Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.6% → 96.7%

Time: 13.7s

Alternatives: 15

Speedup: 0.8×

• 32.0% 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: 92.6% 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: 96.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (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 + (y * z)) + (t * a)) + ((z * a) * b);
	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 + (y * z)) + (t * a)) + ((z * a) * b);
	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 + (y * z)) + (t * a)) + ((z * a) * b)
	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(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	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 + (y * z)) + (t * a)) + ((z * a) * b);
	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[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $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 98.1%

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

   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. associate-+l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*l* 0.0%

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

   3. Simplified 0.0%

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

      1. add-cube-cbrt 0.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 0.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 0.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 0.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 0.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 35.7%

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

      1. distribute-lft-in 92.9%

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

      2. *-commutative 92.9%

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

   8. Simplified 92.9%

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

4. Final simplification 97.8%

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

Alternative 2: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-180}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-21}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+62} \lor \neg \left(z \leq 1.56 \cdot 10^{+100}\right) \land z \leq 2.5 \cdot 10^{+216}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -30000.0)
   (* y z)
   (if (<= z -2.95e-133)
     x
     (if (<= z -1.5e-180)
       (* t a)
       (if (<= z 1.7e-279)
         x
         (if (<= z 5.9e-21)
           (* t a)
           (if (<= z 5.7e+41)
             x
             (if (or (<= z 7.5e+62)
                     (and (not (<= z 1.56e+100)) (<= z 2.5e+216)))
               (* y z)
               (* a (* z b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -30000.0) {
		tmp = y * z;
	} else if (z <= -2.95e-133) {
		tmp = x;
	} else if (z <= -1.5e-180) {
		tmp = t * a;
	} else if (z <= 1.7e-279) {
		tmp = x;
	} else if (z <= 5.9e-21) {
		tmp = t * a;
	} else if (z <= 5.7e+41) {
		tmp = x;
	} else if ((z <= 7.5e+62) || (!(z <= 1.56e+100) && (z <= 2.5e+216))) {
		tmp = y * z;
	} else {
		tmp = a * (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 <= (-30000.0d0)) then
        tmp = y * z
    else if (z <= (-2.95d-133)) then
        tmp = x
    else if (z <= (-1.5d-180)) then
        tmp = t * a
    else if (z <= 1.7d-279) then
        tmp = x
    else if (z <= 5.9d-21) then
        tmp = t * a
    else if (z <= 5.7d+41) then
        tmp = x
    else if ((z <= 7.5d+62) .or. (.not. (z <= 1.56d+100)) .and. (z <= 2.5d+216)) then
        tmp = y * z
    else
        tmp = a * (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 <= -30000.0) {
		tmp = y * z;
	} else if (z <= -2.95e-133) {
		tmp = x;
	} else if (z <= -1.5e-180) {
		tmp = t * a;
	} else if (z <= 1.7e-279) {
		tmp = x;
	} else if (z <= 5.9e-21) {
		tmp = t * a;
	} else if (z <= 5.7e+41) {
		tmp = x;
	} else if ((z <= 7.5e+62) || (!(z <= 1.56e+100) && (z <= 2.5e+216))) {
		tmp = y * z;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -30000.0:
		tmp = y * z
	elif z <= -2.95e-133:
		tmp = x
	elif z <= -1.5e-180:
		tmp = t * a
	elif z <= 1.7e-279:
		tmp = x
	elif z <= 5.9e-21:
		tmp = t * a
	elif z <= 5.7e+41:
		tmp = x
	elif (z <= 7.5e+62) or (not (z <= 1.56e+100) and (z <= 2.5e+216)):
		tmp = y * z
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -30000.0)
		tmp = Float64(y * z);
	elseif (z <= -2.95e-133)
		tmp = x;
	elseif (z <= -1.5e-180)
		tmp = Float64(t * a);
	elseif (z <= 1.7e-279)
		tmp = x;
	elseif (z <= 5.9e-21)
		tmp = Float64(t * a);
	elseif (z <= 5.7e+41)
		tmp = x;
	elseif ((z <= 7.5e+62) || (!(z <= 1.56e+100) && (z <= 2.5e+216)))
		tmp = Float64(y * z);
	else
		tmp = Float64(a * Float64(z * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -30000.0)
		tmp = y * z;
	elseif (z <= -2.95e-133)
		tmp = x;
	elseif (z <= -1.5e-180)
		tmp = t * a;
	elseif (z <= 1.7e-279)
		tmp = x;
	elseif (z <= 5.9e-21)
		tmp = t * a;
	elseif (z <= 5.7e+41)
		tmp = x;
	elseif ((z <= 7.5e+62) || (~((z <= 1.56e+100)) && (z <= 2.5e+216)))
		tmp = y * z;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -30000.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.95e-133], x, If[LessEqual[z, -1.5e-180], N[(t * a), $MachinePrecision], If[LessEqual[z, 1.7e-279], x, If[LessEqual[z, 5.9e-21], N[(t * a), $MachinePrecision], If[LessEqual[z, 5.7e+41], x, If[Or[LessEqual[z, 7.5e+62], And[N[Not[LessEqual[z, 1.56e+100]], $MachinePrecision], LessEqual[z, 2.5e+216]]], N[(y * z), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3e4 or 5.70000000000000021e41 < z < 7.49999999999999998e62 or 1.55999999999999998e100 < z < 2.4999999999999999e216

