Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 93.2% → 96.7%

Time: 13.1s

Alternatives: 16

Speedup: 0.5×

• 32.6% 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: 93.2% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l* 7.7%

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

   3. Simplified 7.7%

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

   4. Taylor expanded in z around inf 77.0%

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

4. Final simplification 96.2%

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

Alternative 2: 94.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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%

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

   3. *-commutative 92.3%

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

   4. *-commutative 92.3%

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

   5. associate-*l* 93.4%

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

   6. distribute-rgt-out 95.3%

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

   7. fma-def 96.1%

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

   8. *-commutative 96.1%

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

   9. +-commutative 96.1%

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

   10. fma-def 96.1%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

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

Alternative 3: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+38} \lor \neg \left(a \leq 1.2 \cdot 10^{-164} \lor \neg \left(a \leq 3.7 \cdot 10^{-147}\right) \land \left(a \leq 6.5 \cdot 10^{-53} \lor \neg \left(a \leq 1.9 \cdot 10^{+14}\right) \land a \leq 1.26 \cdot 10^{+54}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.8e+38)
         (not
          (or (<= a 1.2e-164)
              (and (not (<= a 3.7e-147))
                   (or (<= a 6.5e-53)
                       (and (not (<= a 1.9e+14)) (<= a 1.26e+54)))))))
   (* a (+ t (* z b)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.8e+38) || !((a <= 1.2e-164) || (!(a <= 3.7e-147) && ((a <= 6.5e-53) || (!(a <= 1.9e+14) && (a <= 1.26e+54)))))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.8d+38)) .or. (.not. (a <= 1.2d-164) .or. (.not. (a <= 3.7d-147)) .and. (a <= 6.5d-53) .or. (.not. (a <= 1.9d+14)) .and. (a <= 1.26d+54))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.8e+38) || !((a <= 1.2e-164) || (!(a <= 3.7e-147) && ((a <= 6.5e-53) || (!(a <= 1.9e+14) && (a <= 1.26e+54)))))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.8e+38) or not ((a <= 1.2e-164) or (not (a <= 3.7e-147) and ((a <= 6.5e-53) or (not (a <= 1.9e+14) and (a <= 1.26e+54))))):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.8e+38) || !((a <= 1.2e-164) || (!(a <= 3.7e-147) && ((a <= 6.5e-53) || (!(a <= 1.9e+14) && (a <= 1.26e+54))))))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.8e+38) || ~(((a <= 1.2e-164) || (~((a <= 3.7e-147)) && ((a <= 6.5e-53) || (~((a <= 1.9e+14)) && (a <= 1.26e+54)))))))
		tmp = a * (t + (z * b));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.8e+38], N[Not[Or[LessEqual[a, 1.2e-164], And[N[Not[LessEqual[a, 3.7e-147]], $MachinePrecision], Or[LessEqual[a, 6.5e-53], And[N[Not[LessEqual[a, 1.9e+14]], $MachinePrecision], LessEqual[a, 1.26e+54]]]]]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e38 or 1.19999999999999992e-164 < a < 3.7000000000000002e-147 or 6.4999999999999997e-53 < a < 1.9e14 or 1.25999999999999995e54 < a

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in a around inf 74.7%

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

   if -2.8e38 < a < 1.19999999999999992e-164 or 3.7000000000000002e-147 < a < 6.4999999999999997e-53 or 1.9e14 < a < 1.25999999999999995e54

