Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 96.5%

Time: 9.7s

Alternatives: 14

Speedup: 0.9×

• 31.8% 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: 92.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(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 98.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*l* 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in z around inf 84.6%

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

4. Final simplification 97.3%

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

Alternative 2: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -5.4e+42)
     t_2
     (if (<= z -8e-6)
       t_1
       (if (<= z -1.75e-40)
         t_2
         (if (<= z 5.5e-32)
           t_1
           (if (<= z 6e+19)
             t_2
             (if (<= z 9.6e+19)
               x
               (if (<= z 1.32e+123) (* a (+ t (* z b))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -5.4e+42) {
		tmp = t_2;
	} else if (z <= -8e-6) {
		tmp = t_1;
	} else if (z <= -1.75e-40) {
		tmp = t_2;
	} else if (z <= 5.5e-32) {
		tmp = t_1;
	} else if (z <= 6e+19) {
		tmp = t_2;
	} else if (z <= 9.6e+19) {
		tmp = x;
	} else if (z <= 1.32e+123) {
		tmp = a * (t + (z * b));
	} 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 + (t * a)
    t_2 = z * (y + (a * b))
    if (z <= (-5.4d+42)) then
        tmp = t_2
    else if (z <= (-8d-6)) then
        tmp = t_1
    else if (z <= (-1.75d-40)) then
        tmp = t_2
    else if (z <= 5.5d-32) then
        tmp = t_1
    else if (z <= 6d+19) then
        tmp = t_2
    else if (z <= 9.6d+19) then
        tmp = x
    else if (z <= 1.32d+123) then
        tmp = a * (t + (z * b))
    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 + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -5.4e+42) {
		tmp = t_2;
	} else if (z <= -8e-6) {
		tmp = t_1;
	} else if (z <= -1.75e-40) {
		tmp = t_2;
	} else if (z <= 5.5e-32) {
		tmp = t_1;
	} else if (z <= 6e+19) {
		tmp = t_2;
	} else if (z <= 9.6e+19) {
		tmp = x;
	} else if (z <= 1.32e+123) {
		tmp = a * (t + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -5.4e+42:
		tmp = t_2
	elif z <= -8e-6:
		tmp = t_1
	elif z <= -1.75e-40:
		tmp = t_2
	elif z <= 5.5e-32:
		tmp = t_1
	elif z <= 6e+19:
		tmp = t_2
	elif z <= 9.6e+19:
		tmp = x
	elif z <= 1.32e+123:
		tmp = a * (t + (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -5.4e+42)
		tmp = t_2;
	elseif (z <= -8e-6)
		tmp = t_1;
	elseif (z <= -1.75e-40)
		tmp = t_2;
	elseif (z <= 5.5e-32)
		tmp = t_1;
	elseif (z <= 6e+19)
		tmp = t_2;
	elseif (z <= 9.6e+19)
		tmp = x;
	elseif (z <= 1.32e+123)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -5.4e+42)
		tmp = t_2;
	elseif (z <= -8e-6)
		tmp = t_1;
	elseif (z <= -1.75e-40)
		tmp = t_2;
	elseif (z <= 5.5e-32)
		tmp = t_1;
	elseif (z <= 6e+19)
		tmp = t_2;
	elseif (z <= 9.6e+19)
		tmp = x;
	elseif (z <= 1.32e+123)
		tmp = a * (t + (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+42], t$95$2, If[LessEqual[z, -8e-6], t$95$1, If[LessEqual[z, -1.75e-40], t$95$2, If[LessEqual[z, 5.5e-32], t$95$1, If[LessEqual[z, 6e+19], t$95$2, If[LessEqual[z, 9.6e+19], x, If[LessEqual[z, 1.32e+123], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4000000000000001e42 or -7.99999999999999964e-6 < z < -1.7500000000000001e-40 or 5.50000000000000024e-32 < z < 6e19 or 1.32e123 < z

