Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 91.9% → 94.9%

Time: 13.0s

Alternatives: 13

Speedup: 1.0×

• 32.4% 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: 91.9% 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: 94.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \mathsf{fma}\left(a, t, x\right)\right) + z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.62e+65)
   (fma a (+ t (* z b)) (fma y z x))
   (+ (fma z y (fma a t x)) (* z (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.62e+65) {
		tmp = fma(a, (t + (z * b)), fma(y, z, x));
	} else {
		tmp = fma(z, y, fma(a, t, x)) + (z * (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.62e+65)
		tmp = fma(a, Float64(t + Float64(z * b)), fma(y, z, x));
	else
		tmp = Float64(fma(z, y, fma(a, t, x)) + Float64(z * Float64(a * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.62e+65], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(y * z + x), $MachinePrecision]), $MachinePrecision], N[(N[(z * y + N[(a * t + x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.61999999999999997e65

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. +-commutative 90.2%

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

      3. *-commutative 90.2%

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

      4. *-commutative 90.2%

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

      5. associate-*l* 94.1%

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

      6. distribute-rgt-out 100.0%

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

      7. fma-def 100.0%

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

      8. *-commutative 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-def 100.0%

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

   3. Simplified 100.0%

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

   if -1.61999999999999997e65 < a

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*l* 97.1%

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

      4. *-commutative 97.1%

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

      5. fma-def 97.1%

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

      6. *-commutative 97.1%

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

      7. +-commutative 97.1%

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

      8. fma-def 97.1%

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

      9. +-commutative 97.1%

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

      10. fma-def 97.1%

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

   3. Simplified 97.1%

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

      1. fma-udef 97.1%

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

      2. fma-udef 97.1%

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

      3. +-commutative 97.1%

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

      4. associate-+r+ 97.1%

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

      5. *-commutative 97.1%

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

      6. *-commutative 97.1%

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

   5. Applied egg-rr 97.1%

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

      1. fma-udef 97.1%

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

      2. +-commutative 97.1%

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

      3. +-commutative 97.1%

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

      4. fma-def 97.6%

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

      5. fma-def 97.6%

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

   7. Applied egg-rr 97.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \mathsf{fma}\left(a, t, x\right)\right) + z \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot y\right) + a \cdot t\right) + b \cdot \left(a \cdot z\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* z y)) (* a t)) (* b (* a z)))))
   (if (<= t_1 INFINITY) t_1 (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * y)) + (a * t)) + (b * (a * z));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * y)) + (a * t)) + (b * (a * z));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * y)) + (a * t)) + (b * (a * z))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * y)) + Float64(a * t)) + Float64(b * Float64(a * z)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * y)) + (a * t)) + (b * (a * z));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (t + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < +inf.0

