Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 94.8%

Time: 9.8s

Alternatives: 15

Speedup: 0.5×

• 32.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2e+68)
   (+ (fma y z x) (* a (+ t (* z b))))
   (+ (* b (* a z)) (+ (+ x (* y z)) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2e+68) {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	} else {
		tmp = (b * (a * z)) + ((x + (y * z)) + (a * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2e+68)
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(b * Float64(a * z)) + Float64(Float64(x + Float64(y * z)) + Float64(a * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2e+68], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.99999999999999991e68

   1. Initial program 77.2%

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

      1. associate-+l+ 77.2%

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

      2. +-commutative 77.2%

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

      3. fma-def 77.2%

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

      4. *-commutative 77.2%

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

      5. associate-*l* 87.4%

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

      6. *-commutative 87.4%

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

      7. distribute-lft-out 92.8%

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

      8. remove-double-neg 92.8%

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

      9. *-commutative 92.8%

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

      10. distribute-lft-neg-out 92.8%

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

      11. sub-neg 92.8%

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

      12. sub-neg 92.8%

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

      13. distribute-lft-neg-in 92.8%

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

      14. remove-double-neg 92.8%

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

   3. Simplified 92.8%

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

   if -1.99999999999999991e68 < a

   1. Initial program 98.5%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \end{array} \]

Alternative 2: 96.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (* a z)) (+ (+ x (* y z)) (* a t)))))
   (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 = (b * (a * z)) + ((x + (y * z)) + (a * t));
	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 = (b * (a * z)) + ((x + (y * z)) + (a * t));
	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 = (b * (a * z)) + ((x + (y * z)) + (a * t))
	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(b * Float64(a * z)) + Float64(Float64(x + Float64(y * z)) + Float64(a * t)))
	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 = (b * (a * z)) + ((x + (y * z)) + (a * t));
	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[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $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 98.4%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in z around inf 66.7%

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

4. Final simplification 96.9%

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

Alternative 3: 37.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+171}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-297}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-140}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;x \leq 820000000:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3e+222)
   x
   (if (<= x -1.25e+171)
     (* a t)
     (if (<= x -7.5e+110)
       x
       (if (<= x -3.2e-297)
         (* y z)
         (if (<= x 2.5e-140)
           (* a t)
           (if (<= x 820000000.0)
             (* b (* a z))
             (if (<= x 5e+94) (* a t) x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+222) {
		tmp = x;
	} else if (x <= -1.25e+171) {
		tmp = a * t;
	} else if (x <= -7.5e+110) {
		tmp = x;
	} else if (x <= -3.2e-297) {
		tmp = y * z;
	} else if (x <= 2.5e-140) {
		tmp = a * t;
	} else if (x <= 820000000.0) {
		tmp = b * (a * z);
	} else if (x <= 5e+94) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3d+222)) then
        tmp = x
    else if (x <= (-1.25d+171)) then
        tmp = a * t
    else if (x <= (-7.5d+110)) then
        tmp = x
    else if (x <= (-3.2d-297)) then
        tmp = y * z
    else if (x <= 2.5d-140) then
        tmp = a * t
    else if (x <= 820000000.0d0) then
        tmp = b * (a * z)
    else if (x <= 5d+94) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+222) {
		tmp = x;
	} else if (x <= -1.25e+171) {
		tmp = a * t;
	} else if (x <= -7.5e+110) {
		tmp = x;
	} else if (x <= -3.2e-297) {
		tmp = y * z;
	} else if (x <= 2.5e-140) {
		tmp = a * t;
	} else if (x <= 820000000.0) {
		tmp = b * (a * z);
	} else if (x <= 5e+94) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3e+222:
		tmp = x
	elif x <= -1.25e+171:
		tmp = a * t
	elif x <= -7.5e+110:
		tmp = x
	elif x <= -3.2e-297:
		tmp = y * z
	elif x <= 2.5e-140:
		tmp = a * t
	elif x <= 820000000.0:
		tmp = b * (a * z)
	elif x <= 5e+94:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3e+222)
		tmp = x;
	elseif (x <= -1.25e+171)
		tmp = Float64(a * t);
	elseif (x <= -7.5e+110)
		tmp = x;
	elseif (x <= -3.2e-297)
		tmp = Float64(y * z);
	elseif (x <= 2.5e-140)
		tmp = Float64(a * t);
	elseif (x <= 820000000.0)
		tmp = Float64(b * Float64(a * z));
	elseif (x <= 5e+94)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3e+222)
		tmp = x;
	elseif (x <= -1.25e+171)
		tmp = a * t;
	elseif (x <= -7.5e+110)
		tmp = x;
	elseif (x <= -3.2e-297)
		tmp = y * z;
	elseif (x <= 2.5e-140)
		tmp = a * t;
	elseif (x <= 820000000.0)
		tmp = b * (a * z);
	elseif (x <= 5e+94)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3e+222], x, If[LessEqual[x, -1.25e+171], N[(a * t), $MachinePrecision], If[LessEqual[x, -7.5e+110], x, If[LessEqual[x, -3.2e-297], N[(y * z), $MachinePrecision], If[LessEqual[x, 2.5e-140], N[(a * t), $MachinePrecision], If[LessEqual[x, 820000000.0], N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+94], N[(a * t), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.00000000000000014e222 or -1.2500000000000001e171 < x < -7.5e110 or 5.0000000000000001e94 < x

