Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.7% → 96.5%

Time: 10.6s

Alternatives: 13

Speedup: 0.6×

• 32.3% 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: 92.7% 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, 0.4× 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 97.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in z around inf 83.4%

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

4. Final simplification 96.6%

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

Alternative 2: 39.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-123}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e+78)
   (* t a)
   (if (<= t -3.4e-184)
     (* y z)
     (if (<= t 1.85e-286)
       x
       (if (<= t 2.05e-123)
         (* y z)
         (if (<= t 8e+44) x (if (<= t 1.15e+58) (* y z) (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+78) {
		tmp = t * a;
	} else if (t <= -3.4e-184) {
		tmp = y * z;
	} else if (t <= 1.85e-286) {
		tmp = x;
	} else if (t <= 2.05e-123) {
		tmp = y * z;
	} else if (t <= 8e+44) {
		tmp = x;
	} else if (t <= 1.15e+58) {
		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 <= (-1d+78)) then
        tmp = t * a
    else if (t <= (-3.4d-184)) then
        tmp = y * z
    else if (t <= 1.85d-286) then
        tmp = x
    else if (t <= 2.05d-123) then
        tmp = y * z
    else if (t <= 8d+44) then
        tmp = x
    else if (t <= 1.15d+58) 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 <= -1e+78) {
		tmp = t * a;
	} else if (t <= -3.4e-184) {
		tmp = y * z;
	} else if (t <= 1.85e-286) {
		tmp = x;
	} else if (t <= 2.05e-123) {
		tmp = y * z;
	} else if (t <= 8e+44) {
		tmp = x;
	} else if (t <= 1.15e+58) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e+78:
		tmp = t * a
	elif t <= -3.4e-184:
		tmp = y * z
	elif t <= 1.85e-286:
		tmp = x
	elif t <= 2.05e-123:
		tmp = y * z
	elif t <= 8e+44:
		tmp = x
	elif t <= 1.15e+58:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e+78)
		tmp = Float64(t * a);
	elseif (t <= -3.4e-184)
		tmp = Float64(y * z);
	elseif (t <= 1.85e-286)
		tmp = x;
	elseif (t <= 2.05e-123)
		tmp = Float64(y * z);
	elseif (t <= 8e+44)
		tmp = x;
	elseif (t <= 1.15e+58)
		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 <= -1e+78)
		tmp = t * a;
	elseif (t <= -3.4e-184)
		tmp = y * z;
	elseif (t <= 1.85e-286)
		tmp = x;
	elseif (t <= 2.05e-123)
		tmp = y * z;
	elseif (t <= 8e+44)
		tmp = x;
	elseif (t <= 1.15e+58)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e+78], N[(t * a), $MachinePrecision], If[LessEqual[t, -3.4e-184], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.85e-286], x, If[LessEqual[t, 2.05e-123], N[(y * z), $MachinePrecision], If[LessEqual[t, 8e+44], x, If[LessEqual[t, 1.15e+58], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000001e78 or 1.15000000000000001e58 < t

   1. Initial program 89.5%

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

      1. associate-+l+ 89.5%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 60.7%

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

   if -1.00000000000000001e78 < t < -3.40000000000000004e-184 or 1.85e-286 < t < 2.05e-123 or 8.0000000000000007e44 < t < 1.15000000000000001e58

   1. Initial program 89.7%

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

      1. associate-+l+ 89.7%

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

      2. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in y around inf 43.8%

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

      1. *-commutative 43.8%

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

   7. Simplified 43.8%

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

   if -3.40000000000000004e-184 < t < 1.85e-286 or 2.05e-123 < t < 8.0000000000000007e44