   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. *-commutative 92.1%

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

      3. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if -3e4 < z < -2.94999999999999982e-133 or -1.5e-180 < z < 1.70000000000000007e-279 or 5.9000000000000003e-21 < z < 5.70000000000000021e41

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. *-commutative 98.7%

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

      3. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around inf 53.3%

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

   if -2.94999999999999982e-133 < z < -1.5e-180 or 1.70000000000000007e-279 < z < 5.9000000000000003e-21

   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%

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

      3. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. add-cube-cbrt 89.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 89.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 89.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 89.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 89.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in t around inf 54.0%

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

   if 7.49999999999999998e62 < z < 1.55999999999999998e100 or 2.4999999999999999e216 < z

   1. Initial program 60.4%

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

      1. associate-+l+ 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*l* 68.2%

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

   3. Simplified 68.2%

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

      1. add-cube-cbrt 67.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 67.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 67.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 67.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 67.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 67.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 81.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-180}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-21}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+62} \lor \neg \left(z \leq 1.56 \cdot 10^{+100}\right) \land z \leq 2.5 \cdot 10^{+216}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 3: 38.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2300000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-181}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-21}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+217}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2300000.0)
   (* y z)
   (if (<= z -1.02e-141)
     x
     (if (<= z -1.15e-181)
       (* t a)
       (if (<= z 4.6e-279)
         x
         (if (<= z 5.6e-21)
           (* t a)
           (if (<= z 3.6e+43)
             x
             (if (<= z 5.5e+62)
               (* y z)
               (if (<= z 1.1e+205)
                 (* z (* a b))
                 (if (<= z 2.4e+217) (* y z) (* a (* z b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2300000.0) {
		tmp = y * z;
	} else if (z <= -1.02e-141) {
		tmp = x;
	} else if (z <= -1.15e-181) {
		tmp = t * a;
	} else if (z <= 4.6e-279) {
		tmp = x;
	} else if (z <= 5.6e-21) {
		tmp = t * a;
	} else if (z <= 3.6e+43) {
		tmp = x;
	} else if (z <= 5.5e+62) {
		tmp = y * z;
	} else if (z <= 1.1e+205) {
		tmp = z * (a * b);
	} else if (z <= 2.4e+217) {
		tmp = y * z;
	} else {
		tmp = a * (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 <= (-2300000.0d0)) then
        tmp = y * z
    else if (z <= (-1.02d-141)) then
        tmp = x
    else if (z <= (-1.15d-181)) then
        tmp = t * a
    else if (z <= 4.6d-279) then
        tmp = x
    else if (z <= 5.6d-21) then
        tmp = t * a
    else if (z <= 3.6d+43) then
        tmp = x
    else if (z <= 5.5d+62) then
        tmp = y * z
    else if (z <= 1.1d+205) then
        tmp = z * (a * b)
    else if (z <= 2.4d+217) then
        tmp = y * z
    else
        tmp = a * (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 <= -2300000.0) {
		tmp = y * z;
	} else if (z <= -1.02e-141) {
		tmp = x;
	} else if (z <= -1.15e-181) {
		tmp = t * a;
	} else if (z <= 4.6e-279) {
		tmp = x;
	} else if (z <= 5.6e-21) {
		tmp = t * a;
	} else if (z <= 3.6e+43) {
		tmp = x;
	} else if (z <= 5.5e+62) {
		tmp = y * z;
	} else if (z <= 1.1e+205) {
		tmp = z * (a * b);
	} else if (z <= 2.4e+217) {
		tmp = y * z;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2300000.0:
		tmp = y * z
	elif z <= -1.02e-141:
		tmp = x
	elif z <= -1.15e-181:
		tmp = t * a
	elif z <= 4.6e-279:
		tmp = x
	elif z <= 5.6e-21:
		tmp = t * a
	elif z <= 3.6e+43:
		tmp = x
	elif z <= 5.5e+62:
		tmp = y * z
	elif z <= 1.1e+205:
		tmp = z * (a * b)
	elif z <= 2.4e+217:
		tmp = y * z
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2300000.0)
		tmp = Float64(y * z);
	elseif (z <= -1.02e-141)
		tmp = x;
	elseif (z <= -1.15e-181)
		tmp = Float64(t * a);
	elseif (z <= 4.6e-279)
		tmp = x;
	elseif (z <= 5.6e-21)
		tmp = Float64(t * a);
	elseif (z <= 3.6e+43)
		tmp = x;
	elseif (z <= 5.5e+62)
		tmp = Float64(y * z);
	elseif (z <= 1.1e+205)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 2.4e+217)
		tmp = Float64(y * z);
	else
		tmp = Float64(a * Float64(z * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2300000.0)
		tmp = y * z;
	elseif (z <= -1.02e-141)
		tmp = x;
	elseif (z <= -1.15e-181)