   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. associate-+l+ 100.0%

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

      2. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 64.5%

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

   if -3.00000000000000014e222 < x < -1.2500000000000001e171 or -3.19999999999999972e-297 < x < 2.50000000000000007e-140 or 8.2e8 < x < 5.0000000000000001e94

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 79.6%

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

   5. Taylor expanded in a around inf 52.4%

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

   if -7.5e110 < x < -3.19999999999999972e-297

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 41.6%

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

      1. *-commutative 41.6%

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

   6. Simplified 41.6%

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

   if 2.50000000000000007e-140 < x < 8.2e8

   1. Initial program 93.7%

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

      1. associate-+l+ 93.7%

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

      2. +-commutative 93.7%

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

      3. fma-def 93.7%

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

      4. *-commutative 93.7%

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

      5. associate-*l* 84.8%

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

      6. *-commutative 84.8%

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

      7. distribute-lft-out 87.9%

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

      8. remove-double-neg 87.9%

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

      9. *-commutative 87.9%

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

      10. distribute-lft-neg-out 87.9%

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

      11. sub-neg 87.9%

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

      12. sub-neg 87.9%

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

      13. distribute-lft-neg-in 87.9%

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

      14. remove-double-neg 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in y around 0 61.5%

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

   5. Taylor expanded in x around 0 55.4%

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

   6. Taylor expanded in t around 0 40.4%

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

      1. associate-*r* 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*l* 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+171}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-297}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-140}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;x \leq 820000000:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 92.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+117}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.6e+117)
   (+ (+ x (* y z)) (+ (* a (* z b)) (* a t)))
   (+ x (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.6e+117) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (a * t));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.6d+117) then
        tmp = (x + (y * z)) + ((a * (z * b)) + (a * t))
    else
        tmp = x + (z * (y + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.6e+117) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (a * t));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.6e+117:
		tmp = (x + (y * z)) + ((a * (z * b)) + (a * t))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.6e+117)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(a * Float64(z * b)) + Float64(a * t)));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.6e+117)
		tmp = (x + (y * z)) + ((a * (z * b)) + (a * t));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.6e+117], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.5999999999999999e117

   1. Initial program 95.1%

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

      1. associate-+l+ 95.1%

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

      2. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   if 2.5999999999999999e117 < b

   1. Initial program 86.4%

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

      1. associate-+l+ 86.4%

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

      2. associate-*l* 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. +-commutative 68.4%

