Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.1% → 99.0%

Time: 12.3s

Alternatives: 14

Speedup: 0.8×

• 31.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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)) + ((a * z) * b)
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)) + ((a * z) * b);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + ((a * z) * b)
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)) + ((a * z) * b);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+153} \lor \neg \left(z \leq 2 \cdot 10^{+51}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+153) (not (<= z 2e+51)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ (fma y z x) (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e+153) || !(z <= 2e+51)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+153) || !(z <= 2e+51))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+153], N[Not[LessEqual[z, 2e+51]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000001e153 or 2e51 < z

   1. Initial program 79.3%

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

      1. associate-+l+ 79.3%

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

      2. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in z around inf 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+l+ 96.4%

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

      3. +-commutative 96.4%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-out 100.0%

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

   7. Simplified 100.0%

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

   if -4.5000000000000001e153 < z < 2e51

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. +-commutative 97.1%

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

      3. fma-define 97.1%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-out 99.9%

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

      8. remove-double-neg 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-lft-neg-out 99.9%

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

      11. sub-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. distribute-lft-neg-out 99.9%

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

      14. *-commutative 99.9%

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

      15. remove-double-neg 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+153} \lor \neg \left(z \leq 2 \cdot 10^{+51}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 39.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-40}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-260}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 11200000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.4e-40)
   (* a t)
   (if (<= a 3.6e-260)
     (* z y)
     (if (<= a 11200000.0) x (if (<= a 1.15e+163) (* a (* z b)) (* a t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.4e-40) {
		tmp = a * t;
	} else if (a <= 3.6e-260) {
		tmp = z * y;
	} else if (a <= 11200000.0) {
		tmp = x;
	} else if (a <= 1.15e+163) {
		tmp = a * (z * b);
	} else {
		tmp = a * t;
	}
	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 (a <= (-5.4d-40)) then
        tmp = a * t
    else if (a <= 3.6d-260) then
        tmp = z * y
    else if (a <= 11200000.0d0) then
        tmp = x
    else if (a <= 1.15d+163) then
        tmp = a * (z * b)
    else
        tmp = a * t
    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 (a <= -5.4e-40) {
		tmp = a * t;
	} else if (a <= 3.6e-260) {
		tmp = z * y;
	} else if (a <= 11200000.0) {
		tmp = x;
	} else if (a <= 1.15e+163) {
		tmp = a * (z * b);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.4e-40:
		tmp = a * t
	elif a <= 3.6e-260:
		tmp = z * y
	elif a <= 11200000.0:
		tmp = x
	elif a <= 1.15e+163:
		tmp = a * (z * b)
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.4e-40)
		tmp = Float64(a * t);
	elseif (a <= 3.6e-260)
		tmp = Float64(z * y);
	elseif (a <= 11200000.0)
		tmp = x;
	elseif (a <= 1.15e+163)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.4e-40)
		tmp = a * t;
	elseif (a <= 3.6e-260)
		tmp = z * y;
	elseif (a <= 11200000.0)
		tmp = x;
	elseif (a <= 1.15e+163)
		tmp = a * (z * b);
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.4e-40], N[(a * t), $MachinePrecision], If[LessEqual[a, 3.6e-260], N[(z * y), $MachinePrecision], If[LessEqual[a, 11200000.0], x, If[LessEqual[a, 1.15e+163], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.4e-40 or 1.15000000000000001e163 < a

   1. Initial program 85.8%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around 0 55.1%

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

   6. Taylor expanded in x around 0 45.0%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -5.4e-40 < a < 3.6000000000000001e-260

   1. Initial program 97.2%

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

      1. associate-+l+ 97.2%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-*r* 83.2%

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

      3. distribute-rgt-in 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in y around inf 56.9%

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

      1. *-commutative 56.9%

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

   10. Simplified 56.9%

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

   if 3.6000000000000001e-260 < a < 1.12e7

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around 0 64.9%

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

   6. Taylor expanded in x around inf 56.7%

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

   if 1.12e7 < a < 1.15000000000000001e163

   1. Initial program 86.2%

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

      1. associate-+l+ 86.2%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. associate-*r* 63.7%