   1. Initial program 97.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l* 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in a around inf 100.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot y\right) + a \cdot t\right) + b \cdot \left(a \cdot z\right) \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot y\right) + a \cdot t\right) + b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 3: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= t -5.2e+90)
     (* a t)
     (if (<= t -2.5e-74)
       (* z y)
       (if (<= t -1e-228)
         t_1
         (if (<= t 2.3e-86)
           x
           (if (<= t 5.5e+44) t_1 (if (<= t 1.05e+75) x (* a t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -5.2e+90) {
		tmp = a * t;
	} else if (t <= -2.5e-74) {
		tmp = z * y;
	} else if (t <= -1e-228) {
		tmp = t_1;
	} else if (t <= 2.3e-86) {
		tmp = x;
	} else if (t <= 5.5e+44) {
		tmp = t_1;
	} else if (t <= 1.05e+75) {
		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) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (t <= (-5.2d+90)) then
        tmp = a * t
    else if (t <= (-2.5d-74)) then
        tmp = z * y
    else if (t <= (-1d-228)) then
        tmp = t_1
    else if (t <= 2.3d-86) then
        tmp = x
    else if (t <= 5.5d+44) then
        tmp = t_1
    else if (t <= 1.05d+75) 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 t_1 = a * (z * b);
	double tmp;
	if (t <= -5.2e+90) {
		tmp = a * t;
	} else if (t <= -2.5e-74) {
		tmp = z * y;
	} else if (t <= -1e-228) {
		tmp = t_1;
	} else if (t <= 2.3e-86) {
		tmp = x;
	} else if (t <= 5.5e+44) {
		tmp = t_1;
	} else if (t <= 1.05e+75) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if t <= -5.2e+90:
		tmp = a * t
	elif t <= -2.5e-74:
		tmp = z * y
	elif t <= -1e-228:
		tmp = t_1
	elif t <= 2.3e-86:
		tmp = x
	elif t <= 5.5e+44:
		tmp = t_1
	elif t <= 1.05e+75:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (t <= -5.2e+90)
		tmp = Float64(a * t);
	elseif (t <= -2.5e-74)
		tmp = Float64(z * y);
	elseif (t <= -1e-228)
		tmp = t_1;
	elseif (t <= 2.3e-86)
		tmp = x;
	elseif (t <= 5.5e+44)
		tmp = t_1;
	elseif (t <= 1.05e+75)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (t <= -5.2e+90)
		tmp = a * t;
	elseif (t <= -2.5e-74)
		tmp = z * y;
	elseif (t <= -1e-228)
		tmp = t_1;
	elseif (t <= 2.3e-86)
		tmp = x;
	elseif (t <= 5.5e+44)
		tmp = t_1;
	elseif (t <= 1.05e+75)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+90], N[(a * t), $MachinePrecision], If[LessEqual[t, -2.5e-74], N[(z * y), $MachinePrecision], If[LessEqual[t, -1e-228], t$95$1, If[LessEqual[t, 2.3e-86], x, If[LessEqual[t, 5.5e+44], t$95$1, If[LessEqual[t, 1.05e+75], x, N[(a * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.1999999999999997e90 or 1.04999999999999999e75 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 55.6%

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

   if -5.1999999999999997e90 < t < -2.49999999999999999e-74

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 47.0%

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

      1. *-commutative 47.0%

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

   6. Simplified 47.0%

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

   if -2.49999999999999999e-74 < t < -1.00000000000000003e-228 or 2.29999999999999996e-86 < t < 5.5000000000000001e44

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*l* 94.6%

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

      4. *-commutative 94.6%

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

      5. fma-def 94.6%

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

      6. *-commutative 94.6%

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

      7. +-commutative 94.6%

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

      8. fma-def 94.6%

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

      9. +-commutative 94.6%

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

      10. fma-def 94.6%

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

   3. Simplified 94.6%

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

      1. fma-udef 94.6%

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

      2. fma-udef 94.6%

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

      3. +-commutative 94.6%

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

      4. associate-+r+ 94.6%

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

      5. *-commutative 94.6%

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

      6. *-commutative 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in b around inf 51.6%

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

      1. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if -1.00000000000000003e-228 < t < 2.29999999999999996e-86 or 5.5000000000000001e44 < t < 1.04999999999999999e75

   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. *-commutative 97.2%

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

      2. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 50.4%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-228}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 4: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.78 \cdot 10^{+65} \lor \neg \left(a \leq 3.2 \cdot 10^{-68}\right) \land \left(a \leq 4.4 \cdot 10^{-48} \lor \neg \left(a \leq 1.32 \cdot 10^{-23}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.78e+65)
         (and (not (<= a 3.2e-68)) (or (<= a 4.4e-48) (not (<= a 1.32e-23)))))
   (* 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 <= -1.78e+65) || (!(a <= 3.2e-68) && ((a <= 4.4e-48) || !(a <= 1.32e-23)))) {
		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 <= (-1.78d+65)) .or. (.not. (a <= 3.2d-68)) .and. (a <= 4.4d-48) .or. (.not. (a <= 1.32d-23))) 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 <= -1.78e+65) || (!(a <= 3.2e-68) && ((a <= 4.4e-48) || !(a <= 1.32e-23)))) {
		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 <= -1.78e+65) or (not (a <= 3.2e-68) and ((a <= 4.4e-48) or not (a <= 1.32e-23))):
		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 <= -1.78e+65) || (!(a <= 3.2e-68) && ((a <= 4.4e-48) || !(a <= 1.32e-23))))
		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 <= -1.78e+65) || (~((a <= 3.2e-68)) && ((a <= 4.4e-48) || ~((a <= 1.32e-23)))))
		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, -1.78e+65], And[N[Not[LessEqual[a, 3.2e-68]], $MachinePrecision], Or[LessEqual[a, 4.4e-48], N[Not[LessEqual[a, 1.32e-23]], $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 < -1.77999999999999995e65 or 3.1999999999999999e-68 < a < 4.40000000000000025e-48 or 1.31999999999999994e-23 < a