		tmp = t * a;
	elseif (z <= 4.6e-279)
		tmp = x;
	elseif (z <= 5.6e-21)
		tmp = t * a;
	elseif (z <= 3.6e+43)
		tmp = x;
	elseif (z <= 5.5e+62)
		tmp = y * z;
	elseif (z <= 1.1e+205)
		tmp = z * (a * b);
	elseif (z <= 2.4e+217)
		tmp = y * z;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2300000.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.02e-141], x, If[LessEqual[z, -1.15e-181], N[(t * a), $MachinePrecision], If[LessEqual[z, 4.6e-279], x, If[LessEqual[z, 5.6e-21], N[(t * a), $MachinePrecision], If[LessEqual[z, 3.6e+43], x, If[LessEqual[z, 5.5e+62], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.1e+205], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+217], N[(y * z), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.3e6 or 3.6000000000000001e43 < z < 5.4999999999999997e62 or 1.0999999999999999e205 < z < 2.3999999999999998e217

   1. Initial program 91.7%

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

      1. associate-+l+ 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 56.8%

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

      1. *-commutative 56.8%

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

   6. Simplified 56.8%

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

   if -2.3e6 < z < -1.02e-141 or -1.14999999999999995e-181 < z < 4.5999999999999999e-279 or 5.60000000000000008e-21 < z < 3.6000000000000001e43

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. *-commutative 98.7%

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

      3. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around inf 53.3%

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

   if -1.02e-141 < z < -1.14999999999999995e-181 or 4.5999999999999999e-279 < z < 5.60000000000000008e-21

   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%

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

      3. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. add-cube-cbrt 89.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 89.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 89.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 89.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 89.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in t around inf 54.0%

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

   if 5.4999999999999997e62 < z < 1.0999999999999999e205

   1. Initial program 92.2%

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

      1. associate-+l+ 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

      1. add-cube-cbrt 95.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 95.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 95.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 95.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 95.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 95.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 31.4%

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

      1. *-commutative 31.4%

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

      2. *-commutative 31.4%

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

      3. associate-*l* 39.5%

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

      4. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   if 2.3999999999999998e217 < z

   1. Initial program 50.4%

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

      1. associate-+l+ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l* 56.3%

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

   3. Simplified 56.3%

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

      1. add-cube-cbrt 56.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 56.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 56.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 56.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 56.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 56.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 88.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2300000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-181}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-21}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+217}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 4: 95.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+63} \lor \neg \left(a \leq 9 \cdot 10^{+127}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.08e+63) (not (<= a 9e+127)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* y z)) (+ (* z (* a b)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.08e+63) || !(a <= 9e+127)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	}
	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 <= (-1.08d+63)) .or. (.not. (a <= 9d+127))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
    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 <= -1.08e+63) || !(a <= 9e+127)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.08e+63) or not (a <= 9e+127):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.08e+63) || !(a <= 9e+127))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(z * Float64(a * b)) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.08e+63) || ~((a <= 9e+127)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.08e+63], N[Not[LessEqual[a, 9e+127]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.08e63 or 9.00000000000000068e127 < a