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

      3. associate-*r* 79.2%

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

      4. distribute-rgt-in 84.7%

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

   6. Simplified 84.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+117}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 5: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+152}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.12e+152)
   (* a t)
   (if (<= a -8.6e+99)
     x
     (if (<= a -2.7e+28)
       (* a t)
       (if (<= a 1.5e-265)
         (* y z)
         (if (<= a 2e-202) x (if (<= a 1.1e+19) (* y z) (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.12e+152) {
		tmp = a * t;
	} else if (a <= -8.6e+99) {
		tmp = x;
	} else if (a <= -2.7e+28) {
		tmp = a * t;
	} else if (a <= 1.5e-265) {
		tmp = y * z;
	} else if (a <= 2e-202) {
		tmp = x;
	} else if (a <= 1.1e+19) {
		tmp = y * z;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.12d+152)) then
        tmp = a * t
    else if (a <= (-8.6d+99)) then
        tmp = x
    else if (a <= (-2.7d+28)) then
        tmp = a * t
    else if (a <= 1.5d-265) then
        tmp = y * z
    else if (a <= 2d-202) then
        tmp = x
    else if (a <= 1.1d+19) then
        tmp = y * z
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.12e+152) {
		tmp = a * t;
	} else if (a <= -8.6e+99) {
		tmp = x;
	} else if (a <= -2.7e+28) {
		tmp = a * t;
	} else if (a <= 1.5e-265) {
		tmp = y * z;
	} else if (a <= 2e-202) {
		tmp = x;
	} else if (a <= 1.1e+19) {
		tmp = y * z;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.12e+152:
		tmp = a * t
	elif a <= -8.6e+99:
		tmp = x
	elif a <= -2.7e+28:
		tmp = a * t
	elif a <= 1.5e-265:
		tmp = y * z
	elif a <= 2e-202:
		tmp = x
	elif a <= 1.1e+19:
		tmp = y * z
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.12e+152)
		tmp = Float64(a * t);
	elseif (a <= -8.6e+99)
		tmp = x;
	elseif (a <= -2.7e+28)
		tmp = Float64(a * t);
	elseif (a <= 1.5e-265)
		tmp = Float64(y * z);
	elseif (a <= 2e-202)
		tmp = x;
	elseif (a <= 1.1e+19)
		tmp = Float64(y * z);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.12e+152)
		tmp = a * t;
	elseif (a <= -8.6e+99)
		tmp = x;
	elseif (a <= -2.7e+28)
		tmp = a * t;
	elseif (a <= 1.5e-265)
		tmp = y * z;
	elseif (a <= 2e-202)
		tmp = x;
	elseif (a <= 1.1e+19)
		tmp = y * z;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.12e+152], N[(a * t), $MachinePrecision], If[LessEqual[a, -8.6e+99], x, If[LessEqual[a, -2.7e+28], N[(a * t), $MachinePrecision], If[LessEqual[a, 1.5e-265], N[(y * z), $MachinePrecision], If[LessEqual[a, 2e-202], x, If[LessEqual[a, 1.1e+19], N[(y * z), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.11999999999999995e152 or -8.6000000000000003e99 < a < -2.7000000000000002e28 or 1.1e19 < a

   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. associate-+l+ 88.9%

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

      2. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around inf 71.1%

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

   5. Taylor expanded in a around inf 54.2%

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

   if -1.11999999999999995e152 < a < -8.6000000000000003e99 or 1.4999999999999999e-265 < a < 2.0000000000000001e-202

   1. Initial program 89.1%

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

      1. associate-+l+ 89.1%

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

      2. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 46.0%

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

   if -2.7000000000000002e28 < a < 1.4999999999999999e-265 or 2.0000000000000001e-202 < a < 1.1e19

   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. associate-+l+ 99.1%

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

      2. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 47.3%

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

      1. *-commutative 47.3%

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

   6. Simplified 47.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+152}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 6: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+152} \lor \neg \left(a \leq -5.2 \cdot 10^{+127}\right) \land \left(a \leq -22500 \lor \neg \left(a \leq 2.05 \cdot 10^{+17}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.12e+152)
         (and (not (<= a -5.2e+127))
              (or (<= a -22500.0) (not (<= a 2.05e+17)))))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.12e+152) || (!(a <= -5.2e+127) && ((a <= -22500.0) || !(a <= 2.05e+17)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.12d+152)) .or. (.not. (a <= (-5.2d+127))) .and. (a <= (-22500.0d0)) .or. (.not. (a <= 2.05d+17))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.12e+152) || (!(a <= -5.2e+127) && ((a <= -22500.0) || !(a <= 2.05e+17)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.12e+152) or (not (a <= -5.2e+127) and ((a <= -22500.0) or not (a <= 2.05e+17))):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.12e+152) || (!(a <= -5.2e+127) && ((a <= -22500.0) || !(a <= 2.05e+17))))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.12e+152) || (~((a <= -5.2e+127)) && ((a <= -22500.0) || ~((a <= 2.05e+17)))))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.12e+152], And[N[Not[LessEqual[a, -5.2e+127]], $MachinePrecision], Or[LessEqual[a, -22500.0], N[Not[LessEqual[a, 2.05e+17]], $MachinePrecision]]]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.11999999999999995e152 or -5.2000000000000004e127 < a < -22500 or 2.05e17 < a