   1. Initial program 86.6%

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

      1. associate-+l+ 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around inf 88.2%

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

   if -5.4000000000000001e42 < z < -7.99999999999999964e-6 or -1.7500000000000001e-40 < z < 5.50000000000000024e-32

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 76.6%

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

      1. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   if 6e19 < z < 9.6e19

   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. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   if 9.6e19 < z < 1.32e123

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around inf 71.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 3: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+110}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-146}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= t -2.65e+110)
     (* t a)
     (if (<= t -1.75e-99)
       x
       (if (<= t -3.8e-185)
         (* y z)
         (if (<= t -8e-197)
           x
           (if (<= t 1.55e-200)
             t_1
             (if (<= t 2.3e-146)
               (* y z)
               (if (<= t 1.75e+80) t_1 (* t a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -2.65e+110) {
		tmp = t * a;
	} else if (t <= -1.75e-99) {
		tmp = x;
	} else if (t <= -3.8e-185) {
		tmp = y * z;
	} else if (t <= -8e-197) {
		tmp = x;
	} else if (t <= 1.55e-200) {
		tmp = t_1;
	} else if (t <= 2.3e-146) {
		tmp = y * z;
	} else if (t <= 1.75e+80) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (t <= (-2.65d+110)) then
        tmp = t * a
    else if (t <= (-1.75d-99)) then
        tmp = x
    else if (t <= (-3.8d-185)) then
        tmp = y * z
    else if (t <= (-8d-197)) then
        tmp = x
    else if (t <= 1.55d-200) then
        tmp = t_1
    else if (t <= 2.3d-146) then
        tmp = y * z
    else if (t <= 1.75d+80) then
        tmp = t_1
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -2.65e+110) {
		tmp = t * a;
	} else if (t <= -1.75e-99) {
		tmp = x;
	} else if (t <= -3.8e-185) {
		tmp = y * z;
	} else if (t <= -8e-197) {
		tmp = x;
	} else if (t <= 1.55e-200) {
		tmp = t_1;
	} else if (t <= 2.3e-146) {
		tmp = y * z;
	} else if (t <= 1.75e+80) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if t <= -2.65e+110:
		tmp = t * a
	elif t <= -1.75e-99:
		tmp = x
	elif t <= -3.8e-185:
		tmp = y * z
	elif t <= -8e-197:
		tmp = x
	elif t <= 1.55e-200:
		tmp = t_1
	elif t <= 2.3e-146:
		tmp = y * z
	elif t <= 1.75e+80:
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (t <= -2.65e+110)
		tmp = Float64(t * a);
	elseif (t <= -1.75e-99)
		tmp = x;
	elseif (t <= -3.8e-185)
		tmp = Float64(y * z);
	elseif (t <= -8e-197)
		tmp = x;
	elseif (t <= 1.55e-200)
		tmp = t_1;
	elseif (t <= 2.3e-146)
		tmp = Float64(y * z);
	elseif (t <= 1.75e+80)
		tmp = t_1;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (t <= -2.65e+110)
		tmp = t * a;
	elseif (t <= -1.75e-99)
		tmp = x;
	elseif (t <= -3.8e-185)
		tmp = y * z;
	elseif (t <= -8e-197)
		tmp = x;
	elseif (t <= 1.55e-200)
		tmp = t_1;
	elseif (t <= 2.3e-146)
		tmp = y * z;
	elseif (t <= 1.75e+80)
		tmp = t_1;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e+110], N[(t * a), $MachinePrecision], If[LessEqual[t, -1.75e-99], x, If[LessEqual[t, -3.8e-185], N[(y * z), $MachinePrecision], If[LessEqual[t, -8e-197], x, If[LessEqual[t, 1.55e-200], t$95$1, If[LessEqual[t, 2.3e-146], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.75e+80], t$95$1, N[(t * a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6499999999999999e110 or 1.74999999999999997e80 < t