   1. Initial program 74.8%

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

      1. associate-+l+ 74.8%

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

      2. +-commutative 74.8%

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

      3. fma-def 74.8%

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

      4. associate-*l* 79.9%

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

      5. *-commutative 79.9%

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

      6. *-commutative 79.9%

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

      7. distribute-rgt-out 89.9%

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

      8. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around 0 93.0%

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

   if -1.08e63 < a < 9.00000000000000068e127

   1. Initial program 99.5%

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

      1. associate-+l+ 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+63} \lor \neg \left(a \leq 9 \cdot 10^{+127}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \end{array} \]

Alternative 5: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+97} \lor \neg \left(a \leq 1.35 \cdot 10^{+239}\right) \land a \leq 4.3 \cdot 10^{+306}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.15e+18)
   (* t a)
   (if (<= a 1.08e-17)
     (+ x (* y z))
     (if (or (<= a 2.5e+97) (and (not (<= a 1.35e+239)) (<= a 4.3e+306)))
       (* a (* z b))
       (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.15e+18) {
		tmp = t * a;
	} else if (a <= 1.08e-17) {
		tmp = x + (y * z);
	} else if ((a <= 2.5e+97) || (!(a <= 1.35e+239) && (a <= 4.3e+306))) {
		tmp = a * (z * b);
	} else {
		tmp = t * a;
	}
	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 <= (-2.15d+18)) then
        tmp = t * a
    else if (a <= 1.08d-17) then
        tmp = x + (y * z)
    else if ((a <= 2.5d+97) .or. (.not. (a <= 1.35d+239)) .and. (a <= 4.3d+306)) then
        tmp = a * (z * b)
    else
        tmp = t * a
    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 <= -2.15e+18) {
		tmp = t * a;
	} else if (a <= 1.08e-17) {
		tmp = x + (y * z);
	} else if ((a <= 2.5e+97) || (!(a <= 1.35e+239) && (a <= 4.3e+306))) {
		tmp = a * (z * b);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.15e+18:
		tmp = t * a
	elif a <= 1.08e-17:
		tmp = x + (y * z)
	elif (a <= 2.5e+97) or (not (a <= 1.35e+239) and (a <= 4.3e+306)):
		tmp = a * (z * b)
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.15e+18)
		tmp = Float64(t * a);
	elseif (a <= 1.08e-17)
		tmp = Float64(x + Float64(y * z));
	elseif ((a <= 2.5e+97) || (!(a <= 1.35e+239) && (a <= 4.3e+306)))
		tmp = Float64(a * Float64(z * b));
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.15e+18)
		tmp = t * a;
	elseif (a <= 1.08e-17)
		tmp = x + (y * z);
	elseif ((a <= 2.5e+97) || (~((a <= 1.35e+239)) && (a <= 4.3e+306)))
		tmp = a * (z * b);
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.15e+18], N[(t * a), $MachinePrecision], If[LessEqual[a, 1.08e-17], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.5e+97], And[N[Not[LessEqual[a, 1.35e+239]], $MachinePrecision], LessEqual[a, 4.3e+306]]], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], N[(t * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.15e18 or 2.49999999999999999e97 < a < 1.3499999999999999e239 or 4.2999999999999998e306 < a

   1. Initial program 82.3%

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

      1. associate-+l+ 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

      1. add-cube-cbrt 72.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 72.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 72.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 72.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 72.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in t around inf 52.1%

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

   if -2.15e18 < a < 1.07999999999999995e-17

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. *-commutative 99.3%

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

      3. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 73.9%

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

   if 1.07999999999999995e-17 < a < 2.49999999999999999e97 or 1.3499999999999999e239 < a < 4.2999999999999998e306