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

      3. distribute-rgt-in 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in a around inf 45.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   10. Simplified 45.1%

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

Alternative 3: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+53} \lor \neg \left(z \leq 1.75 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + a \cdot t\right) + \left(x + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+53) (not (<= z 1.75e+59)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ (+ (* a (* z b)) (* a t)) (+ x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+53) || !(z <= 1.75e+59)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = ((a * (z * b)) + (a * t)) + (x + (z * 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 <= (-4.2d+53)) .or. (.not. (z <= 1.75d+59))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = ((a * (z * b)) + (a * t)) + (x + (z * 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 <= -4.2e+53) || !(z <= 1.75e+59)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = ((a * (z * b)) + (a * t)) + (x + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+53) or not (z <= 1.75e+59):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = ((a * (z * b)) + (a * t)) + (x + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+53) || !(z <= 1.75e+59))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(Float64(Float64(a * Float64(z * b)) + Float64(a * t)) + Float64(x + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+53) || ~((z <= 1.75e+59)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = ((a * (z * b)) + (a * t)) + (x + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+53], N[Not[LessEqual[z, 1.75e+59]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000004e53 or 1.75e59 < z

   1. Initial program 78.3%

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

      1. associate-+l+ 78.3%

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

      2. associate-*l* 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-+l+ 95.9%

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

      3. +-commutative 95.9%

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

      4. associate-/l* 98.9%

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

      5. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   if -4.2000000000000004e53 < z < 1.75e59

   1. Initial program 99.4%

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

      1. associate-+l+ 99.4%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+53} \lor \neg \left(z \leq 1.75 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + a \cdot t\right) + \left(x + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+257}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+80} \lor \neg \left(z \leq 7.6 \cdot 10^{-114}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.95e+257)
   (* a (* z b))
   (if (or (<= z -6.8e+80) (not (<= z 7.6e-114)))
     (+ x (* z y))
     (+ x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.95e+257) {
		tmp = a * (z * b);
	} else if ((z <= -6.8e+80) || !(z <= 7.6e-114)) {
		tmp = x + (z * y);
	} else {
		tmp = x + (a * t);
	}
	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 <= (-1.95d+257)) then
        tmp = a * (z * b)
    else if ((z <= (-6.8d+80)) .or. (.not. (z <= 7.6d-114))) then
        tmp = x + (z * y)
    else
        tmp = x + (a * t)
    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 <= -1.95e+257) {
		tmp = a * (z * b);
	} else if ((z <= -6.8e+80) || !(z <= 7.6e-114)) {
		tmp = x + (z * y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.95e+257:
		tmp = a * (z * b)
	elif (z <= -6.8e+80) or not (z <= 7.6e-114):
		tmp = x + (z * y)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.95e+257)
		tmp = Float64(a * Float64(z * b));
	elseif ((z <= -6.8e+80) || !(z <= 7.6e-114))
		tmp = Float64(x + Float64(z * y));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.95e+257)
		tmp = a * (z * b);
	elseif ((z <= -6.8e+80) || ~((z <= 7.6e-114)))
		tmp = x + (z * y);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.95e+257], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.8e+80], N[Not[LessEqual[z, 7.6e-114]], $MachinePrecision]], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000003e257

   1. Initial program 83.2%

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

      1. associate-+l+ 83.2%

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

      2. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in t around 0 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*r* 91.7%

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

      3. distribute-rgt-in 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around inf 83.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 83.7%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   10. Simplified 83.7%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -1.95000000000000003e257 < z < -6.79999999999999984e80 or 7.5999999999999997e-114 < z

   1. Initial program 84.9%

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

      1. associate-+l+ 84.9%

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

      2. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in b around 0 74.4%

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

   6. Taylor expanded in a around 0 62.3%

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

      1. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if -6.79999999999999984e80 < z < 7.5999999999999997e-114