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in a around inf 74.9%

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

   if -1.77999999999999995e65 < a < 3.1999999999999999e-68 or 4.40000000000000025e-48 < a < 1.31999999999999994e-23

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in a around 0 72.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.78 \cdot 10^{+65} \lor \neg \left(a \leq 3.2 \cdot 10^{-68}\right) \land \left(a \leq 4.4 \cdot 10^{-48} \lor \neg \left(a \leq 1.32 \cdot 10^{-23}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 5: 92.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. *-commutative 95.0%

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

   2. associate-*l* 95.0%

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

3. Simplified 95.0%

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

4. Final simplification 95.0%

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

Alternative 6: 83.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+126} \lor \neg \left(z \leq 4.1 \cdot 10^{+131}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e+126) (not (<= z 4.1e+131)))
   (* z (+ y (* a b)))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e+126) || !(z <= 4.1e+131)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((a * t) + (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 <= (-9.5d+126)) .or. (.not. (z <= 4.1d+131))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + ((a * t) + (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 <= -9.5e+126) || !(z <= 4.1e+131)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e+126) or not (z <= 4.1e+131):
		tmp = z * (y + (a * b))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e+126) || !(z <= 4.1e+131))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e+126) || ~((z <= 4.1e+131)))
		tmp = z * (y + (a * b));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e+126], N[Not[LessEqual[z, 4.1e+131]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999951e126 or 4.10000000000000007e131 < z

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in z around inf 84.0%

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

   if -9.49999999999999951e126 < z < 4.10000000000000007e131

   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. *-commutative 97.9%

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

      2. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in b around 0 84.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+126} \lor \neg \left(z \leq 4.1 \cdot 10^{+131}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]

Alternative 7: 83.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+137)
   (+ x (* a (* z b)))
   (if (<= b 1.5e+50) (+ x (+ (* a t) (* z y))) (+ x (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+137) {
		tmp = x + (a * (z * b));
	} else if (b <= 1.5e+50) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (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 (b <= (-6.5d+137)) then
        tmp = x + (a * (z * b))
    else if (b <= 1.5d+50) then
        tmp = x + ((a * t) + (z * y))
    else
        tmp = x + (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 (b <= -6.5e+137) {
		tmp = x + (a * (z * b));
	} else if (b <= 1.5e+50) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+137:
		tmp = x + (a * (z * b))
	elif b <= 1.5e+50:
		tmp = x + ((a * t) + (z * y))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+137)
		tmp = Float64(x + Float64(a * Float64(z * b)));
	elseif (b <= 1.5e+50)
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	else
		tmp = Float64(x + 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 (b <= -6.5e+137)
		tmp = x + (a * (z * b));
	elseif (b <= 1.5e+50)
		tmp = x + ((a * t) + (z * y));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+137], N[(x + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+50], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.5000000000000002e137

   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. *-commutative 97.2%

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

      2. associate-*l* 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. +-commutative 81.1%

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

      3. associate-*r* 78.6%

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

      4. distribute-rgt-in 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in y around 0 81.1%