   1. Initial program 91.7%

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

      1. associate-+l+ 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around inf 63.5%

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

   if -2.6499999999999999e110 < t < -1.7499999999999999e-99 or -3.7999999999999999e-185 < t < -7.9999999999999999e-197

   1. Initial program 94.8%

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

      1. associate-+l+ 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around inf 45.1%

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

   if -1.7499999999999999e-99 < t < -3.7999999999999999e-185 or 1.5499999999999999e-200 < t < 2.3000000000000001e-146

   1. Initial program 90.1%

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

      1. associate-+l+ 90.1%

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

      2. *-commutative 90.1%

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

      3. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 54.6%

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

      1. *-commutative 54.6%

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

   6. Simplified 54.6%

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

   if -7.9999999999999999e-197 < t < 1.5499999999999999e-200 or 2.3000000000000001e-146 < t < 1.74999999999999997e80

   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. *-commutative 94.3%

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

      3. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around inf 61.2%

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

   5. Taylor expanded in y around 0 45.8%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+110}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-146}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 4: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+57}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -1.25e+40)
     t_2
     (if (<= z -1.75e-5)
       t_1
       (if (<= z -2.5e-44)
         t_2
         (if (<= z 1.75e-63)
           t_1
           (if (<= z 4.2e+57)
             (+ x (* a (* z b)))
             (if (<= z 3.55e+112) (* a (+ t (* z b))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -1.25e+40) {
		tmp = t_2;
	} else if (z <= -1.75e-5) {
		tmp = t_1;
	} else if (z <= -2.5e-44) {
		tmp = t_2;
	} else if (z <= 1.75e-63) {
		tmp = t_1;
	} else if (z <= 4.2e+57) {
		tmp = x + (a * (z * b));
	} else if (z <= 3.55e+112) {
		tmp = a * (t + (z * b));
	} 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 + (t * a)
    t_2 = z * (y + (a * b))
    if (z <= (-1.25d+40)) then
        tmp = t_2
    else if (z <= (-1.75d-5)) then
        tmp = t_1
    else if (z <= (-2.5d-44)) then
        tmp = t_2
    else if (z <= 1.75d-63) then
        tmp = t_1
    else if (z <= 4.2d+57) then
        tmp = x + (a * (z * b))
    else if (z <= 3.55d+112) then
        tmp = a * (t + (z * b))
    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 + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -1.25e+40) {
		tmp = t_2;
	} else if (z <= -1.75e-5) {
		tmp = t_1;
	} else if (z <= -2.5e-44) {
		tmp = t_2;
	} else if (z <= 1.75e-63) {
		tmp = t_1;
	} else if (z <= 4.2e+57) {
		tmp = x + (a * (z * b));
	} else if (z <= 3.55e+112) {
		tmp = a * (t + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -1.25e+40:
		tmp = t_2
	elif z <= -1.75e-5:
		tmp = t_1
	elif z <= -2.5e-44:
		tmp = t_2
	elif z <= 1.75e-63:
		tmp = t_1
	elif z <= 4.2e+57:
		tmp = x + (a * (z * b))
	elif z <= 3.55e+112:
		tmp = a * (t + (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.25e+40)
		tmp = t_2;
	elseif (z <= -1.75e-5)
		tmp = t_1;
	elseif (z <= -2.5e-44)
		tmp = t_2;
	elseif (z <= 1.75e-63)
		tmp = t_1;
	elseif (z <= 4.2e+57)
		tmp = Float64(x + Float64(a * Float64(z * b)));
	elseif (z <= 3.55e+112)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.25e+40)
		tmp = t_2;
	elseif (z <= -1.75e-5)
		tmp = t_1;
	elseif (z <= -2.5e-44)
		tmp = t_2;
	elseif (z <= 1.75e-63)
		tmp = t_1;
	elseif (z <= 4.2e+57)
		tmp = x + (a * (z * b));
	elseif (z <= 3.55e+112)
		tmp = a * (t + (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+40], t$95$2, If[LessEqual[z, -1.75e-5], t$95$1, If[LessEqual[z, -2.5e-44], t$95$2, If[LessEqual[z, 1.75e-63], t$95$1, If[LessEqual[z, 4.2e+57], N[(x + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+112], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25000000000000001e40 or -1.7499999999999998e-5 < z < -2.50000000000000019e-44 or 3.55e112 < z