   1. Initial program 89.2%

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

      1. associate-+l+ 89.2%

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

      2. +-commutative 89.2%

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

      3. fma-def 89.2%

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

      4. *-commutative 89.2%

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

      5. associate-*l* 94.0%

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

      6. *-commutative 94.0%

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

      7. distribute-lft-out 97.4%

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

      8. remove-double-neg 97.4%

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

      9. *-commutative 97.4%

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

      10. distribute-lft-neg-out 97.4%

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

      11. sub-neg 97.4%

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

      12. sub-neg 97.4%

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

      13. distribute-lft-neg-in 97.4%

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

      14. remove-double-neg 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around 0 88.4%

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

   5. Taylor expanded in x around 0 80.1%

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

   if -1.11999999999999995e152 < a < -5.2000000000000004e127 or -22500 < a < 2.05e17

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around 0 74.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+152} \lor \neg \left(a \leq -5.2 \cdot 10^{+127}\right) \land \left(a \leq -22500 \lor \neg \left(a \leq 2.05 \cdot 10^{+17}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 7: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot t\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 2100000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a t))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -5.3e-52)
     t_2
     (if (<= z 3.75e-152)
       t_1
       (if (<= z 5.2e-61)
         (* a (+ t (* z b)))
         (if (<= z 2100000000000.0) 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 = z * (y + (a * b));
	double tmp;
	if (z <= -5.3e-52) {
		tmp = t_2;
	} else if (z <= 3.75e-152) {
		tmp = t_1;
	} else if (z <= 5.2e-61) {
		tmp = a * (t + (z * b));
	} else if (z <= 2100000000000.0) {
		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 = z * (y + (a * b))
    if (z <= (-5.3d-52)) then
        tmp = t_2
    else if (z <= 3.75d-152) then
        tmp = t_1
    else if (z <= 5.2d-61) then
        tmp = a * (t + (z * b))
    else if (z <= 2100000000000.0d0) 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 = z * (y + (a * b));
	double tmp;
	if (z <= -5.3e-52) {
		tmp = t_2;
	} else if (z <= 3.75e-152) {
		tmp = t_1;
	} else if (z <= 5.2e-61) {
		tmp = a * (t + (z * b));
	} else if (z <= 2100000000000.0) {
		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 = z * (y + (a * b))
	tmp = 0
	if z <= -5.3e-52:
		tmp = t_2
	elif z <= 3.75e-152:
		tmp = t_1
	elif z <= 5.2e-61:
		tmp = a * (t + (z * b))
	elif z <= 2100000000000.0:
		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(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -5.3e-52)
		tmp = t_2;
	elseif (z <= 3.75e-152)
		tmp = t_1;
	elseif (z <= 5.2e-61)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (z <= 2100000000000.0)
		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 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -5.3e-52)
		tmp = t_2;
	elseif (z <= 3.75e-152)
		tmp = t_1;
	elseif (z <= 5.2e-61)
		tmp = a * (t + (z * b));
	elseif (z <= 2100000000000.0)
		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[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e-52], t$95$2, If[LessEqual[z, 3.75e-152], t$95$1, If[LessEqual[z, 5.2e-61], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2100000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3000000000000003e-52 or 2.1e12 < z

   1. Initial program 88.4%

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

      1. associate-+l+ 88.4%

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

      2. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in z around inf 72.9%

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

   if -5.3000000000000003e-52 < z < 3.75e-152 or 5.20000000000000021e-61 < z < 2.1e12

   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. associate-+l+ 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 80.2%