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in a around 0 80.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+38} \lor \neg \left(a \leq 1.2 \cdot 10^{-164} \lor \neg \left(a \leq 3.7 \cdot 10^{-147}\right) \land \left(a \leq 6.5 \cdot 10^{-53} \lor \neg \left(a \leq 1.9 \cdot 10^{+14}\right) \land a \leq 1.26 \cdot 10^{+54}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 4: 57.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot t\\ \mathbf{if}\;y \leq -2 \cdot 10^{+236}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+109}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a t))))
   (if (<= y -2e+236)
     (* z y)
     (if (<= y -2.4e+226)
       t_1
       (if (<= y -1.5e+109)
         (* z y)
         (if (<= y 8.8e+43)
           t_1
           (if (<= y 3.2e+89)
             (* a (* z b))
             (if (<= y 5e+209) t_1 (* z y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double tmp;
	if (y <= -2e+236) {
		tmp = z * y;
	} else if (y <= -2.4e+226) {
		tmp = t_1;
	} else if (y <= -1.5e+109) {
		tmp = z * y;
	} else if (y <= 8.8e+43) {
		tmp = t_1;
	} else if (y <= 3.2e+89) {
		tmp = a * (z * b);
	} else if (y <= 5e+209) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * t)
    if (y <= (-2d+236)) then
        tmp = z * y
    else if (y <= (-2.4d+226)) then
        tmp = t_1
    else if (y <= (-1.5d+109)) then
        tmp = z * y
    else if (y <= 8.8d+43) then
        tmp = t_1
    else if (y <= 3.2d+89) then
        tmp = a * (z * b)
    else if (y <= 5d+209) then
        tmp = t_1
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double tmp;
	if (y <= -2e+236) {
		tmp = z * y;
	} else if (y <= -2.4e+226) {
		tmp = t_1;
	} else if (y <= -1.5e+109) {
		tmp = z * y;
	} else if (y <= 8.8e+43) {
		tmp = t_1;
	} else if (y <= 3.2e+89) {
		tmp = a * (z * b);
	} else if (y <= 5e+209) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * t)
	tmp = 0
	if y <= -2e+236:
		tmp = z * y
	elif y <= -2.4e+226:
		tmp = t_1
	elif y <= -1.5e+109:
		tmp = z * y
	elif y <= 8.8e+43:
		tmp = t_1
	elif y <= 3.2e+89:
		tmp = a * (z * b)
	elif y <= 5e+209:
		tmp = t_1
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * t))
	tmp = 0.0
	if (y <= -2e+236)
		tmp = Float64(z * y);
	elseif (y <= -2.4e+226)
		tmp = t_1;
	elseif (y <= -1.5e+109)
		tmp = Float64(z * y);
	elseif (y <= 8.8e+43)
		tmp = t_1;
	elseif (y <= 3.2e+89)
		tmp = Float64(a * Float64(z * b));
	elseif (y <= 5e+209)
		tmp = t_1;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * t);
	tmp = 0.0;
	if (y <= -2e+236)
		tmp = z * y;
	elseif (y <= -2.4e+226)
		tmp = t_1;
	elseif (y <= -1.5e+109)
		tmp = z * y;
	elseif (y <= 8.8e+43)
		tmp = t_1;
	elseif (y <= 3.2e+89)
		tmp = a * (z * b);
	elseif (y <= 5e+209)
		tmp = t_1;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+236], N[(z * y), $MachinePrecision], If[LessEqual[y, -2.4e+226], t$95$1, If[LessEqual[y, -1.5e+109], N[(z * y), $MachinePrecision], If[LessEqual[y, 8.8e+43], t$95$1, If[LessEqual[y, 3.2e+89], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+209], t$95$1, N[(z * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000011e236 or -2.4e226 < y < -1.50000000000000008e109 or 4.99999999999999964e209 < y

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   if -2.00000000000000011e236 < y < -2.4e226 or -1.50000000000000008e109 < y < 8.80000000000000002e43 or 3.19999999999999987e89 < y < 4.99999999999999964e209

   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. *-commutative 92.2%

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

      2. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 64.2%

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

   if 8.80000000000000002e43 < y < 3.19999999999999987e89

   1. Initial program 88.9%

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

      1. +-commutative 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*l* 88.7%

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

      4. *-commutative 88.7%

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

      5. fma-def 88.7%

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

      6. *-commutative 88.7%

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

      7. +-commutative 88.7%

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

      8. fma-def 88.7%

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

      9. +-commutative 88.7%

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

      10. fma-def 88.7%

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

   3. Simplified 88.7%

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

      1. fma-udef 88.7%

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

      2. fma-udef 88.7%

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

      3. +-commutative 88.7%

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

      4. associate-+r+ 88.7%

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

      5. *-commutative 88.7%

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

      6. *-commutative 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in b around inf 79.5%