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around inf 87.6%

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

   if -1.25000000000000001e40 < z < -1.7499999999999998e-5 or -2.50000000000000019e-44 < z < 1.75000000000000002e-63

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 78.0%

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

      1. +-commutative 78.0%

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

   6. Simplified 78.0%

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

   if 1.75000000000000002e-63 < z < 4.19999999999999982e57

   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%

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

      3. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around 0 75.2%

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

   5. Taylor expanded in t around 0 67.4%

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

   if 4.19999999999999982e57 < z < 3.55e112

   1. Initial program 86.6%

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

      1. associate-+l+ 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in a around inf 72.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-5}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-63}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+57}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 5: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* a (+ t (* z b)))))
   (if (<= a -6.3e+35)
     t_2
     (if (<= a -5.7e-21)
       t_1
       (if (<= a -1.42e-65)
         t_2
         (if (<= a -2.8e-176) (* y z) (if (<= a 3.7e-47) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -6.3e+35) {
		tmp = t_2;
	} else if (a <= -5.7e-21) {
		tmp = t_1;
	} else if (a <= -1.42e-65) {
		tmp = t_2;
	} else if (a <= -2.8e-176) {
		tmp = y * z;
	} else if (a <= 3.7e-47) {
		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 + (t * a)
    t_2 = a * (t + (z * b))
    if (a <= (-6.3d+35)) then
        tmp = t_2
    else if (a <= (-5.7d-21)) then
        tmp = t_1
    else if (a <= (-1.42d-65)) then
        tmp = t_2
    else if (a <= (-2.8d-176)) then
        tmp = y * z
    else if (a <= 3.7d-47) 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 + (t * a);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -6.3e+35) {
		tmp = t_2;
	} else if (a <= -5.7e-21) {
		tmp = t_1;
	} else if (a <= -1.42e-65) {
		tmp = t_2;
	} else if (a <= -2.8e-176) {
		tmp = y * z;
	} else if (a <= 3.7e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = a * (t + (z * b))
	tmp = 0
	if a <= -6.3e+35:
		tmp = t_2
	elif a <= -5.7e-21:
		tmp = t_1
	elif a <= -1.42e-65:
		tmp = t_2
	elif a <= -2.8e-176:
		tmp = y * z
	elif a <= 3.7e-47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -6.3e+35)
		tmp = t_2;
	elseif (a <= -5.7e-21)
		tmp = t_1;
	elseif (a <= -1.42e-65)
		tmp = t_2;
	elseif (a <= -2.8e-176)
		tmp = Float64(y * z);
	elseif (a <= 3.7e-47)
		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 + (t * a);
	t_2 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -6.3e+35)
		tmp = t_2;
	elseif (a <= -5.7e-21)
		tmp = t_1;
	elseif (a <= -1.42e-65)
		tmp = t_2;
	elseif (a <= -2.8e-176)
		tmp = y * z;
	elseif (a <= 3.7e-47)
		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[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.3e+35], t$95$2, If[LessEqual[a, -5.7e-21], t$95$1, If[LessEqual[a, -1.42e-65], t$95$2, If[LessEqual[a, -2.8e-176], N[(y * z), $MachinePrecision], If[LessEqual[a, 3.7e-47], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.29999999999999969e35 or -5.6999999999999996e-21 < a < -1.41999999999999993e-65 or 3.7e-47 < 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. *-commutative 88.9%