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

      1. +-commutative 80.2%

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

   6. Simplified 80.2%

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

   if 3.75e-152 < z < 5.20000000000000021e-61

   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. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-out 99.9%

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

      8. remove-double-neg 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-lft-neg-out 99.9%

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

      11. sub-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. distribute-lft-neg-in 99.9%

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

      14. remove-double-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.8%

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

   5. Taylor expanded in x around 0 83.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-152}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 2100000000000:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 8: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(y \cdot z + a \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+18}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.9e+129)
   (+ (* b (* a z)) (+ (* y z) (* a t)))
   (if (<= b 2.4e+18) (+ (+ x (* y z)) (* a t)) (+ x (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+129) {
		tmp = (b * (a * z)) + ((y * z) + (a * t));
	} else if (b <= 2.4e+18) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.9d+129)) then
        tmp = (b * (a * z)) + ((y * z) + (a * t))
    else if (b <= 2.4d+18) then
        tmp = (x + (y * z)) + (a * t)
    else
        tmp = x + (z * (y + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+129) {
		tmp = (b * (a * z)) + ((y * z) + (a * t));
	} else if (b <= 2.4e+18) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.9e+129:
		tmp = (b * (a * z)) + ((y * z) + (a * t))
	elif b <= 2.4e+18:
		tmp = (x + (y * z)) + (a * t)
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.9e+129)
		tmp = Float64(Float64(b * Float64(a * z)) + Float64(Float64(y * z) + Float64(a * t)));
	elseif (b <= 2.4e+18)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(a * t));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.9e+129)
		tmp = (b * (a * z)) + ((y * z) + (a * t));
	elseif (b <= 2.4e+18)
		tmp = (x + (y * z)) + (a * t);
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.9e+129], N[(N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+18], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.90000000000000003e129

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 87.0%

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

   if -1.90000000000000003e129 < b < 2.4e18

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around inf 94.0%

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

   if 2.4e18 < b

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. +-commutative 69.2%

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

      3. associate-*r* 76.6%

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

      4. distribute-rgt-in 82.2%

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

   6. Simplified 82.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(y \cdot z + a \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+18}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 9: 58.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+152} \lor \neg \left(a \leq -1.05 \cdot 10^{+101} \lor \neg \left(a \leq -1.55 \cdot 10^{+31}\right) \land a \leq 7.4 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.05e+152)
         (not
          (or (<= a -1.05e+101) (and (not (<= a -1.55e+31)) (<= a 7.4e+18)))))
   (* a t)
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.05e+152) || !((a <= -1.05e+101) || (!(a <= -1.55e+31) && (a <= 7.4e+18)))) {
		tmp = a * t;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.05d+152)) .or. (.not. (a <= (-1.05d+101)) .or. (.not. (a <= (-1.55d+31))) .and. (a <= 7.4d+18))) then
        tmp = a * t
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.05e+152) || !((a <= -1.05e+101) || (!(a <= -1.55e+31) && (a <= 7.4e+18)))) {
		tmp = a * t;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.05e+152) or not ((a <= -1.05e+101) or (not (a <= -1.55e+31) and (a <= 7.4e+18))):
		tmp = a * t
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.05e+152) || !((a <= -1.05e+101) || (!(a <= -1.55e+31) && (a <= 7.4e+18))))
		tmp = Float64(a * t);
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.05e+152) || ~(((a <= -1.05e+101) || (~((a <= -1.55e+31)) && (a <= 7.4e+18)))))
		tmp = a * t;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.05e+152], N[Not[Or[LessEqual[a, -1.05e+101], And[N[Not[LessEqual[a, -1.55e+31]], $MachinePrecision], LessEqual[a, 7.4e+18]]]], $MachinePrecision]], N[(a * t), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.0499999999999999e152 or -1.05e101 < a < -1.5500000000000001e31 or 7.4e18 < a

   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. associate-+l+ 88.9%

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

      2. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around inf 71.1%

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

   5. Taylor expanded in a around inf 54.2%

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

   if -2.0499999999999999e152 < a < -1.05e101 or -1.5500000000000001e31 < a < 7.4e18