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

      1. *-commutative 79.5%

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

   8. Simplified 79.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+236}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+226}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+109}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+209}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 5: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot t\\ t_2 := x + z \cdot y\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -54000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a t))) (t_2 (+ x (* z y))))
   (if (<= y -1.8e+107)
     t_2
     (if (<= y -1.12e+47)
       t_1
       (if (<= y -54000.0)
         t_2
         (if (<= y 8.8e+43)
           t_1
           (if (<= y 9.4e+89) (* a (* z b)) (if (<= y 7.8e+206) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double t_2 = x + (z * y);
	double tmp;
	if (y <= -1.8e+107) {
		tmp = t_2;
	} else if (y <= -1.12e+47) {
		tmp = t_1;
	} else if (y <= -54000.0) {
		tmp = t_2;
	} else if (y <= 8.8e+43) {
		tmp = t_1;
	} else if (y <= 9.4e+89) {
		tmp = a * (z * b);
	} else if (y <= 7.8e+206) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * t)
    t_2 = x + (z * y)
    if (y <= (-1.8d+107)) then
        tmp = t_2
    else if (y <= (-1.12d+47)) then
        tmp = t_1
    else if (y <= (-54000.0d0)) then
        tmp = t_2
    else if (y <= 8.8d+43) then
        tmp = t_1
    else if (y <= 9.4d+89) then
        tmp = a * (z * b)
    else if (y <= 7.8d+206) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double t_2 = x + (z * y);
	double tmp;
	if (y <= -1.8e+107) {
		tmp = t_2;
	} else if (y <= -1.12e+47) {
		tmp = t_1;
	} else if (y <= -54000.0) {
		tmp = t_2;
	} else if (y <= 8.8e+43) {
		tmp = t_1;
	} else if (y <= 9.4e+89) {
		tmp = a * (z * b);
	} else if (y <= 7.8e+206) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * t)
	t_2 = x + (z * y)
	tmp = 0
	if y <= -1.8e+107:
		tmp = t_2
	elif y <= -1.12e+47:
		tmp = t_1
	elif y <= -54000.0:
		tmp = t_2
	elif y <= 8.8e+43:
		tmp = t_1
	elif y <= 9.4e+89:
		tmp = a * (z * b)
	elif y <= 7.8e+206:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * t))
	t_2 = Float64(x + Float64(z * y))
	tmp = 0.0
	if (y <= -1.8e+107)
		tmp = t_2;
	elseif (y <= -1.12e+47)
		tmp = t_1;
	elseif (y <= -54000.0)
		tmp = t_2;
	elseif (y <= 8.8e+43)
		tmp = t_1;
	elseif (y <= 9.4e+89)
		tmp = Float64(a * Float64(z * b));
	elseif (y <= 7.8e+206)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * t);
	t_2 = x + (z * y);
	tmp = 0.0;
	if (y <= -1.8e+107)
		tmp = t_2;
	elseif (y <= -1.12e+47)
		tmp = t_1;
	elseif (y <= -54000.0)
		tmp = t_2;
	elseif (y <= 8.8e+43)
		tmp = t_1;
	elseif (y <= 9.4e+89)
		tmp = a * (z * b);
	elseif (y <= 7.8e+206)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+107], t$95$2, If[LessEqual[y, -1.12e+47], t$95$1, If[LessEqual[y, -54000.0], t$95$2, If[LessEqual[y, 8.8e+43], t$95$1, If[LessEqual[y, 9.4e+89], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+206], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e107 or -1.12000000000000007e47 < y < -54000 or 7.8e206 < y

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in a around 0 78.0%

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

   if -1.7999999999999999e107 < y < -1.12000000000000007e47 or -54000 < y < 8.80000000000000002e43 or 9.40000000000000043e89 < y < 7.8e206

   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. *-commutative 92.1%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 65.4%

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

   if 8.80000000000000002e43 < y < 9.40000000000000043e89

   1. Initial program 88.9%

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

      1. +-commutative 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*l* 88.7%

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

      4. *-commutative 88.7%

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

      5. fma-def 88.7%

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

      6. *-commutative 88.7%

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

      7. +-commutative 88.7%

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

      8. fma-def 88.7%

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

      9. +-commutative 88.7%

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

      10. fma-def 88.7%

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

   3. Simplified 88.7%

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

      1. fma-udef 88.7%

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

      2. fma-udef 88.7%

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

      3. +-commutative 88.7%

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

      4. associate-+r+ 88.7%

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

      5. *-commutative 88.7%

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

      6. *-commutative 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in b around inf 79.5%

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

      1. *-commutative 79.5%

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

   8. Simplified 79.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+107}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+47}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;y \leq -54000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+206}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 6: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;a \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))) (t_2 (* z (+ y (* a b)))))
   (if (<= a -1.28e+39)
     t_1
     (if (<= a 1.4e-165)
       (+ x (* z y))
       (if (<= a 5.7e-96)
         t_2
         (if (<= a 1.5e-15)
           (+ x (* b (* a z)))
           (if (<= a 1.26e+54) t_2 t_1)))))))

