 46.1%

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

      1. fma-define 46.2%

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

      2. +-commutative 46.2%

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

      3. fma-define 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -0.640000000000000013 < z < -1.5000000000000001e-149

   1. Initial program 90.8%

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

      1. fma-define 90.8%

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

      2. +-commutative 90.8%

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

      3. fma-define 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around 0 75.3%

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

   6. Taylor expanded in b around inf 72.2%

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

   if -1.5000000000000001e-149 < z < 1.29999999999999992e-5

   1. Initial program 89.9%

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

      1. fma-define 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 88.9%

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

      1. associate-/l* 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around -inf 54.8%

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

      1. associate-*r* 54.8%

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

      2. neg-mul-1 54.8%

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

      3. sub-neg 54.8%

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

      4. metadata-eval 54.8%

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

   10. Simplified 54.8%

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

   11. Taylor expanded in z around 0 63.7%

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

       1. mul-1-neg 63.7%

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

       2. distribute-rgt-neg-in 63.7%

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

       3. div-sub 63.9%

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

       4. sub-neg 63.9%

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

       5. distribute-neg-in 63.9%

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

       6. mul-1-neg 63.9%

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

       7. remove-double-neg 63.9%

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

       8. remove-double-neg 63.9%

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

   13. Simplified 63.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.64:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44} \lor \neg \left(z \leq 2.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e-44) (not (<= z 2.3e-5)))
   (/ (- t a) (- b y))
   (+ x (* z (+ x (/ (- t a) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e-44) || !(z <= 2.3e-5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x + ((t - a) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.9d-44)) .or. (.not. (z <= 2.3d-5))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (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 b) {
	double tmp;
	if ((z <= -2.9e-44) || !(z <= 2.3e-5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x + ((t - a) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.9e-44) or not (z <= 2.3e-5):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (x + ((t - a) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e-44) || !(z <= 2.3e-5))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(x + Float64(Float64(t - a) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.9e-44) || ~((z <= 2.3e-5)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (x + ((t - a) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e-44], N[Not[LessEqual[z, 2.3e-5]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e-44 or 2.3e-5 < z

   1. Initial program 49.9%

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

      1. fma-define 50.0%

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

      2. +-commutative 50.0%

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

      3. fma-define 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in z around inf 84.2%

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

   if -2.9000000000000001e-44 < z < 2.3e-5

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around inf 87.7%

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

      1. associate-/l* 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in y around -inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. sub-neg 51.8%

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

      4. metadata-eval 51.8%

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

   10. Simplified 51.8%

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

   11. Taylor expanded in z around 0 61.4%

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

       1. mul-1-neg 61.4%

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

       2. distribute-rgt-neg-in 61.4%

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

       3. div-sub 61.5%

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

       4. sub-neg 61.5%

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

       5. distribute-neg-in 61.5%

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

       6. mul-1-neg 61.5%

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

       7. remove-double-neg 61.5%

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

       8. remove-double-neg 61.5%

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

   13. Simplified 61.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44} \lor \neg \left(z \leq 2.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t - a}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.45 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+62}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.45e+55)
     t_1
     (if (<= y -3.4e-85) (/ t (- b y)) (if (<= y 7e+62) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.45e+55) {
		tmp = t_1;
	} else if (y <= -3.4e-85) {
		tmp = t / (b - y);
	} else if (y <= 7e+62) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.45d+55)) then
        tmp = t_1
    else if (y <= (-3.4d-85)) then
        tmp = t / (b - y)
    else if (y <= 7d+62) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.45e+55) {
		tmp = t_1;
	} else if (y <= -3.4e-85) {
		tmp = t / (b - y);
	} else if (y <= 7e+62) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.45e+55:
		tmp = t_1
	elif y <= -3.4e-85:
		tmp = t / (b - y)
	elif y <= 7e+62:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.45e+55)
		tmp = t_1;
	elseif (y <= -3.4e-85)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 7e+62)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.45e+55)
		tmp = t_1;
	elseif (y <= -3.4e-85)
		tmp = t / (b - y);
	elseif (y <= 7e+62)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.45e+55], t$95$1, If[LessEqual[y, -3.4e-85], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+62], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4500000000000002e55 or 6.99999999999999967e62 < y

   1. Initial program 54.8%

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

      1. fma-define 54.8%

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

      2. +-commutative 54.8%

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

      3. fma-define 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in y around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 61.0%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -3.4500000000000002e55 < y < -3.4e-85

   1. Initial program 69.5%

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

      1. fma-define 69.5%

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

      2. +-commutative 69.5%

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

      3. fma-define 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around inf 69.9%

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

   6. Taylor expanded in t around inf 47.3%

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

   if -3.4e-85 < y < 6.99999999999999967e62

   1. Initial program 76.6%

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

      1. fma-define 76.6%

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

      2. +-commutative 76.6%

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

      3. fma-define 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in y around 0 62.8%

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

Alternative 10: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-149} \lor \neg \left(z \leq 2.4 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.5e-149) (not (<= z 2.4e-87))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e-149) || !(z <= 2.4e-87)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.5d-149)) .or. (.not. (z <= 2.4d-87))) then
        tmp = (t - a) / (b - 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 b) {
	double tmp;
	if ((z <= -1.5e-149) || !(z <= 2.4e-87)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.5e-149) or not (z <= 2.4e-87):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.5e-149) || !(z <= 2.4e-87))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.5e-149) || ~((z <= 2.4e-87)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.5e-149], N[Not[LessEqual[z, 2.4e-87]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.5000000000000001e-149 or 2.4e-87 < z

   1. Initial program 59.5%

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

      1. fma-define 59.5%

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

      2. +-commutative 59.5%

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

      3. fma-define 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in z around inf 73.4%