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

      3. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in a around inf 83.1%

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

   if -6.29999999999999969e35 < a < -5.6999999999999996e-21 or -2.8000000000000001e-176 < a < 3.7e-47

   1. Initial program 99.0%

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

      1. associate-+l+ 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 58.5%

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

      1. +-commutative 58.5%

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

   6. Simplified 58.5%

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

   if -1.41999999999999993e-65 < a < -2.8000000000000001e-176

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around inf 64.8%

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

      1. *-commutative 64.8%

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

   6. Simplified 64.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-21}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-65}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-47}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 6: 72.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-63}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+57}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -6.5e+39)
     t_1
     (if (<= z -4.8e-54)
       (+ (* t a) (* y z))
       (if (<= z 1.85e-63)
         (+ x (* t a))
         (if (<= z 8.5e+57)
           (+ x (* a (* z b)))
           (if (<= z 7.2e+115) (* a (+ t (* z b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -6.5e+39) {
		tmp = t_1;
	} else if (z <= -4.8e-54) {
		tmp = (t * a) + (y * z);
	} else if (z <= 1.85e-63) {
		tmp = x + (t * a);
	} else if (z <= 8.5e+57) {
		tmp = x + (a * (z * b));
	} else if (z <= 7.2e+115) {
		tmp = a * (t + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y + (a * b))
    if (z <= (-6.5d+39)) then
        tmp = t_1
    else if (z <= (-4.8d-54)) then
        tmp = (t * a) + (y * z)
    else if (z <= 1.85d-63) then
        tmp = x + (t * a)
    else if (z <= 8.5d+57) then
        tmp = x + (a * (z * b))
    else if (z <= 7.2d+115) then
        tmp = a * (t + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -6.5e+39) {
		tmp = t_1;
	} else if (z <= -4.8e-54) {
		tmp = (t * a) + (y * z);
	} else if (z <= 1.85e-63) {
		tmp = x + (t * a);
	} else if (z <= 8.5e+57) {
		tmp = x + (a * (z * b));
	} else if (z <= 7.2e+115) {
		tmp = a * (t + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -6.5e+39:
		tmp = t_1
	elif z <= -4.8e-54:
		tmp = (t * a) + (y * z)
	elif z <= 1.85e-63:
		tmp = x + (t * a)
	elif z <= 8.5e+57:
		tmp = x + (a * (z * b))
	elif z <= 7.2e+115:
		tmp = a * (t + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -6.5e+39)
		tmp = t_1;
	elseif (z <= -4.8e-54)
		tmp = Float64(Float64(t * a) + Float64(y * z));
	elseif (z <= 1.85e-63)
		tmp = Float64(x + Float64(t * a));
	elseif (z <= 8.5e+57)
		tmp = Float64(x + Float64(a * Float64(z * b)));
	elseif (z <= 7.2e+115)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -6.5e+39)
		tmp = t_1;
	elseif (z <= -4.8e-54)
		tmp = (t * a) + (y * z);
	elseif (z <= 1.85e-63)
		tmp = x + (t * a);
	elseif (z <= 8.5e+57)
		tmp = x + (a * (z * b));
	elseif (z <= 7.2e+115)
		tmp = a * (t + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+39], t$95$1, If[LessEqual[z, -4.8e-54], N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-63], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+57], N[(x + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+115], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5000000000000001e39 or 7.2000000000000001e115 < z

   1. Initial program 84.3%

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

      1. associate-+l+ 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around inf 88.0%

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

   if -6.5000000000000001e39 < z < -4.80000000000000026e-54

   1. Initial program 95.3%

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

      1. associate-+l+ 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in b around 0 77.8%