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 = z * (y + (a * b));
	double tmp;
	if (a <= -1.28e+39) {
		tmp = t_1;
	} else if (a <= 1.4e-165) {
		tmp = x + (z * y);
	} else if (a <= 5.7e-96) {
		tmp = t_2;
	} else if (a <= 1.5e-15) {
		tmp = x + (b * (a * z));
	} else if (a <= 1.26e+54) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    t_2 = z * (y + (a * b))
    if (a <= (-1.28d+39)) then
        tmp = t_1
    else if (a <= 1.4d-165) then
        tmp = x + (z * y)
    else if (a <= 5.7d-96) then
        tmp = t_2
    else if (a <= 1.5d-15) then
        tmp = x + (b * (a * z))
    else if (a <= 1.26d+54) then
        tmp = t_2
    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 = a * (t + (z * b));
	double t_2 = z * (y + (a * b));
	double tmp;
	if (a <= -1.28e+39) {
		tmp = t_1;
	} else if (a <= 1.4e-165) {
		tmp = x + (z * y);
	} else if (a <= 5.7e-96) {
		tmp = t_2;
	} else if (a <= 1.5e-15) {
		tmp = x + (b * (a * z));
	} else if (a <= 1.26e+54) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	t_2 = z * (y + (a * b))
	tmp = 0
	if a <= -1.28e+39:
		tmp = t_1
	elif a <= 1.4e-165:
		tmp = x + (z * y)
	elif a <= 5.7e-96:
		tmp = t_2
	elif a <= 1.5e-15:
		tmp = x + (b * (a * z))
	elif a <= 1.26e+54:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (a <= -1.28e+39)
		tmp = t_1;
	elseif (a <= 1.4e-165)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 5.7e-96)
		tmp = t_2;
	elseif (a <= 1.5e-15)
		tmp = Float64(x + Float64(b * Float64(a * z)));
	elseif (a <= 1.26e+54)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (a <= -1.28e+39)
		tmp = t_1;
	elseif (a <= 1.4e-165)
		tmp = x + (z * y);
	elseif (a <= 5.7e-96)
		tmp = t_2;
	elseif (a <= 1.5e-15)
		tmp = x + (b * (a * z));
	elseif (a <= 1.26e+54)
		tmp = t_2;
	else
		tmp = t_1;
	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[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.28e+39], t$95$1, If[LessEqual[a, 1.4e-165], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e-96], t$95$2, If[LessEqual[a, 1.5e-15], N[(x + N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.26e+54], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.27999999999999994e39 or 1.25999999999999995e54 < a

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in a around inf 75.3%

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

   if -1.27999999999999994e39 < a < 1.4e-165

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 82.0%

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

   if 1.4e-165 < a < 5.70000000000000009e-96 or 1.5e-15 < a < 1.25999999999999995e54

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 72.4%

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

   if 5.70000000000000009e-96 < a < 1.5e-15

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-*r* 88.4%

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

      3. distribute-rgt-in 88.4%

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

      4. +-commutative 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in y around 0 77.2%

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

   8. Taylor expanded in z around 0 77.1%

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

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*r* 77.1%

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

   10. Simplified 77.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 7: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 15500:\\ \;\;\;\;x + z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))) (t_2 (* z (+ y (* a b)))))
   (if (<= a -9.8e+33)
     t_1
     (if (<= a 1.55e-165)
       (+ x (* z y))
       (if (<= a 1.38e-95)
         t_2
         (if (<= a 15500.0)
           (+ x (* z (* a b)))
           (if (<= a 1.26e+54) t_2 t_1)))))))

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 = z * (y + (a * b));
	double tmp;
	if (a <= -9.8e+33) {
		tmp = t_1;
	} else if (a <= 1.55e-165) {
		tmp = x + (z * y);
	} else if (a <= 1.38e-95) {
		tmp = t_2;
	} else if (a <= 15500.0) {
		tmp = x + (z * (a * b));
	} else if (a <= 1.26e+54) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    t_2 = z * (y + (a * b))
    if (a <= (-9.8d+33)) then
        tmp = t_1
    else if (a <= 1.55d-165) then
        tmp = x + (z * y)
    else if (a <= 1.38d-95) then
        tmp = t_2
    else if (a <= 15500.0d0) then
        tmp = x + (z * (a * b))
    else if (a <= 1.26d+54) then
        tmp = t_2
    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 = a * (t + (z * b));
	double t_2 = z * (y + (a * b));
	double tmp;
	if (a <= -9.8e+33) {
		tmp = t_1;
	} else if (a <= 1.55e-165) {
		tmp = x + (z * y);
	} else if (a <= 1.38e-95) {
		tmp = t_2;
	} else if (a <= 15500.0) {
		tmp = x + (z * (a * b));
	} else if (a <= 1.26e+54) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	t_2 = z * (y + (a * b))
	tmp = 0
	if a <= -9.8e+33:
		tmp = t_1
	elif a <= 1.55e-165:
		tmp = x + (z * y)
	elif a <= 1.38e-95:
		tmp = t_2
	elif a <= 15500.0:
		tmp = x + (z * (a * b))
	elif a <= 1.26e+54:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (a <= -9.8e+33)
		tmp = t_1;
	elseif (a <= 1.55e-165)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 1.38e-95)
		tmp = t_2;
	elseif (a <= 15500.0)
		tmp = Float64(x + Float64(z * Float64(a * b)));
	elseif (a <= 1.26e+54)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (a <= -9.8e+33)
		tmp = t_1;
	elseif (a <= 1.55e-165)
		tmp = x + (z * y);
	elseif (a <= 1.38e-95)
		tmp = t_2;
	elseif (a <= 15500.0)
		tmp = x + (z * (a * b));
	elseif (a <= 1.26e+54)
		tmp = t_2;
	else
		tmp = t_1;
	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[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+33], t$95$1, If[LessEqual[a, 1.55e-165], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.38e-95], t$95$2, If[LessEqual[a, 15500.0], N[(x + N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.26e+54], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.80000000000000027e33 or 1.25999999999999995e54 < a