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

   if -6.5000000000000002e137 < b < 1.4999999999999999e50

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in b around 0 91.8%

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

   if 1.4999999999999999e50 < b

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. +-commutative 76.4%

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

      3. associate-*r* 87.6%

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

      4. distribute-rgt-in 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 8: 62.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.86 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+44} \lor \neg \left(a \leq 4200000000000\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.86e+230)
   (* z (* a b))
   (if (or (<= a -6e+44) (not (<= a 4200000000000.0)))
     (+ x (* a t))
     (+ x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.86e+230) {
		tmp = z * (a * b);
	} else if ((a <= -6e+44) || !(a <= 4200000000000.0)) {
		tmp = x + (a * t);
	} 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 <= (-1.86d+230)) then
        tmp = z * (a * b)
    else if ((a <= (-6d+44)) .or. (.not. (a <= 4200000000000.0d0))) then
        tmp = x + (a * t)
    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 <= -1.86e+230) {
		tmp = z * (a * b);
	} else if ((a <= -6e+44) || !(a <= 4200000000000.0)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.86e+230:
		tmp = z * (a * b)
	elif (a <= -6e+44) or not (a <= 4200000000000.0):
		tmp = x + (a * t)
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.86e+230)
		tmp = Float64(z * Float64(a * b));
	elseif ((a <= -6e+44) || !(a <= 4200000000000.0))
		tmp = Float64(x + Float64(a * t));
	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 <= -1.86e+230)
		tmp = z * (a * b);
	elseif ((a <= -6e+44) || ~((a <= 4200000000000.0)))
		tmp = x + (a * t);
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.86e+230], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -6e+44], N[Not[LessEqual[a, 4200000000000.0]], $MachinePrecision]], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.86e230

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*l* 94.0%

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

      4. *-commutative 94.0%

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

      5. fma-def 94.0%

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

      6. *-commutative 94.0%

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

      7. +-commutative 94.0%

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

      8. fma-def 94.0%

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

      9. +-commutative 94.0%

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

      10. fma-def 94.0%

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

   3. Simplified 94.0%

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

      1. fma-udef 94.0%

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

      2. fma-udef 94.0%

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

      3. +-commutative 94.0%

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

      4. associate-+r+ 94.0%

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

      5. *-commutative 94.0%

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

      6. *-commutative 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in b around inf 71.7%

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

      1. *-commutative 71.7%

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

   8. Simplified 71.7%

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

   9. Taylor expanded in a around 0 71.7%

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

       1. associate-*r* 76.9%

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

   11. Simplified 76.9%

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

   if -1.86e230 < a < -5.99999999999999974e44 or 4.2e12 < a

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 63.6%

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

   if -5.99999999999999974e44 < a < 4.2e12

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 68.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.86 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+44} \lor \neg \left(a \leq 4200000000000\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 9: 59.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+42}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+118}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.6e+131)
   (* z y)
   (if (<= z 2.8e+42)
     (+ x (* a t))
     (if (<= z 2.15e+118) (* z y) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.6e+131) {
		tmp = z * y;
	} else if (z <= 2.8e+42) {
		tmp = x + (a * t);
	} else if (z <= 2.15e+118) {
		tmp = z * y;
	} else {
		tmp = z * (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 (z <= (-2.6d+131)) then
        tmp = z * y
    else if (z <= 2.8d+42) then
        tmp = x + (a * t)
    else if (z <= 2.15d+118) then
        tmp = z * y
    else
        tmp = z * (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 (z <= -2.6e+131) {
		tmp = z * y;
	} else if (z <= 2.8e+42) {
		tmp = x + (a * t);
	} else if (z <= 2.15e+118) {
		tmp = z * y;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.6e+131:
		tmp = z * y
	elif z <= 2.8e+42:
		tmp = x + (a * t)
	elif z <= 2.15e+118:
		tmp = z * y
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.6e+131)
		tmp = Float64(z * y);
	elseif (z <= 2.8e+42)
		tmp = Float64(x + Float64(a * t));
	elseif (z <= 2.15e+118)
		tmp = Float64(z * y);
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.6e+131)
		tmp = z * y;
	elseif (z <= 2.8e+42)
		tmp = x + (a * t);
	elseif (z <= 2.15e+118)
		tmp = z * y;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.6e+131], N[(z * y), $MachinePrecision], If[LessEqual[z, 2.8e+42], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+118], N[(z * y), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e131 or 2.7999999999999999e42 < z < 2.1500000000000002e118

   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. *-commutative 88.8%

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

      2. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   if -2.6e131 < z < 2.7999999999999999e42

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 69.1%

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

   if 2.1500000000000002e118 < z

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l* 91.8%

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

      4. *-commutative 91.8%

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

      5. fma-def 91.8%

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

      6. *-commutative 91.8%

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

      7. +-commutative 91.8%

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

      8. fma-def 91.8%

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

      9. +-commutative 91.8%

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

      10. fma-def 91.8%

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

   3. Simplified 91.8%

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

      1. fma-udef 91.8%

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

      2. fma-udef 91.8%

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

      3. +-commutative 91.8%

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

      4. associate-+r+ 91.8%

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

      5. *-commutative 91.8%

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

      6. *-commutative 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   9. Taylor expanded in a around 0 55.2%