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

   5. Taylor expanded in x around 0 68.8%

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

   if -4.80000000000000026e-54 < z < 1.85000000000000006e-63

   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. *-commutative 99.1%

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

      3. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around 0 78.7%

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

      1. +-commutative 78.7%

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

   6. Simplified 78.7%

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

   if 1.85000000000000006e-63 < z < 8.5000000000000001e57

   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%

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

      3. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around 0 75.2%

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

   5. Taylor expanded in t around 0 67.4%

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

   if 8.5000000000000001e57 < z < 7.2000000000000001e115

   1. Initial program 86.6%

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

      1. associate-+l+ 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in a around inf 72.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-63}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+57}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 7: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot a + y \cdot z\\ \mathbf{if}\;b \leq -6.7 \cdot 10^{+100}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* t a) (* y z))))
   (if (<= b -6.7e+100)
     (+ x (* a (+ t (* z b))))
     (if (<= b 5.5e+61) (+ x t_1) (+ (* (* z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * a) + (y * z);
	double tmp;
	if (b <= -6.7e+100) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 5.5e+61) {
		tmp = x + t_1;
	} else {
		tmp = ((z * a) * b) + 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 = (t * a) + (y * z)
    if (b <= (-6.7d+100)) then
        tmp = x + (a * (t + (z * b)))
    else if (b <= 5.5d+61) then
        tmp = x + t_1
    else
        tmp = ((z * a) * b) + 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 = (t * a) + (y * z);
	double tmp;
	if (b <= -6.7e+100) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 5.5e+61) {
		tmp = x + t_1;
	} else {
		tmp = ((z * a) * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * a) + (y * z)
	tmp = 0
	if b <= -6.7e+100:
		tmp = x + (a * (t + (z * b)))
	elif b <= 5.5e+61:
		tmp = x + t_1
	else:
		tmp = ((z * a) * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * a) + Float64(y * z))
	tmp = 0.0
	if (b <= -6.7e+100)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (b <= 5.5e+61)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(Float64(z * a) * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * a) + (y * z);
	tmp = 0.0;
	if (b <= -6.7e+100)
		tmp = x + (a * (t + (z * b)));
	elseif (b <= 5.5e+61)
		tmp = x + t_1;
	else
		tmp = ((z * a) * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.7e+100], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+61], N[(x + t$95$1), $MachinePrecision], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.6999999999999997e100

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. +-commutative 88.8%

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

      3. fma-def 88.8%

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

      4. associate-*l* 86.9%

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

      5. *-commutative 86.9%

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

      6. *-commutative 86.9%

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

      7. distribute-rgt-out 90.7%

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

      8. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around 0 94.6%

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

   if -6.6999999999999997e100 < b < 5.50000000000000036e61

   1. Initial program 93.3%

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

      1. associate-+l+ 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in b around 0 91.8%

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

   if 5.50000000000000036e61 < b

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 86.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+100}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]

Alternative 8: 92.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+126}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.4e+126)
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* y z)) (+ (* z (* a b)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.4e+126) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.4d+126)) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.4e+126) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.4e+126:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.4e+126)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(z * Float64(a * b)) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.4e+126)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.4e+126], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.3999999999999997e126

   1. Initial program 86.8%

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

      1. associate-+l+ 86.8%

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

      2. +-commutative 86.8%

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

      3. fma-def 86.8%

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

      4. associate-*l* 84.6%

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

      5. *-commutative 84.6%

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

      6. *-commutative 84.6%

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

      7. distribute-rgt-out 89.0%

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

      8. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in y around 0 93.6%

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

   if -9.3999999999999997e126 < b

   1. Initial program 94.4%

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

      1. associate-+l+ 94.4%

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

      2. *-commutative 94.4%

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

      3. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+126}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \end{array} \]