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in a around inf 75.3%

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

   if -9.80000000000000027e33 < a < 1.54999999999999998e-165

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 82.0%

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

   if 1.54999999999999998e-165 < a < 1.38e-95 or 15500 < a < 1.25999999999999995e54

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 75.0%

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

   if 1.38e-95 < a < 15500

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-*r* 86.0%

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

      3. distribute-rgt-in 86.0%

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

      4. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in y around 0 72.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;a \leq 15500:\\ \;\;\;\;x + z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ t_2 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-97}:\\ \;\;\;\;t_2 + z \cdot y\\ \mathbf{elif}\;a \leq 290000:\\ \;\;\;\;x + t_2\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))) (t_2 (* z (* a b))))
   (if (<= a -3e+36)
     t_1
     (if (<= a 1.55e-165)
       (+ x (* z y))
       (if (<= a 2.4e-97)
         (+ t_2 (* z y))
         (if (<= a 290000.0)
           (+ x t_2)
           (if (<= a 1.26e+54) (* z (+ y (* a b))) t_1)))))))

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 = z * (a * b);
	double tmp;
	if (a <= -3e+36) {
		tmp = t_1;
	} else if (a <= 1.55e-165) {
		tmp = x + (z * y);
	} else if (a <= 2.4e-97) {
		tmp = t_2 + (z * y);
	} else if (a <= 290000.0) {
		tmp = x + t_2;
	} else if (a <= 1.26e+54) {
		tmp = z * (y + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    t_2 = z * (a * b)
    if (a <= (-3d+36)) then
        tmp = t_1
    else if (a <= 1.55d-165) then
        tmp = x + (z * y)
    else if (a <= 2.4d-97) then
        tmp = t_2 + (z * y)
    else if (a <= 290000.0d0) then
        tmp = x + t_2
    else if (a <= 1.26d+54) then
        tmp = z * (y + (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double t_2 = z * (a * b);
	double tmp;
	if (a <= -3e+36) {
		tmp = t_1;
	} else if (a <= 1.55e-165) {
		tmp = x + (z * y);
	} else if (a <= 2.4e-97) {
		tmp = t_2 + (z * y);
	} else if (a <= 290000.0) {
		tmp = x + t_2;
	} else if (a <= 1.26e+54) {
		tmp = z * (y + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	t_2 = z * (a * b)
	tmp = 0
	if a <= -3e+36:
		tmp = t_1
	elif a <= 1.55e-165:
		tmp = x + (z * y)
	elif a <= 2.4e-97:
		tmp = t_2 + (z * y)
	elif a <= 290000.0:
		tmp = x + t_2
	elif a <= 1.26e+54:
		tmp = z * (y + (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	t_2 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (a <= -3e+36)
		tmp = t_1;
	elseif (a <= 1.55e-165)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 2.4e-97)
		tmp = Float64(t_2 + Float64(z * y));
	elseif (a <= 290000.0)
		tmp = Float64(x + t_2);
	elseif (a <= 1.26e+54)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	t_2 = z * (a * b);
	tmp = 0.0;
	if (a <= -3e+36)
		tmp = t_1;
	elseif (a <= 1.55e-165)
		tmp = x + (z * y);
	elseif (a <= 2.4e-97)
		tmp = t_2 + (z * y);
	elseif (a <= 290000.0)
		tmp = x + t_2;
	elseif (a <= 1.26e+54)
		tmp = z * (y + (a * b));
	else
		tmp = t_1;
	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[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+36], t$95$1, If[LessEqual[a, 1.55e-165], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-97], N[(t$95$2 + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 290000.0], N[(x + t$95$2), $MachinePrecision], If[LessEqual[a, 1.26e+54], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3e36 or 1.25999999999999995e54 < a