   1. Initial program 97.7%

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

      1. associate-+l+ 97.7%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 77.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+257}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+80} \lor \neg \left(z \leq 7.6 \cdot 10^{-114}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+81} \lor \neg \left(z \leq 1.16 \cdot 10^{-108}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e+81) (not (<= z 1.16e-108)))
   (+ x (* z (+ y (* a b))))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e+81) || !(z <= 1.16e-108)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	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 <= (-3d+81)) .or. (.not. (z <= 1.16d-108))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = x + (a * (t + (z * b)))
    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 <= -3e+81) || !(z <= 1.16e-108)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e+81) or not (z <= 1.16e-108):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e+81) || !(z <= 1.16e-108))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e+81) || ~((z <= 1.16e-108)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e+81], N[Not[LessEqual[z, 1.16e-108]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999997e81 or 1.16e-108 < z

   1. Initial program 84.7%

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

      1. associate-+l+ 84.7%

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

      2. associate-*l* 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-*r* 84.1%

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

      3. distribute-rgt-in 90.3%

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

   7. Simplified 90.3%

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

   if -2.99999999999999997e81 < z < 1.16e-108

   1. Initial program 97.7%

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

      1. associate-+l+ 97.7%

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

      2. +-commutative 97.7%

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

      3. fma-define 97.7%

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

      4. associate-*l* 98.4%

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

      5. *-commutative 98.4%

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

      6. *-commutative 98.4%

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

      7. distribute-rgt-out 100.0%

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

      8. remove-double-neg 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-lft-neg-out 100.0%

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

      14. *-commutative 100.0%

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

      15. remove-double-neg 100.0%

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

      16. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 89.2%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+81} \lor \neg \left(z \leq 1.16 \cdot 10^{-108}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-35} \lor \neg \left(a \leq 1.16 \cdot 10^{-95}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3e-35) (not (<= a 1.16e-95)))
   (+ x (* a (+ t (* z b))))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3e-35) || !(a <= 1.16e-95)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (z * 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 ((a <= (-3d-35)) .or. (.not. (a <= 1.16d-95))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + (z * 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 ((a <= -3e-35) || !(a <= 1.16e-95)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3e-35) or not (a <= 1.16e-95):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3e-35) || !(a <= 1.16e-95))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3e-35) || ~((a <= 1.16e-95)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3e-35], N[Not[LessEqual[a, 1.16e-95]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.99999999999999989e-35 or 1.15999999999999997e-95 < a

   1. Initial program 87.2%

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

      1. associate-+l+ 87.2%

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

      2. +-commutative 87.2%

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

      3. fma-define 87.2%

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

      4. associate-*l* 92.8%

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

      5. *-commutative 92.8%

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

      6. *-commutative 92.8%

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

      7. distribute-rgt-out 96.0%

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

      8. remove-double-neg 96.0%

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

      9. *-commutative 96.0%

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

      10. distribute-lft-neg-out 96.0%

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

      11. sub-neg 96.0%

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

      12. sub-neg 96.0%

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

      13. distribute-lft-neg-out 96.0%

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

      14. *-commutative 96.0%

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

      15. remove-double-neg 96.0%

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

      16. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 85.9%

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

   if -2.99999999999999989e-35 < a < 1.15999999999999997e-95

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in b around 0 93.3%

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

   6. Taylor expanded in a around 0 83.1%

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

      1. *-commutative 83.1%

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

   8. Simplified 83.1%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-35} \lor \neg \left(a \leq 1.16 \cdot 10^{-95}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \left(a + a \cdot \left(b \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e+39)
   (+ x (* t (+ a (* a (* b (/ z t))))))
   (if (<= b 3.2e+50) (+ x (+ (* a t) (* z y))) (+ x (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+39) {
		tmp = x + (t * (a + (a * (b * (z / t)))));
	} else if (b <= 3.2e+50) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	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 (b <= (-6.4d+39)) then
        tmp = x + (t * (a + (a * (b * (z / t)))))
    else if (b <= 3.2d+50) then
        tmp = x + ((a * t) + (z * y))
    else
        tmp = x + (a * (t + (z * b)))
    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 (b <= -6.4e+39) {
		tmp = x + (t * (a + (a * (b * (z / t)))));
	} else if (b <= 3.2e+50) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.4e+39:
		tmp = x + (t * (a + (a * (b * (z / t)))))
	elif b <= 3.2e+50:
		tmp = x + ((a * t) + (z * y))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.4e+39)
		tmp = Float64(x + Float64(t * Float64(a + Float64(a * Float64(b * Float64(z / t))))));
	elseif (b <= 3.2e+50)
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.4e+39)
		tmp = x + (t * (a + (a * (b * (z / t)))));
	elseif (b <= 3.2e+50)
		tmp = x + ((a * t) + (z * y));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.4e+39], N[(x + N[(t * N[(a + N[(a * N[(b * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+50], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.39999999999999986e39