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

       1. associate-*r* 55.2%

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

   11. Simplified 55.2%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+42}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+118}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 10: 74.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+54} \lor \neg \left(z \leq 10^{-37}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+54) (not (<= z 1e-37)))
   (* z (+ y (* a b)))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+54) || !(z <= 1e-37)) {
		tmp = z * (y + (a * b));
	} 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 <= (-1.3d+54)) .or. (.not. (z <= 1d-37))) then
        tmp = z * (y + (a * b))
    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 <= -1.3e+54) || !(z <= 1e-37)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.3e+54) or not (z <= 1e-37):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.3e+54) || !(z <= 1e-37))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	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 <= -1.3e+54) || ~((z <= 1e-37)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.3e+54], N[Not[LessEqual[z, 1e-37]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000003e54 or 1.00000000000000007e-37 < z

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 74.7%

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

   if -1.30000000000000003e54 < z < 1.00000000000000007e-37

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 76.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+54} \lor \neg \left(z \leq 10^{-37}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 11: 40.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+93}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -3.65 \cdot 10^{-101}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.1e+93)
   (* a t)
   (if (<= t -3.65e-101) (* z y) (if (<= t 9e+74) x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.1e+93) {
		tmp = a * t;
	} else if (t <= -3.65e-101) {
		tmp = z * y;
	} else if (t <= 9e+74) {
		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 (t <= (-5.1d+93)) then
        tmp = a * t
    else if (t <= (-3.65d-101)) then
        tmp = z * y
    else if (t <= 9d+74) 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 (t <= -5.1e+93) {
		tmp = a * t;
	} else if (t <= -3.65e-101) {
		tmp = z * y;
	} else if (t <= 9e+74) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.1e+93:
		tmp = a * t
	elif t <= -3.65e-101:
		tmp = z * y
	elif t <= 9e+74:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.1e+93)
		tmp = Float64(a * t);
	elseif (t <= -3.65e-101)
		tmp = Float64(z * y);
	elseif (t <= 9e+74)
		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 (t <= -5.1e+93)
		tmp = a * t;
	elseif (t <= -3.65e-101)
		tmp = z * y;
	elseif (t <= 9e+74)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.1e+93], N[(a * t), $MachinePrecision], If[LessEqual[t, -3.65e-101], N[(z * y), $MachinePrecision], If[LessEqual[t, 9e+74], x, N[(a * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0999999999999996e93 or 8.9999999999999999e74 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 55.6%

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

   if -5.0999999999999996e93 < t < -3.65e-101

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 42.9%

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

      1. *-commutative 42.9%

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

   6. Simplified 42.9%

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

   if -3.65e-101 < t < 8.9999999999999999e74

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 42.2%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+93}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -3.65 \cdot 10^{-101}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 12: 39.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+90}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.4e+90) (* a t) (if (<= t 1e+75) x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+90) {
		tmp = a * t;
	} else if (t <= 1e+75) {
		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 (t <= (-1.4d+90)) then
        tmp = a * t
    else if (t <= 1d+75) 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 (t <= -1.4e+90) {
		tmp = a * t;
	} else if (t <= 1e+75) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.4e+90:
		tmp = a * t
	elif t <= 1e+75:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.4e+90)
		tmp = Float64(a * t);
	elseif (t <= 1e+75)
		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 (t <= -1.4e+90)
		tmp = a * t;
	elseif (t <= 1e+75)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.4e+90], N[(a * t), $MachinePrecision], If[LessEqual[t, 1e+75], x, N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e90 or 9.99999999999999927e74 < t

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 55.6%

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

   if -1.4e90 < t < 9.99999999999999927e74

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 39.4%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+90}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 13: 26.9% 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 95.0%

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

   1. *-commutative 95.0%

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

   2. associate-*l* 95.0%

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

3. Simplified 95.0%

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

4. Taylor expanded in x around inf 27.9%

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

5. Final simplification 27.9%

   \[\leadsto x \]

Developer target: 97.2% accurate, 0.9× 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 2023285 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

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