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in a around inf 75.3%

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

   if -3e36 < a < 1.54999999999999998e-165

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 82.0%

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

   if 1.54999999999999998e-165 < a < 2.4e-97

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. distribute-lft-in 80.2%

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

   6. Applied egg-rr 80.2%

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

   if 2.4e-97 < a < 2.9e5

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-*r* 86.0%

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

      3. distribute-rgt-in 86.0%

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

      4. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in y around 0 72.2%

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

   if 2.9e5 < a < 1.25999999999999995e54

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in z around inf 69.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \left(a \cdot b\right) + z \cdot y\\ \mathbf{elif}\;a \leq 290000:\\ \;\;\;\;x + z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 9: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot b\right)\\ t_2 := x + a \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a b))))) (t_2 (+ x (* a t))))
   (if (<= t -7.2e+170)
     t_2
     (if (<= t 1.9e+79)
       t_1
       (if (<= t 2.1e+154)
         t_2
         (if (<= t 1.55e+171) t_1 (* a (+ t (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double t_2 = x + (a * t);
	double tmp;
	if (t <= -7.2e+170) {
		tmp = t_2;
	} else if (t <= 1.9e+79) {
		tmp = t_1;
	} else if (t <= 2.1e+154) {
		tmp = t_2;
	} else if (t <= 1.55e+171) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y + (a * b)))
    t_2 = x + (a * t)
    if (t <= (-7.2d+170)) then
        tmp = t_2
    else if (t <= 1.9d+79) then
        tmp = t_1
    else if (t <= 2.1d+154) then
        tmp = t_2
    else if (t <= 1.55d+171) then
        tmp = t_1
    else
        tmp = 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 t_1 = x + (z * (y + (a * b)));
	double t_2 = x + (a * t);
	double tmp;
	if (t <= -7.2e+170) {
		tmp = t_2;
	} else if (t <= 1.9e+79) {
		tmp = t_1;
	} else if (t <= 2.1e+154) {
		tmp = t_2;
	} else if (t <= 1.55e+171) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * b)))
	t_2 = x + (a * t)
	tmp = 0
	if t <= -7.2e+170:
		tmp = t_2
	elif t <= 1.9e+79:
		tmp = t_1
	elif t <= 2.1e+154:
		tmp = t_2
	elif t <= 1.55e+171:
		tmp = t_1
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	t_2 = Float64(x + Float64(a * t))
	tmp = 0.0
	if (t <= -7.2e+170)
		tmp = t_2;
	elseif (t <= 1.9e+79)
		tmp = t_1;
	elseif (t <= 2.1e+154)
		tmp = t_2;
	elseif (t <= 1.55e+171)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * b)));
	t_2 = x + (a * t);
	tmp = 0.0;
	if (t <= -7.2e+170)
		tmp = t_2;
	elseif (t <= 1.9e+79)
		tmp = t_1;
	elseif (t <= 2.1e+154)
		tmp = t_2;
	elseif (t <= 1.55e+171)
		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[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+170], t$95$2, If[LessEqual[t, 1.9e+79], t$95$1, If[LessEqual[t, 2.1e+154], t$95$2, If[LessEqual[t, 1.55e+171], t$95$1, N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.1999999999999999e170 or 1.9000000000000001e79 < t < 2.09999999999999994e154

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 86.9%

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

   if -7.1999999999999999e170 < t < 1.9000000000000001e79 or 2.09999999999999994e154 < t < 1.5499999999999999e171

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-*r* 84.7%

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

      3. distribute-rgt-in 86.9%

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

      4. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if 1.5499999999999999e171 < t

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*l* 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around inf 71.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+79}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+154}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+171}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 10: 93.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z \cdot y\right) + a \cdot t\right) + z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.35e+129)
   (+ (* a (+ t (* z b))) (* z y))
   (+ (+ (+ x (* z y)) (* a t)) (* z (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.35e+129) {
		tmp = (a * (t + (z * b))) + (z * y);
	} else {
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.35d+129)) then
        tmp = (a * (t + (z * b))) + (z * y)
    else
        tmp = ((x + (z * y)) + (a * t)) + (z * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.35e+129) {
		tmp = (a * (t + (z * b))) + (z * y);
	} else {
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.35e+129:
		tmp = (a * (t + (z * b))) + (z * y)
	else:
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.35e+129)
		tmp = Float64(Float64(a * Float64(t + Float64(z * b))) + Float64(z * y));
	else
		tmp = Float64(Float64(Float64(x + Float64(z * y)) + Float64(a * t)) + Float64(z * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.35e+129)
		tmp = (a * (t + (z * b))) + (z * y);
	else
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.35e+129], N[(N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e129