   1. Initial program 91.2%

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

      1. associate-+l+ 91.2%

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

      2. +-commutative 91.2%

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

      3. fma-define 91.2%

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

      4. associate-*l* 78.6%

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

      5. *-commutative 78.6%

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

      6. *-commutative 78.6%

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

      7. distribute-rgt-out 78.6%

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

      8. remove-double-neg 78.6%

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

      9. *-commutative 78.6%

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

      10. distribute-lft-neg-out 78.6%

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

      11. sub-neg 78.6%

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

      12. sub-neg 78.6%

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

      13. distribute-lft-neg-out 78.6%

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

      14. *-commutative 78.6%

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

      15. remove-double-neg 78.6%

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

      16. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around 0 78.8%

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

   6. Taylor expanded in t around inf 74.8%

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

      1. associate-/l* 74.7%

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

      2. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

   if -6.39999999999999986e39 < b < 3.19999999999999983e50

   1. Initial program 91.9%

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

      1. associate-+l+ 91.9%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in b around 0 95.6%

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

   if 3.19999999999999983e50 < b

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. +-commutative 88.8%

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

      3. fma-define 88.8%

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

      4. associate-*l* 85.1%

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

      5. *-commutative 85.1%

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

      6. *-commutative 85.1%

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

      7. distribute-rgt-out 88.9%

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

      8. remove-double-neg 88.9%

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

      9. *-commutative 88.9%

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

      10. distribute-lft-neg-out 88.9%

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

      11. sub-neg 88.9%

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

      12. sub-neg 88.9%

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

      13. distribute-lft-neg-out 88.9%

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

      14. *-commutative 88.9%

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

      15. remove-double-neg 88.9%

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

      16. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around 0 89.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \left(a + a \cdot \left(b \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+42}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+50}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e+42)
   (+ x (* z (+ y (* a b))))
   (if (<= b 3.3e+50) (+ x (+ (* a t) (* z y))) (+ x (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+42) {
		tmp = x + (z * (y + (a * b)));
	} else if (b <= 3.3e+50) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	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 (b <= (-7d+42)) then
        tmp = x + (z * (y + (a * b)))
    else if (b <= 3.3d+50) then
        tmp = x + ((a * t) + (z * y))
    else
        tmp = x + (a * (t + (z * b)))
    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 (b <= -7e+42) {
		tmp = x + (z * (y + (a * b)));
	} else if (b <= 3.3e+50) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+42:
		tmp = x + (z * (y + (a * b)))
	elif b <= 3.3e+50:
		tmp = x + ((a * t) + (z * y))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+42)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	elseif (b <= 3.3e+50)
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e+42)
		tmp = x + (z * (y + (a * b)));
	elseif (b <= 3.3e+50)
		tmp = x + ((a * t) + (z * y));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+42], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+50], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.00000000000000047e42

   1. Initial program 91.2%

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

      1. associate-+l+ 91.2%

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

      2. associate-*l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-*r* 72.3%

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

      3. distribute-rgt-in 81.0%

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

   7. Simplified 81.0%

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

   if -7.00000000000000047e42 < b < 3.3e50

   1. Initial program 91.9%

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

      1. associate-+l+ 91.9%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in b around 0 95.6%