Alternative 9: 39.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+109)
   (* t a)
   (if (<= t -3.4e-99)
     x
     (if (<= t -1.4e-260)
       (* y z)
       (if (<= t 1.75e-186) x (if (<= t 2.3e-13) (* y z) (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+109) {
		tmp = t * a;
	} else if (t <= -3.4e-99) {
		tmp = x;
	} else if (t <= -1.4e-260) {
		tmp = y * z;
	} else if (t <= 1.75e-186) {
		tmp = x;
	} else if (t <= 2.3e-13) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.8d+109)) then
        tmp = t * a
    else if (t <= (-3.4d-99)) then
        tmp = x
    else if (t <= (-1.4d-260)) then
        tmp = y * z
    else if (t <= 1.75d-186) then
        tmp = x
    else if (t <= 2.3d-13) then
        tmp = y * z
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+109) {
		tmp = t * a;
	} else if (t <= -3.4e-99) {
		tmp = x;
	} else if (t <= -1.4e-260) {
		tmp = y * z;
	} else if (t <= 1.75e-186) {
		tmp = x;
	} else if (t <= 2.3e-13) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.8e+109:
		tmp = t * a
	elif t <= -3.4e-99:
		tmp = x
	elif t <= -1.4e-260:
		tmp = y * z
	elif t <= 1.75e-186:
		tmp = x
	elif t <= 2.3e-13:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+109)
		tmp = Float64(t * a);
	elseif (t <= -3.4e-99)
		tmp = x;
	elseif (t <= -1.4e-260)
		tmp = Float64(y * z);
	elseif (t <= 1.75e-186)
		tmp = x;
	elseif (t <= 2.3e-13)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.8e+109)
		tmp = t * a;
	elseif (t <= -3.4e-99)
		tmp = x;
	elseif (t <= -1.4e-260)
		tmp = y * z;
	elseif (t <= 1.75e-186)
		tmp = x;
	elseif (t <= 2.3e-13)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+109], N[(t * a), $MachinePrecision], If[LessEqual[t, -3.4e-99], x, If[LessEqual[t, -1.4e-260], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.75e-186], x, If[LessEqual[t, 2.3e-13], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999975e109 or 2.29999999999999979e-13 < t

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 56.4%

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

   if -4.79999999999999975e109 < t < -3.40000000000000007e-99 or -1.3999999999999999e-260 < t < 1.74999999999999995e-186

   1. Initial program 96.3%

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

      1. associate-+l+ 96.3%

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

      2. *-commutative 96.3%

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

      3. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 39.8%

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

   if -3.40000000000000007e-99 < t < -1.3999999999999999e-260 or 1.74999999999999995e-186 < t < 2.29999999999999979e-13

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

   6. Simplified 42.2%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 10: 81.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+67} \lor \neg \left(z \leq 1.65 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.25e+67) (not (<= z 1.65e+123)))
   (* 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 <= -2.25e+67) || !(z <= 1.65e+123)) {
		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 <= (-2.25d+67)) .or. (.not. (z <= 1.65d+123))) 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 <= -2.25e+67) || !(z <= 1.65e+123)) {
		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 <= -2.25e+67) or not (z <= 1.65e+123):
		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 <= -2.25e+67) || !(z <= 1.65e+123))
		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 <= -2.25e+67) || ~((z <= 1.65e+123)))
		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, -2.25e+67], N[Not[LessEqual[z, 1.65e+123]], $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 < -2.2499999999999999e67 or 1.65000000000000001e123 < z

   1. Initial program 83.5%

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

      1. associate-+l+ 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around inf 89.6%

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

   if -2.2499999999999999e67 < z < 1.65000000000000001e123

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. fma-def 97.7%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-out 98.8%

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

      8. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 86.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+67} \lor \neg \left(z \leq 1.65 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 11: 87.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-63} \lor \neg \left(a \leq 6 \cdot 10^{-54}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.12e-63) (not (<= a 6e-54)))
   (+ x (* a (+ t (* z b))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.12e-63) || !(a <= 6e-54)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((t * a) + (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-63)) .or. (.not. (a <= 6d-54))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + ((t * a) + (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-63) || !(a <= 6e-54)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.12e-63) or not (a <= 6e-54):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.12e-63) || !(a <= 6e-54))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(t * a) + 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-63) || ~((a <= 6e-54)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.12e-63], N[Not[LessEqual[a, 6e-54]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.12000000000000002e-63 or 6.00000000000000018e-54 < a