   1. Initial program 86.8%

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

      1. associate-+l+ 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*l* 86.2%

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

   3. Simplified 86.2%

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

      1. add-cube-cbrt 86.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 86.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 86.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 86.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 86.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 59.8%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+97} \lor \neg \left(a \leq 1.35 \cdot 10^{+239}\right) \land a \leq 4.3 \cdot 10^{+306}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 6: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ t_2 := x + t_1\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-36}:\\ \;\;\;\;t_1 + y \cdot z\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))) (t_2 (+ x t_1)))
   (if (<= a -2.7e+181)
     t_2
     (if (<= a -4.4e-36)
       (+ t_1 (* y z))
       (if (<= a 3.5e-19) (+ (+ x (* y z)) (* t a)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double t_2 = x + t_1;
	double tmp;
	if (a <= -2.7e+181) {
		tmp = t_2;
	} else if (a <= -4.4e-36) {
		tmp = t_1 + (y * z);
	} else if (a <= 3.5e-19) {
		tmp = (x + (y * z)) + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    t_2 = x + t_1
    if (a <= (-2.7d+181)) then
        tmp = t_2
    else if (a <= (-4.4d-36)) then
        tmp = t_1 + (y * z)
    else if (a <= 3.5d-19) then
        tmp = (x + (y * z)) + (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double t_2 = x + t_1;
	double tmp;
	if (a <= -2.7e+181) {
		tmp = t_2;
	} else if (a <= -4.4e-36) {
		tmp = t_1 + (y * z);
	} else if (a <= 3.5e-19) {
		tmp = (x + (y * z)) + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	t_2 = x + t_1
	tmp = 0
	if a <= -2.7e+181:
		tmp = t_2
	elif a <= -4.4e-36:
		tmp = t_1 + (y * z)
	elif a <= 3.5e-19:
		tmp = (x + (y * z)) + (t * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (a <= -2.7e+181)
		tmp = t_2;
	elseif (a <= -4.4e-36)
		tmp = Float64(t_1 + Float64(y * z));
	elseif (a <= 3.5e-19)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(t * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	t_2 = x + t_1;
	tmp = 0.0;
	if (a <= -2.7e+181)
		tmp = t_2;
	elseif (a <= -4.4e-36)
		tmp = t_1 + (y * z);
	elseif (a <= 3.5e-19)
		tmp = (x + (y * z)) + (t * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[a, -2.7e+181], t$95$2, If[LessEqual[a, -4.4e-36], N[(t$95$1 + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-19], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.70000000000000007e181 or 3.50000000000000015e-19 < a

   1. Initial program 84.8%

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

      1. associate-+l+ 84.8%

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

      2. +-commutative 84.8%

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

      3. fma-def 84.8%

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

      4. associate-*l* 87.0%

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

      5. *-commutative 87.0%

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

      6. *-commutative 87.0%

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

      7. distribute-rgt-out 94.7%

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

      8. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 95.0%

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

   if -2.70000000000000007e181 < a < -4.3999999999999999e-36

   1. Initial program 89.2%

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

      1. associate-+l+ 89.2%

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

      2. +-commutative 89.2%

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

      3. fma-def 89.2%

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

      4. associate-*l* 92.6%

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

      5. *-commutative 92.6%

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

      6. *-commutative 92.6%

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

      7. distribute-rgt-out 94.4%

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

      8. *-commutative 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around 0 89.4%