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

   if 3.3e50 < b

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. +-commutative 88.8%

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

      3. fma-define 88.8%

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

      4. associate-*l* 85.1%

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

      5. *-commutative 85.1%

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

      6. *-commutative 85.1%

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

      7. distribute-rgt-out 88.9%

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

      8. remove-double-neg 88.9%

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

      9. *-commutative 88.9%

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

      10. distribute-lft-neg-out 88.9%

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

      11. sub-neg 88.9%

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

      12. sub-neg 88.9%

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

      13. distribute-lft-neg-out 88.9%

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

      14. *-commutative 88.9%

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

      15. remove-double-neg 88.9%

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

      16. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around 0 89.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+42}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+50}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-39}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-260}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e-39)
   (* a t)
   (if (<= a 4.2e-260) (* z y) (if (<= a 5e+28) x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e-39) {
		tmp = a * t;
	} else if (a <= 4.2e-260) {
		tmp = z * y;
	} else if (a <= 5e+28) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	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 (a <= (-8d-39)) then
        tmp = a * t
    else if (a <= 4.2d-260) then
        tmp = z * y
    else if (a <= 5d+28) then
        tmp = x
    else
        tmp = a * t
    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 (a <= -8e-39) {
		tmp = a * t;
	} else if (a <= 4.2e-260) {
		tmp = z * y;
	} else if (a <= 5e+28) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8e-39:
		tmp = a * t
	elif a <= 4.2e-260:
		tmp = z * y
	elif a <= 5e+28:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8e-39)
		tmp = Float64(a * t);
	elseif (a <= 4.2e-260)
		tmp = Float64(z * y);
	elseif (a <= 5e+28)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8e-39)
		tmp = a * t;
	elseif (a <= 4.2e-260)
		tmp = z * y;
	elseif (a <= 5e+28)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8e-39], N[(a * t), $MachinePrecision], If[LessEqual[a, 4.2e-260], N[(z * y), $MachinePrecision], If[LessEqual[a, 5e+28], x, N[(a * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.99999999999999943e-39 or 4.99999999999999957e28 < a

   1. Initial program 85.5%

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

      1. associate-+l+ 85.4%

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

      2. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around 0 54.1%

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

   6. Taylor expanded in x around 0 43.0%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -7.99999999999999943e-39 < a < 4.20000000000000009e-260

   1. Initial program 97.2%

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

      1. associate-+l+ 97.2%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-*r* 83.2%

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

      3. distribute-rgt-in 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in y around inf 56.9%

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

      1. *-commutative 56.9%

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

   10. Simplified 56.9%

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

   if 4.20000000000000009e-260 < a < 4.99999999999999957e28

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around 0 60.2%

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

   6. Taylor expanded in x around inf 52.6%

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

Alternative 10: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+193}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2e+193)
   (+ x (* a (+ t (* z b))))
   (+ x (+ (* a t) (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2e+193) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	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 (a <= (-2d+193)) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + ((a * t) + (z * (y + (a * b))))
    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 (a <= -2e+193) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2e+193:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + ((a * t) + (z * (y + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2e+193)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * Float64(y + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2e+193)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + ((a * t) + (z * (y + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2e+193], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000013e193

   1. Initial program 83.9%

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

      1. associate-+l+ 83.9%

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

      2. +-commutative 83.9%

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

      3. fma-define 83.9%

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

      4. associate-*l* 91.6%

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

      5. *-commutative 91.6%

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

      6. *-commutative 91.6%

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

      7. distribute-rgt-out 99.9%

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

      8. remove-double-neg 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-lft-neg-out 99.9%

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

      11. sub-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. distribute-lft-neg-out 99.9%

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

      14. *-commutative 99.9%

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

      15. remove-double-neg 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.9%

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

   if -2.00000000000000013e193 < a

   1. Initial program 91.9%

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

      1. associate-+l+ 91.9%

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

      2. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around 0 96.6%

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

Alternative 11: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-37} \lor \neg \left(a \leq 14000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.4e-37) (not (<= a 14000.0)))
   (* a (+ t (* z b)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.4e-37) || !(a <= 14000.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * 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 ((a <= (-4.4d-37)) .or. (.not. (a <= 14000.0d0))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (z * 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 ((a <= -4.4e-37) || !(a <= 14000.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.4e-37) or not (a <= 14000.0):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.4e-37) || !(a <= 14000.0))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.4e-37) || ~((a <= 14000.0)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.4e-37], N[Not[LessEqual[a, 14000.0]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.40000000000000004e-37 or 14000 < a