   1. Initial program 97.3%

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

      1. associate-+l+ 97.3%

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

      2. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in a around 0 72.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+152} \lor \neg \left(a \leq -1.05 \cdot 10^{+101} \lor \neg \left(a \leq -1.55 \cdot 10^{+31}\right) \land a \leq 7.4 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 10: 82.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+41} \lor \neg \left(z \leq 1.8 \cdot 10^{+125}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.1e+41) (not (<= z 1.8e+125)))
   (* z (+ y (* a b)))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.1e+41) || !(z <= 1.8e+125)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.1d+41)) .or. (.not. (z <= 1.8d+125))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.1e+41) || !(z <= 1.8e+125)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.1e+41) or not (z <= 1.8e+125):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.1e+41) || !(z <= 1.8e+125))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.1e+41) || ~((z <= 1.8e+125)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.1e+41], N[Not[LessEqual[z, 1.8e+125]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.09999999999999998e41 or 1.8000000000000002e125 < z

   1. Initial program 86.4%

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

      1. associate-+l+ 86.4%

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

      2. associate-*l* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around inf 79.6%

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

   if -6.09999999999999998e41 < z < 1.8000000000000002e125

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. +-commutative 98.1%

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

      3. fma-def 98.1%

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

      4. *-commutative 98.1%

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

      5. associate-*l* 98.1%

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

      6. *-commutative 98.1%

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

      7. distribute-lft-out 100.0%

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

      8. remove-double-neg 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-lft-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 84.8%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+41} \lor \neg \left(z \leq 1.8 \cdot 10^{+125}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 11: 87.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+24} \lor \neg \left(a \leq 2.35 \cdot 10^{+15}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.02e+24) (not (<= a 2.35e+15)))
   (+ x (* a (+ t (* z b))))
   (+ x (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.02e+24) || !(a <= 2.35e+15)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.02d+24)) .or. (.not. (a <= 2.35d+15))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + (z * (y + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.02e+24) || !(a <= 2.35e+15)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.02e+24) or not (a <= 2.35e+15):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.02e+24) || !(a <= 2.35e+15))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.02e+24) || ~((a <= 2.35e+15)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.02e+24], N[Not[LessEqual[a, 2.35e+15]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.02000000000000004e24 or 2.35e15 < a

   1. Initial program 87.8%

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

      1. associate-+l+ 87.8%

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

      2. +-commutative 87.8%

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

      3. fma-def 87.8%

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

      4. *-commutative 87.8%

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

      5. associate-*l* 93.3%

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

      6. *-commutative 93.3%

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

      7. distribute-lft-out 96.6%

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

      8. remove-double-neg 96.6%

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

      9. *-commutative 96.6%

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

      10. distribute-lft-neg-out 96.6%

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

      11. sub-neg 96.6%

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

      12. sub-neg 96.6%

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

      13. distribute-lft-neg-in 96.6%

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

      14. remove-double-neg 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around 0 88.7%

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

   if -1.02000000000000004e24 < a < 2.35e15

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in t around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-*r* 86.2%

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

      4. distribute-rgt-in 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+24} \lor \neg \left(a \leq 2.35 \cdot 10^{+15}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 12: 86.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+86}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.2e+86)
   (+ x (* a (+ t (* z b))))
   (if (<= b 9.8e+17) (+ (+ x (* y z)) (* a t)) (+ x (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+86) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 9.8e+17) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.2d+86)) then
        tmp = x + (a * (t + (z * b)))
    else if (b <= 9.8d+17) then
        tmp = (x + (y * z)) + (a * t)
    else
        tmp = x + (z * (y + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+86) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 9.8e+17) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.2e+86:
		tmp = x + (a * (t + (z * b)))
	elif b <= 9.8e+17:
		tmp = (x + (y * z)) + (a * t)
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.2e+86)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (b <= 9.8e+17)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(a * t));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.2e+86)
		tmp = x + (a * (t + (z * b)));
	elseif (b <= 9.8e+17)
		tmp = (x + (y * z)) + (a * t);
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.2e+86], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e+17], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.19999999999999958e86