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

   if -4.3999999999999999e-36 < a < 3.50000000000000015e-19

   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. associate-+l+ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 92.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+181}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + y \cdot z\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 7: 39.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -100000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-183}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6600000000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -100000.0)
   (* y z)
   (if (<= z -3e-136)
     x
     (if (<= z -3.65e-183)
       (* t a)
       (if (<= z 2.6e-279) x (if (<= z 6600000000.0) (* t a) (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -100000.0) {
		tmp = y * z;
	} else if (z <= -3e-136) {
		tmp = x;
	} else if (z <= -3.65e-183) {
		tmp = t * a;
	} else if (z <= 2.6e-279) {
		tmp = x;
	} else if (z <= 6600000000.0) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	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 <= (-100000.0d0)) then
        tmp = y * z
    else if (z <= (-3d-136)) then
        tmp = x
    else if (z <= (-3.65d-183)) then
        tmp = t * a
    else if (z <= 2.6d-279) then
        tmp = x
    else if (z <= 6600000000.0d0) then
        tmp = t * a
    else
        tmp = y * z
    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 <= -100000.0) {
		tmp = y * z;
	} else if (z <= -3e-136) {
		tmp = x;
	} else if (z <= -3.65e-183) {
		tmp = t * a;
	} else if (z <= 2.6e-279) {
		tmp = x;
	} else if (z <= 6600000000.0) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -100000.0:
		tmp = y * z
	elif z <= -3e-136:
		tmp = x
	elif z <= -3.65e-183:
		tmp = t * a
	elif z <= 2.6e-279:
		tmp = x
	elif z <= 6600000000.0:
		tmp = t * a
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -100000.0)
		tmp = Float64(y * z);
	elseif (z <= -3e-136)
		tmp = x;
	elseif (z <= -3.65e-183)
		tmp = Float64(t * a);
	elseif (z <= 2.6e-279)
		tmp = x;
	elseif (z <= 6600000000.0)
		tmp = Float64(t * a);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -100000.0)
		tmp = y * z;
	elseif (z <= -3e-136)
		tmp = x;
	elseif (z <= -3.65e-183)
		tmp = t * a;
	elseif (z <= 2.6e-279)
		tmp = x;
	elseif (z <= 6600000000.0)
		tmp = t * a;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -100000.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -3e-136], x, If[LessEqual[z, -3.65e-183], N[(t * a), $MachinePrecision], If[LessEqual[z, 2.6e-279], x, If[LessEqual[z, 6600000000.0], N[(t * a), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e5 or 6.6e9 < z

   1. Initial program 86.4%

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

      1. associate-+l+ 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in y around inf 46.0%

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

      1. *-commutative 46.0%

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

   6. Simplified 46.0%

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

   if -1e5 < z < -2.9999999999999998e-136 or -3.64999999999999999e-183 < z < 2.6000000000000002e-279

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around inf 52.8%

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

   if -2.9999999999999998e-136 < z < -3.64999999999999999e-183 or 2.6000000000000002e-279 < z < 6.6e9

   1. Initial program 97.3%

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

      1. associate-+l+ 97.3%

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

      2. *-commutative 97.3%

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

      3. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

      1. add-cube-cbrt 89.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 89.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 89.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 89.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 89.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 89.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in t around inf 51.1%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -100000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-183}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6600000000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 8: 82.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+49} \lor \neg \left(z \leq 8.5 \cdot 10^{+18}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e+49) (not (<= z 8.5e+18)))
   (* 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 <= -4.4e+49) || !(z <= 8.5e+18)) {
		tmp = 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 <= (-4.4d+49)) .or. (.not. (z <= 8.5d+18))) then
        tmp = 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 <= -4.4e+49) || !(z <= 8.5e+18)) {
		tmp = 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 <= -4.4e+49) or not (z <= 8.5e+18):
		tmp = 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 <= -4.4e+49) || !(z <= 8.5e+18))
		tmp = 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 <= -4.4e+49) || ~((z <= 8.5e+18)))
		tmp = 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, -4.4e+49], N[Not[LessEqual[z, 8.5e+18]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $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 < -4.4000000000000001e49 or 8.5e18 < z

   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+ 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around inf 80.9%

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

   if -4.4000000000000001e49 < z < 8.5e18

   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. +-commutative 98.0%

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

      3. fma-def 98.0%

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

      4. associate-*l* 98.6%

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

      5. *-commutative 98.6%

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

      6. *-commutative 98.6%

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

      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. *-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. Taylor expanded in y around 0 88.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+49} \lor \neg \left(z \leq 8.5 \cdot 10^{+18}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 9: 87.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -240000000000 \lor \neg \left(z \leq 1.15 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -240000000000.0) (not (<= z 1.15e-7)))
   (+ 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 <= -240000000000.0) || !(z <= 1.15e-7)) {
		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 <= (-240000000000.0d0)) .or. (.not. (z <= 1.15d-7))) 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 <= -240000000000.0) || !(z <= 1.15e-7)) {
		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 <= -240000000000.0) or not (z <= 1.15e-7):
		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 <= -240000000000.0) || !(z <= 1.15e-7))
		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 <= -240000000000.0) || ~((z <= 1.15e-7)))
		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, -240000000000.0], N[Not[LessEqual[z, 1.15e-7]], $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 < -2.4e11 or 1.14999999999999997e-7 < z