   1. Initial program 85.8%

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

      1. associate-+l+ 85.7%

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

      2. +-commutative 85.7%

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

      3. fma-define 85.7%

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

      4. associate-*l* 91.9%

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

      5. *-commutative 91.9%

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

      6. *-commutative 91.9%

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

      7. distribute-rgt-out 95.6%

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

      8. remove-double-neg 95.6%

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

      9. *-commutative 95.6%

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

      10. distribute-lft-neg-out 95.6%

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

      11. sub-neg 95.6%

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

      12. sub-neg 95.6%

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

      13. distribute-lft-neg-out 95.6%

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

      14. *-commutative 95.6%

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

      15. remove-double-neg 95.6%

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

      16. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 87.1%

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

   6. Taylor expanded in x around 0 76.7%

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

   if -4.40000000000000004e-37 < a < 14000

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in b around 0 93.3%

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

   6. Taylor expanded in a around 0 80.6%

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

      1. *-commutative 80.6%

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

   8. Simplified 80.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-37} \lor \neg \left(a \leq 14000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+153}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-108}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e+153)
   (* z (* a b))
   (if (<= z 6.1e-108) (+ x (* a t)) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+153) {
		tmp = z * (a * b);
	} else if (z <= 6.1e-108) {
		tmp = x + (a * t);
	} else {
		tmp = z * 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 <= (-4.6d+153)) then
        tmp = z * (a * b)
    else if (z <= 6.1d-108) then
        tmp = x + (a * t)
    else
        tmp = z * 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 <= -4.6e+153) {
		tmp = z * (a * b);
	} else if (z <= 6.1e-108) {
		tmp = x + (a * t);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e+153:
		tmp = z * (a * b)
	elif z <= 6.1e-108:
		tmp = x + (a * t)
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+153)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 6.1e-108)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e+153)
		tmp = z * (a * b);
	elseif (z <= 6.1e-108)
		tmp = x + (a * t);
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+153], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e-108], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000003e153

   1. Initial program 85.4%

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

      1. associate-+l+ 85.4%

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

      2. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in z around inf 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-+l+ 94.0%

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

      3. +-commutative 94.0%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in b around inf 97.0%

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

   9. Taylor expanded in a around inf 56.9%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -4.6000000000000003e153 < z < 6.10000000000000007e-108

   1. Initial program 96.5%

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

      1. associate-+l+ 96.5%

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

      2. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around 0 75.2%

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

   if 6.10000000000000007e-108 < z

   1. Initial program 84.9%

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

      1. associate-+l+ 84.9%

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

      2. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-*r* 81.8%

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

      3. distribute-rgt-in 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around inf 48.7%

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

      1. *-commutative 48.7%

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

   10. Simplified 48.7%

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

Alternative 13: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e+49) x (if (<= x 2.3e+49) (* a t) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+49) {
		tmp = x;
	} else if (x <= 2.3e+49) {
		tmp = a * t;
	} 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 (x <= (-3.3d+49)) then
        tmp = x
    else if (x <= 2.3d+49) then
        tmp = a * t
    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 (x <= -3.3e+49) {
		tmp = x;
	} else if (x <= 2.3e+49) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e+49:
		tmp = x
	elif x <= 2.3e+49:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e+49)
		tmp = x;
	elseif (x <= 2.3e+49)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.3e+49)
		tmp = x;
	elseif (x <= 2.3e+49)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e+49], x, If[LessEqual[x, 2.3e+49], N[(a * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2999999999999998e49 or 2.30000000000000002e49 < x

   1. Initial program 92.1%

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

      1. associate-+l+ 92.1%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around 0 61.2%

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

   6. Taylor expanded in x around inf 49.0%

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

   if -3.2999999999999998e49 < x < 2.30000000000000002e49

   1. Initial program 90.5%

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

      1. associate-+l+ 90.5%

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

      2. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 45.5%

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

   6. Taylor expanded in x around 0 38.1%

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

Alternative 14: 26.1% accurate, 15.0× 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 91.2%

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

   1. associate-+l+ 91.2%

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

   2. associate-*l* 91.5%

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

3. Simplified 91.5%

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

5. Taylor expanded in z around 0 51.6%

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

6. Taylor expanded in x around inf 24.5%

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

Developer Target 1: 97.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} 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 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    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 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

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