   1. Initial program 93.7%

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

      1. associate-+l+ 93.7%

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

      2. +-commutative 93.7%

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

      3. fma-def 93.7%

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

      4. *-commutative 93.7%

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

      5. associate-*l* 85.7%

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

      6. *-commutative 85.7%

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

      7. distribute-lft-out 87.8%

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

      8. remove-double-neg 87.8%

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

      9. *-commutative 87.8%

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

      10. distribute-lft-neg-out 87.8%

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

      11. sub-neg 87.8%

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

      12. sub-neg 87.8%

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

      13. distribute-lft-neg-in 87.8%

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

      14. remove-double-neg 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around 0 79.4%

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

   if -9.19999999999999958e86 < b < 9.8e17

   1. Initial program 95.6%

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

      1. associate-+l+ 95.6%

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

      2. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in t around inf 95.9%

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

   if 9.8e17 < b

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. +-commutative 69.2%

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

      3. associate-*r* 76.6%

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

      4. distribute-rgt-in 82.2%

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

   6. Simplified 82.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+86}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 13: 38.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+171} \lor \neg \left(x \leq -4.8 \cdot 10^{+103}\right) \land x \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3e+222)
   x
   (if (or (<= x -1.25e+171) (and (not (<= x -4.8e+103)) (<= x 8.6e+93)))
     (* a t)
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+222) {
		tmp = x;
	} else if ((x <= -1.25e+171) || (!(x <= -4.8e+103) && (x <= 8.6e+93))) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3d+222)) then
        tmp = x
    else if ((x <= (-1.25d+171)) .or. (.not. (x <= (-4.8d+103))) .and. (x <= 8.6d+93)) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+222) {
		tmp = x;
	} else if ((x <= -1.25e+171) || (!(x <= -4.8e+103) && (x <= 8.6e+93))) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3e+222:
		tmp = x
	elif (x <= -1.25e+171) or (not (x <= -4.8e+103) and (x <= 8.6e+93)):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3e+222)
		tmp = x;
	elseif ((x <= -1.25e+171) || (!(x <= -4.8e+103) && (x <= 8.6e+93)))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3e+222)
		tmp = x;
	elseif ((x <= -1.25e+171) || (~((x <= -4.8e+103)) && (x <= 8.6e+93)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3e+222], x, If[Or[LessEqual[x, -1.25e+171], And[N[Not[LessEqual[x, -4.8e+103]], $MachinePrecision], LessEqual[x, 8.6e+93]]], N[(a * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000014e222 or -1.2500000000000001e171 < x < -4.7999999999999997e103 or 8.6e93 < x

   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. associate-+l+ 100.0%

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

      2. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around inf 61.9%

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

   if -3.00000000000000014e222 < x < -1.2500000000000001e171 or -4.7999999999999997e103 < x < 8.6e93

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 75.1%

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

   5. Taylor expanded in a around inf 38.9%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+171} \lor \neg \left(x \leq -4.8 \cdot 10^{+103}\right) \land x \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 64.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+30} \lor \neg \left(a \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7e+30) (not (<= a 5e+16))) (+ x (* a t)) (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e+30) || !(a <= 5e+16)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-7d+30)) .or. (.not. (a <= 5d+16))) then
        tmp = x + (a * t)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e+30) || !(a <= 5e+16)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7e+30) or not (a <= 5e+16):
		tmp = x + (a * t)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7e+30) || !(a <= 5e+16))
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7e+30) || ~((a <= 5e+16)))
		tmp = x + (a * t);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7e+30], N[Not[LessEqual[a, 5e+16]], $MachinePrecision]], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.00000000000000042e30 or 5e16 < a

   1. Initial program 87.8%

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

      1. associate-+l+ 87.8%

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

      2. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around 0 60.0%

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

      1. +-commutative 60.0%

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

   6. Simplified 60.0%

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

   if -7.00000000000000042e30 < a < 5e16

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around 0 72.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+30} \lor \neg \left(a \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 15: 26.4% 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 93.8%

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

   1. associate-+l+ 93.8%

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

   2. associate-*l* 92.3%

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

3. Simplified 92.3%

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

4. Taylor expanded in x around inf 23.0%

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

5. Final simplification 23.0%

   \[\leadsto x \]

Developer target: 97.3% 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 2023334 
(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)))