   1. Initial program 80.8%

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

      1. associate-+l+ 80.8%

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

      2. +-commutative 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

      5. associate-*l* 90.2%

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

      6. distribute-rgt-out 97.5%

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

      7. fma-def 100.0%

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

      8. *-commutative 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 90.4%

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

   if -1.35e129 < a

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z \cdot y\right) + a \cdot t\right) + z \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 11: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+175}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+63}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+175)
   (+ x (* a t))
   (if (<= t 1.35e+63)
     (+ x (* z (+ y (* a b))))
     (+ (* a (+ t (* z b))) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+175) {
		tmp = x + (a * t);
	} else if (t <= 1.35e+63) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (a * (t + (z * b))) + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.8d+175)) then
        tmp = x + (a * t)
    else if (t <= 1.35d+63) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (a * (t + (z * b))) + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+175) {
		tmp = x + (a * t);
	} else if (t <= 1.35e+63) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (a * (t + (z * b))) + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.8e+175:
		tmp = x + (a * t)
	elif t <= 1.35e+63:
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (a * (t + (z * b))) + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+175)
		tmp = Float64(x + Float64(a * t));
	elseif (t <= 1.35e+63)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(a * Float64(t + Float64(z * b))) + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.8e+175)
		tmp = x + (a * t);
	elseif (t <= 1.35e+63)
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (a * (t + (z * b))) + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+175], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+63], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8e175

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 96.8%

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

   if -4.8e175 < t < 1.35000000000000009e63

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-*r* 83.8%

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

      3. distribute-rgt-in 86.2%

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

      4. +-commutative 86.2%

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

   6. Simplified 86.2%

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

   if 1.35000000000000009e63 < t

   1. Initial program 85.0%

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

      1. associate-+l+ 85.0%

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

      2. +-commutative 85.0%

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

      3. *-commutative 85.0%

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

      4. *-commutative 85.0%

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

      5. associate-*l* 86.7%

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

      6. distribute-rgt-out 95.0%

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

      7. fma-def 96.7%

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

      8. *-commutative 96.7%

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

      9. +-commutative 96.7%

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

      10. fma-def 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around 0 83.4%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+175}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+63}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + z \cdot y\\ \end{array} \]

Alternative 12: 39.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -54000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -54000.0)
   (* z y)
   (if (<= y 3.6e-280) (* a t) (if (<= y 4e+77) (* a (* z b)) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -54000.0) {
		tmp = z * y;
	} else if (y <= 3.6e-280) {
		tmp = a * t;
	} else if (y <= 4e+77) {
		tmp = a * (z * b);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-54000.0d0)) then
        tmp = z * y
    else if (y <= 3.6d-280) then
        tmp = a * t
    else if (y <= 4d+77) then
        tmp = a * (z * b)
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -54000.0) {
		tmp = z * y;
	} else if (y <= 3.6e-280) {
		tmp = a * t;
	} else if (y <= 4e+77) {
		tmp = a * (z * b);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -54000.0:
		tmp = z * y
	elif y <= 3.6e-280:
		tmp = a * t
	elif y <= 4e+77:
		tmp = a * (z * b)
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -54000.0)
		tmp = Float64(z * y);
	elseif (y <= 3.6e-280)
		tmp = Float64(a * t);
	elseif (y <= 4e+77)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -54000.0)
		tmp = z * y;
	elseif (y <= 3.6e-280)
		tmp = a * t;
	elseif (y <= 4e+77)
		tmp = a * (z * b);
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -54000.0], N[(z * y), $MachinePrecision], If[LessEqual[y, 3.6e-280], N[(a * t), $MachinePrecision], If[LessEqual[y, 4e+77], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -54000 or 3.99999999999999993e77 < y

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

   if -54000 < y < 3.59999999999999994e-280

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 40.0%

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

   if 3.59999999999999994e-280 < y < 3.99999999999999993e77

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*l* 93.9%

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

      4. *-commutative 93.9%

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

      5. fma-def 93.9%

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

      6. *-commutative 93.9%

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

      7. +-commutative 93.9%

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

      8. fma-def 93.9%

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

      9. +-commutative 93.9%

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

      10. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-udef 93.9%

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

      2. fma-udef 93.9%

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

      3. +-commutative 93.9%

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

      4. associate-+r+ 93.9%

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

      5. *-commutative 93.9%

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

      6. *-commutative 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in b around inf 40.0%

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

      1. *-commutative 40.0%

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

   8. Simplified 40.0%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -54000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 13: 39.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-280}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -50000.0)
   (* z y)
   (if (<= y 3.1e-280) (* a t) (if (<= y 8.5e+71) (* b (* a z)) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -50000.0) {
		tmp = z * y;
	} else if (y <= 3.1e-280) {
		tmp = a * t;
	} else if (y <= 8.5e+71) {
		tmp = b * (a * z);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-50000.0d0)) then
        tmp = z * y
    else if (y <= 3.1d-280) then
        tmp = a * t
    else if (y <= 8.5d+71) then
        tmp = b * (a * z)
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -50000.0) {
		tmp = z * y;
	} else if (y <= 3.1e-280) {
		tmp = a * t;
	} else if (y <= 8.5e+71) {
		tmp = b * (a * z);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -50000.0:
		tmp = z * y
	elif y <= 3.1e-280:
		tmp = a * t
	elif y <= 8.5e+71:
		tmp = b * (a * z)
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -50000.0)
		tmp = Float64(z * y);
	elseif (y <= 3.1e-280)
		tmp = Float64(a * t);
	elseif (y <= 8.5e+71)
		tmp = Float64(b * Float64(a * z));
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -50000.0)
		tmp = z * y;
	elseif (y <= 3.1e-280)
		tmp = a * t;
	elseif (y <= 8.5e+71)
		tmp = b * (a * z);
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -50000.0], N[(z * y), $MachinePrecision], If[LessEqual[y, 3.1e-280], N[(a * t), $MachinePrecision], If[LessEqual[y, 8.5e+71], N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e4 or 8.4999999999999996e71 < y