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

   if -1.5000000000000001e-149 < z < 2.4e-87

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

      2. +-commutative 89.4%

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

      3. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 58.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-149} \lor \neg \left(z \leq 2.4 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+55} \lor \neg \left(y \leq 3.7 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.05e+55) (not (<= y 3.7e-35))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e+55) || !(y <= 3.7e-35)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.05d+55)) .or. (.not. (y <= 3.7d-35))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e+55) || !(y <= 3.7e-35)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.05e+55) or not (y <= 3.7e-35):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.05e+55) || !(y <= 3.7e-35))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.05e+55) || ~((y <= 3.7e-35)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.05e+55], N[Not[LessEqual[y, 3.7e-35]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.04999999999999991e55 or 3.6999999999999999e-35 < y

   1. Initial program 56.1%

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

      1. fma-define 56.2%

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

      2. +-commutative 56.2%

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

      3. fma-define 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -2.04999999999999991e55 < y < 3.6999999999999999e-35

   1. Initial program 77.1%

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

      1. fma-define 77.1%

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

      2. +-commutative 77.1%

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

      3. fma-define 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 70.2%

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

   6. Taylor expanded in t around inf 41.3%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+55} \lor \neg \left(y \leq 3.7 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-44} \lor \neg \left(z \leq 3.7 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.5e-44) (not (<= z 3.7e-44))) (/ t (- b y)) (+ x (* z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-44) || !(z <= 3.7e-44)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.5d-44)) .or. (.not. (z <= 3.7d-44))) then
        tmp = t / (b - y)
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-44) || !(z <= 3.7e-44)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.5e-44) or not (z <= 3.7e-44):
		tmp = t / (b - y)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.5e-44) || !(z <= 3.7e-44))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.5e-44) || ~((z <= 3.7e-44)))
		tmp = t / (b - y);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.5e-44], N[Not[LessEqual[z, 3.7e-44]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000008e-44 or 3.7e-44 < z

   1. Initial program 52.6%

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

      1. fma-define 52.6%

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

      2. +-commutative 52.6%

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

      3. fma-define 52.7%

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

   3. Simplified 52.7%

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

   5. Taylor expanded in z around inf 80.7%

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

   6. Taylor expanded in t around inf 42.7%

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

   if -7.50000000000000008e-44 < z < 3.7e-44

   1. Initial program 89.3%

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

      1. fma-define 89.3%

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

      2. +-commutative 89.3%

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

      3. fma-define 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in y around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 49.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   8. Taylor expanded in z around 0 49.3%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-44} \lor \neg \left(z \leq 3.7 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -23000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -23000.0) (not (<= z 1.0))) (/ x (- z)) (+ x (* z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -23000.0) || !(z <= 1.0)) {
		tmp = x / -z;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-23000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x / -z
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -23000.0) || !(z <= 1.0)) {
		tmp = x / -z;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -23000.0) or not (z <= 1.0):
		tmp = x / -z
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -23000.0) || !(z <= 1.0))
		tmp = Float64(x / Float64(-z));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -23000.0) || ~((z <= 1.0)))
		tmp = x / -z;
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -23000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x / (-z)), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -23000 or 1 < z

   1. Initial program 45.7%

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

      1. fma-define 45.8%

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

      2. +-commutative 45.8%

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

      3. fma-define 45.8%

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

   3. Simplified 45.8%

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

   5. Taylor expanded in y around inf 16.2%

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

      1. mul-1-neg 16.2%

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

      2. unsub-neg 16.2%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 16.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   8. Taylor expanded in z around inf 16.1%

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

      1. associate-*r/ 16.1%

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

      2. mul-1-neg 16.1%

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

   10. Simplified 16.1%

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

   if -23000 < z < 1

   1. Initial program 90.2%

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

      1. fma-define 90.2%

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

      2. +-commutative 90.2%

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

      3. fma-define 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around inf 43.1%

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

      1. mul-1-neg 43.1%

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

      2. unsub-neg 43.1%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   8. Taylor expanded in z around 0 42.8%

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

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-46} \lor \neg \left(z \leq 510000000000\right):\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.8e-46) (not (<= z 510000000000.0))) (/ x (- z)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.8e-46) || !(z <= 510000000000.0)) {
		tmp = x / -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.8d-46)) .or. (.not. (z <= 510000000000.0d0))) then
        tmp = x / -z
    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 b) {
	double tmp;
	if ((z <= -9.8e-46) || !(z <= 510000000000.0)) {
		tmp = x / -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.8e-46) or not (z <= 510000000000.0):
		tmp = x / -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.8e-46) || !(z <= 510000000000.0))
		tmp = Float64(x / Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.8e-46) || ~((z <= 510000000000.0)))
		tmp = x / -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.8e-46], N[Not[LessEqual[z, 510000000000.0]], $MachinePrecision]], N[(x / (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000002e-46 or 5.1e11 < z

   1. Initial program 49.6%

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

      1. fma-define 49.6%

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

      2. +-commutative 49.6%

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

      3. fma-define 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in y around inf 15.2%

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

      1. mul-1-neg 15.2%

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

      2. unsub-neg 15.2%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 15.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   8. Taylor expanded in z around inf 15.1%

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

      1. associate-*r/ 15.1%

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

      2. mul-1-neg 15.1%

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

   10. Simplified 15.1%

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

   if -9.8000000000000002e-46 < z < 5.1e11

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

      2. +-commutative 89.4%

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

      3. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 46.1%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-46} \lor \neg \left(z \leq 510000000000\right):\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.1% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 67.8%

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

   1. fma-define 67.8%

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

   2. +-commutative 67.8%

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

   3. fma-define 67.8%

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

3. Simplified 67.8%

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

5. Taylor expanded in z around 0 22.9%

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

Developer Target 1: 73.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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