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. +-commutative 90.2%

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

      3. fma-def 90.2%

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

      4. associate-*l* 95.3%

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

      5. *-commutative 95.3%

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

      6. *-commutative 95.3%

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

      7. distribute-rgt-out 96.6%

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

      8. *-commutative 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 90.7%

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

   if -1.12000000000000002e-63 < a < 6.00000000000000018e-54

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in b around 0 90.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-63} \lor \neg \left(a \leq 6 \cdot 10^{-54}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]

Alternative 12: 59.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+186}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+129}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.85e+186)
   (* y z)
   (if (<= z -7.5e+58)
     (* z (* a b))
     (if (<= z 1.85e+129) (+ x (* t a)) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+186) {
		tmp = y * z;
	} else if (z <= -7.5e+58) {
		tmp = z * (a * b);
	} else if (z <= 1.85e+129) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.85d+186)) then
        tmp = y * z
    else if (z <= (-7.5d+58)) then
        tmp = z * (a * b)
    else if (z <= 1.85d+129) then
        tmp = x + (t * a)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+186) {
		tmp = y * z;
	} else if (z <= -7.5e+58) {
		tmp = z * (a * b);
	} else if (z <= 1.85e+129) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.85e+186:
		tmp = y * z
	elif z <= -7.5e+58:
		tmp = z * (a * b)
	elif z <= 1.85e+129:
		tmp = x + (t * a)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.85e+186)
		tmp = Float64(y * z);
	elseif (z <= -7.5e+58)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 1.85e+129)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.85e+186)
		tmp = y * z;
	elseif (z <= -7.5e+58)
		tmp = z * (a * b);
	elseif (z <= 1.85e+129)
		tmp = x + (t * a);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.85e+186], N[(y * z), $MachinePrecision], If[LessEqual[z, -7.5e+58], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+129], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e186 or 1.84999999999999989e129 < z

   1. Initial program 82.0%

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

      1. associate-+l+ 82.0%

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

      2. *-commutative 82.0%

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

      3. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   if -1.85e186 < z < -7.5000000000000001e58

   1. Initial program 88.3%

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

      1. associate-+l+ 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 77.2%

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

   5. Taylor expanded in y around 0 48.3%

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

   if -7.5000000000000001e58 < z < 1.84999999999999989e129

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 67.6%

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

      1. +-commutative 67.6%

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

   6. Simplified 67.6%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+186}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+129}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 13: 39.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+109} \lor \neg \left(t \leq 1.42 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.8e+109) (not (<= t 1.42e+78))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.8e+109) || !(t <= 1.42e+78)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.8d+109)) .or. (.not. (t <= 1.42d+78))) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.8e+109) || !(t <= 1.42e+78)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.8e+109) or not (t <= 1.42e+78):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.8e+109) || !(t <= 1.42e+78))
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.8e+109) || ~((t <= 1.42e+78)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.8e+109], N[Not[LessEqual[t, 1.42e+78]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999975e109 or 1.42e78 < t

   1. Initial program 91.7%

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

      1. associate-+l+ 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around inf 63.5%

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

   if -4.79999999999999975e109 < t < 1.42e78

   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%

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

      3. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around inf 32.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+109} \lor \neg \left(t \leq 1.42 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 26.6% 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 93.0%

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

   1. associate-+l+ 93.0%

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

   2. *-commutative 93.0%

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

   3. associate-*l* 92.7%

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

3. Simplified 92.7%

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

4. Taylor expanded in x around inf 24.9%

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

5. Final simplification 24.9%

   \[\leadsto x \]

Developer target: 97.5% 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 2023299 
(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)))