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

   if -5e4 < y < 3.10000000000000021e-280

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 40.0%

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

   if 3.10000000000000021e-280 < y < 8.4999999999999996e71

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*l* 93.9%

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

      4. *-commutative 93.9%

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

      5. fma-def 93.9%

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

      6. *-commutative 93.9%

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

      7. +-commutative 93.9%

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

      8. fma-def 93.9%

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

      9. +-commutative 93.9%

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

      10. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-udef 93.9%

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

      2. fma-udef 93.9%

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

      3. +-commutative 93.9%

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

      4. associate-+r+ 93.9%

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

      5. *-commutative 93.9%

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

      6. *-commutative 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in b around inf 40.0%

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

      1. *-commutative 40.0%

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

   8. Simplified 40.0%

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

   9. Taylor expanded in a around 0 40.0%

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

       1. associate-*r* 36.2%

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

       2. *-commutative 36.2%

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

       3. associate-*r* 40.7%

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

   11. Simplified 40.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-280}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 14: 39.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -52000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-300}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -52000.0)
   (* z y)
   (if (<= y 4.4e-300) (* a t) (if (<= y 2.2e+43) x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -52000.0) {
		tmp = z * y;
	} else if (y <= 4.4e-300) {
		tmp = a * t;
	} else if (y <= 2.2e+43) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-52000.0d0)) then
        tmp = z * y
    else if (y <= 4.4d-300) then
        tmp = a * t
    else if (y <= 2.2d+43) then
        tmp = x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -52000.0) {
		tmp = z * y;
	} else if (y <= 4.4e-300) {
		tmp = a * t;
	} else if (y <= 2.2e+43) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -52000.0:
		tmp = z * y
	elif y <= 4.4e-300:
		tmp = a * t
	elif y <= 2.2e+43:
		tmp = x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -52000.0)
		tmp = Float64(z * y);
	elseif (y <= 4.4e-300)
		tmp = Float64(a * t);
	elseif (y <= 2.2e+43)
		tmp = x;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -52000.0)
		tmp = z * y;
	elseif (y <= 4.4e-300)
		tmp = a * t;
	elseif (y <= 2.2e+43)
		tmp = x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -52000.0], N[(z * y), $MachinePrecision], If[LessEqual[y, 4.4e-300], N[(a * t), $MachinePrecision], If[LessEqual[y, 2.2e+43], x, N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -52000 or 2.20000000000000001e43 < y

   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. *-commutative 91.7%

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

      2. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   6. Simplified 51.1%

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

   if -52000 < y < 4.40000000000000004e-300

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 41.0%

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

   if 4.40000000000000004e-300 < y < 2.20000000000000001e43

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around inf 40.1%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -52000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-300}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 15: 38.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-115}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e-115) (* a t) (if (<= t 6.6e-18) x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e-115) {
		tmp = a * t;
	} else if (t <= 6.6e-18) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.2d-115)) then
        tmp = a * t
    else if (t <= 6.6d-18) then
        tmp = x
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e-115) {
		tmp = a * t;
	} else if (t <= 6.6e-18) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e-115:
		tmp = a * t
	elif t <= 6.6e-18:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e-115)
		tmp = Float64(a * t);
	elseif (t <= 6.6e-18)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e-115)
		tmp = a * t;
	elseif (t <= 6.6e-18)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e-115], N[(a * t), $MachinePrecision], If[LessEqual[t, 6.6e-18], x, N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e-115 or 6.6000000000000003e-18 < t

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in t around inf 42.7%

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

   if -3.2e-115 < t < 6.6000000000000003e-18

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around inf 38.2%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-115}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 16: 26.5% 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 92.3%

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

   1. *-commutative 92.3%

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

   2. associate-*l* 91.5%

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

3. Simplified 91.5%

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

4. Taylor expanded in x around inf 25.4%

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

5. Final simplification 25.4%

   \[\leadsto x \]

Developer target: 97.7% 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 2023283 
(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)))