   1. Initial program 86.5%

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

      1. associate-+l+ 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. +-commutative 78.2%

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

      3. associate-*r* 87.3%

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

      4. distribute-rgt-in 91.6%

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

   6. Simplified 91.6%

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

   if -2.4e11 < z < 1.14999999999999997e-7

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. +-commutative 97.8%

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

      3. fma-def 97.8%

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

      4. associate-*l* 98.5%

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

      5. *-commutative 98.5%

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

      6. *-commutative 98.5%

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

      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. *-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. Taylor expanded in y around 0 89.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -240000000000 \lor \neg \left(z \leq 1.15 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 10: 80.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+54}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + y \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.08e+54)
   (+ (* (* z a) b) (* y z))
   (if (<= z 3e+18) (+ x (* a (+ t (* z b)))) (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.08e+54) {
		tmp = ((z * a) * b) + (y * z);
	} else if (z <= 3e+18) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = 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 (z <= (-1.08d+54)) then
        tmp = ((z * a) * b) + (y * z)
    else if (z <= 3d+18) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = 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 (z <= -1.08e+54) {
		tmp = ((z * a) * b) + (y * z);
	} else if (z <= 3e+18) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.08e+54:
		tmp = ((z * a) * b) + (y * z)
	elif z <= 3e+18:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.08e+54)
		tmp = Float64(Float64(Float64(z * a) * b) + Float64(y * z));
	elseif (z <= 3e+18)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = 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 (z <= -1.08e+54)
		tmp = ((z * a) * b) + (y * z);
	elseif (z <= 3e+18)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.08e+54], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+18], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000008e54

   1. Initial program 91.8%

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

      1. associate-+l+ 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 84.3%

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

      1. +-commutative 84.3%

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

      2. distribute-lft-in 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-*r* 76.4%

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

   6. Applied egg-rr 76.4%

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

   7. Taylor expanded in z around 0 76.4%

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

      1. associate-*r* 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*l* 84.3%

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

   9. Simplified 84.3%

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

   if -1.08000000000000008e54 < z < 3e18

   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. +-commutative 98.0%

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

      3. fma-def 98.0%

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

      4. associate-*l* 98.6%

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

      5. *-commutative 98.6%

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

      6. *-commutative 98.6%

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

      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. *-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. Taylor expanded in y around 0 88.9%

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

   if 3e18 < z

   1. Initial program 77.6%

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

      1. associate-+l+ 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in z around inf 76.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+54}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + y \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 11: 62.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= z -2.2e+15)
     t_1
     (if (<= z 5.6) (+ x (* t a)) (if (<= z 2.8e+217) t_1 (* a (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -2.2e+15) {
		tmp = t_1;
	} else if (z <= 5.6) {
		tmp = x + (t * a);
	} else if (z <= 2.8e+217) {
		tmp = t_1;
	} else {
		tmp = a * (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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (z <= (-2.2d+15)) then
        tmp = t_1
    else if (z <= 5.6d0) then
        tmp = x + (t * a)
    else if (z <= 2.8d+217) then
        tmp = t_1
    else
        tmp = a * (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 t_1 = x + (y * z);
	double tmp;
	if (z <= -2.2e+15) {
		tmp = t_1;
	} else if (z <= 5.6) {
		tmp = x + (t * a);
	} else if (z <= 2.8e+217) {
		tmp = t_1;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if z <= -2.2e+15:
		tmp = t_1
	elif z <= 5.6:
		tmp = x + (t * a)
	elif z <= 2.8e+217:
		tmp = t_1
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -2.2e+15)
		tmp = t_1;
	elseif (z <= 5.6)
		tmp = Float64(x + Float64(t * a));
	elseif (z <= 2.8e+217)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(z * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (z <= -2.2e+15)
		tmp = t_1;
	elseif (z <= 5.6)
		tmp = x + (t * a);
	elseif (z <= 2.8e+217)
		tmp = t_1;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+15], t$95$1, If[LessEqual[z, 5.6], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+217], t$95$1, N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e15 or 5.5999999999999996 < z < 2.79999999999999994e217

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. *-commutative 92.3%

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

      3. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around 0 65.5%

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

   if -2.2e15 < z < 5.5999999999999996

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around 0 76.6%

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

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   if 2.79999999999999994e217 < z

   1. Initial program 50.4%

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

      1. associate-+l+ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l* 56.3%

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

   3. Simplified 56.3%

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

      1. add-cube-cbrt 56.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 56.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 56.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 56.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 56.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 56.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 88.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 5.6:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+217}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 12: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-28} \lor \neg \left(a \leq 1.7 \cdot 10^{-25}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3e-28) (not (<= a 1.7e-25)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3e-28) || !(a <= 1.7e-25)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	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-28)) .or. (.not. (a <= 1.7d-25))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    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-28) || !(a <= 1.7e-25)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3e-28) or not (a <= 1.7e-25):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3e-28) || !(a <= 1.7e-25))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3e-28) || ~((a <= 1.7e-25)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3e-28], N[Not[LessEqual[a, 1.7e-25]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.00000000000000003e-28 or 1.70000000000000001e-25 < a

   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. *-commutative 86.2%

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

      3. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

      1. add-cube-cbrt 80.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 80.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 80.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 80.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 80.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 80.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in z around inf 72.4%

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

      1. distribute-lft-in 78.6%

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

      2. *-commutative 78.6%

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

   8. Simplified 78.6%

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

   if -3.00000000000000003e-28 < a < 1.70000000000000001e-25

   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. associate-+l+ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 79.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-28} \lor \neg \left(a \leq 1.7 \cdot 10^{-25}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 13: 74.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+14} \lor \neg \left(z \leq 1800000000000\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.45e+14) (not (<= z 1800000000000.0)))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.45e+14) || !(z <= 1800000000000.0)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	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 <= (-2.45d+14)) .or. (.not. (z <= 1800000000000.0d0))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    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 <= -2.45e+14) || !(z <= 1800000000000.0)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.45e+14) or not (z <= 1800000000000.0):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.45e+14) || !(z <= 1800000000000.0))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.45e+14) || ~((z <= 1800000000000.0)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.45e+14], N[Not[LessEqual[z, 1800000000000.0]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e14 or 1.8e12 < z

   1. Initial program 86.0%

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

      1. associate-+l+ 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in z around inf 79.9%

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

   if -2.45e14 < z < 1.8e12

   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. *-commutative 97.9%

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

      3. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in z around 0 76.6%

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

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+14} \lor \neg \left(z \leq 1800000000000\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 14: 38.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-45} \lor \neg \left(t \leq 2.75 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.8e-45) (not (<= t 2.75e+26))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.8e-45) || !(t <= 2.75e+26)) {
		tmp = t * a;
	} 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 ((t <= (-3.8d-45)) .or. (.not. (t <= 2.75d+26))) then
        tmp = t * a
    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 ((t <= -3.8e-45) || !(t <= 2.75e+26)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.8e-45) or not (t <= 2.75e+26):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.8e-45) || !(t <= 2.75e+26))
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.8e-45) || ~((t <= 2.75e+26)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.8e-45], N[Not[LessEqual[t, 2.75e+26]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.79999999999999997e-45 or 2.7499999999999998e26 < t

   1. Initial program 91.0%

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

      1. associate-+l+ 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

      1. add-cube-cbrt 86.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + y \cdot z} \cdot \sqrt[3]{x + y \cdot z}\right) \cdot \sqrt[3]{x + y \cdot z}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      2. pow3 86.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + y \cdot z}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      3. +-commutative 86.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot z + x}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      4. *-commutative 86.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot y} + x}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

      5. fma-def 86.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, y, x\right)}}\right)}^{3} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   5. Applied egg-rr 86.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, y, x\right)}\right)}^{3}} + \left(t \cdot a + z \cdot \left(a \cdot b\right)\right) \]

   6. Taylor expanded in t around inf 45.6%

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

   if -3.79999999999999997e-45 < t < 2.7499999999999998e26

   1. Initial program 94.9%

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

      1. associate-+l+ 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 40.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-45} \lor \neg \left(t \leq 2.75 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 26.8% 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 92.7%

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

   1. associate-+l+ 92.7%

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

   2. *-commutative 92.7%

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

   3. associate-*l* 90.3%

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

3. Simplified 90.3%

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

4. Taylor expanded in x around inf 26.6%

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

5. Final simplification 26.6%

   \[\leadsto x \]

Developer target: 97.4% 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 2023305 
(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)))