   1. Initial program 95.7%

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

      1. associate-+l+ 95.7%

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

      2. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around inf 44.8%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-184}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-123}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;y \leq -6 \cdot 10^{+86}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-123}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{-230}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= y -6e+86)
     (* y z)
     (if (<= y -1.7e-123)
       (* t a)
       (if (<= y -1.25e-301)
         t_1
         (if (<= y 1e-230)
           (* t a)
           (if (<= y 4.2e-112) t_1 (if (<= y 1.8e+24) x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (y <= -6e+86) {
		tmp = y * z;
	} else if (y <= -1.7e-123) {
		tmp = t * a;
	} else if (y <= -1.25e-301) {
		tmp = t_1;
	} else if (y <= 1e-230) {
		tmp = t * a;
	} else if (y <= 4.2e-112) {
		tmp = t_1;
	} else if (y <= 1.8e+24) {
		tmp = x;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * a) * b
    if (y <= (-6d+86)) then
        tmp = y * z
    else if (y <= (-1.7d-123)) then
        tmp = t * a
    else if (y <= (-1.25d-301)) then
        tmp = t_1
    else if (y <= 1d-230) then
        tmp = t * a
    else if (y <= 4.2d-112) then
        tmp = t_1
    else if (y <= 1.8d+24) then
        tmp = x
    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 t_1 = (z * a) * b;
	double tmp;
	if (y <= -6e+86) {
		tmp = y * z;
	} else if (y <= -1.7e-123) {
		tmp = t * a;
	} else if (y <= -1.25e-301) {
		tmp = t_1;
	} else if (y <= 1e-230) {
		tmp = t * a;
	} else if (y <= 4.2e-112) {
		tmp = t_1;
	} else if (y <= 1.8e+24) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if y <= -6e+86:
		tmp = y * z
	elif y <= -1.7e-123:
		tmp = t * a
	elif y <= -1.25e-301:
		tmp = t_1
	elif y <= 1e-230:
		tmp = t * a
	elif y <= 4.2e-112:
		tmp = t_1
	elif y <= 1.8e+24:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (y <= -6e+86)
		tmp = Float64(y * z);
	elseif (y <= -1.7e-123)
		tmp = Float64(t * a);
	elseif (y <= -1.25e-301)
		tmp = t_1;
	elseif (y <= 1e-230)
		tmp = Float64(t * a);
	elseif (y <= 4.2e-112)
		tmp = t_1;
	elseif (y <= 1.8e+24)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (y <= -6e+86)
		tmp = y * z;
	elseif (y <= -1.7e-123)
		tmp = t * a;
	elseif (y <= -1.25e-301)
		tmp = t_1;
	elseif (y <= 1e-230)
		tmp = t * a;
	elseif (y <= 4.2e-112)
		tmp = t_1;
	elseif (y <= 1.8e+24)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[y, -6e+86], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.7e-123], N[(t * a), $MachinePrecision], If[LessEqual[y, -1.25e-301], t$95$1, If[LessEqual[y, 1e-230], N[(t * a), $MachinePrecision], If[LessEqual[y, 4.2e-112], t$95$1, If[LessEqual[y, 1.8e+24], x, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999954e86 or 1.79999999999999992e24 < y

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. associate-*l* 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in y around inf 57.7%

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

      1. *-commutative 57.7%

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

   7. Simplified 57.7%

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

   if -5.99999999999999954e86 < y < -1.7e-123 or -1.25000000000000003e-301 < y < 1.00000000000000005e-230

   1. Initial program 96.5%

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

      1. associate-+l+ 96.5%

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

      2. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in t around inf 55.4%

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

   if -1.7e-123 < y < -1.25000000000000003e-301 or 1.00000000000000005e-230 < y < 4.2000000000000001e-112

   1. Initial program 96.6%

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

      1. associate-+l+ 96.6%

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

      2. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around inf 53.5%

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

   6. Taylor expanded in y around 0 48.4%

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

      1. associate-*r* 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-*r* 51.7%

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

   8. Simplified 51.7%

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

   if 4.2000000000000001e-112 < y < 1.79999999999999992e24

   1. Initial program 91.9%

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

      1. associate-+l+ 91.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 37.7%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+86}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-123}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-301}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq 10^{-230}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-112}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -13500:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-289}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-126}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+170}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= b -6.6e+28)
     t_1
     (if (<= b -13500.0)
       x
       (if (<= b -7.4e-289)
         (* t a)
         (if (<= b 4.7e-126) (* y z) (if (<= b 1.8e+170) (* t a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (b <= -6.6e+28) {
		tmp = t_1;
	} else if (b <= -13500.0) {
		tmp = x;
	} else if (b <= -7.4e-289) {
		tmp = t * a;
	} else if (b <= 4.7e-126) {
		tmp = y * z;
	} else if (b <= 1.8e+170) {
		tmp = t * a;
	} 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 * (a * b)
    if (b <= (-6.6d+28)) then
        tmp = t_1
    else if (b <= (-13500.0d0)) then
        tmp = x
    else if (b <= (-7.4d-289)) then
        tmp = t * a
    else if (b <= 4.7d-126) then
        tmp = y * z
    else if (b <= 1.8d+170) then
        tmp = t * a
    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 * (a * b);
	double tmp;
	if (b <= -6.6e+28) {
		tmp = t_1;
	} else if (b <= -13500.0) {
		tmp = x;
	} else if (b <= -7.4e-289) {
		tmp = t * a;
	} else if (b <= 4.7e-126) {
		tmp = y * z;
	} else if (b <= 1.8e+170) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if b <= -6.6e+28:
		tmp = t_1
	elif b <= -13500.0:
		tmp = x
	elif b <= -7.4e-289:
		tmp = t * a
	elif b <= 4.7e-126:
		tmp = y * z
	elif b <= 1.8e+170:
		tmp = t * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (b <= -6.6e+28)
		tmp = t_1;
	elseif (b <= -13500.0)
		tmp = x;
	elseif (b <= -7.4e-289)
		tmp = Float64(t * a);
	elseif (b <= 4.7e-126)
		tmp = Float64(y * z);
	elseif (b <= 1.8e+170)
		tmp = Float64(t * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (b <= -6.6e+28)
		tmp = t_1;
	elseif (b <= -13500.0)
		tmp = x;
	elseif (b <= -7.4e-289)
		tmp = t * a;
	elseif (b <= 4.7e-126)
		tmp = y * z;
	elseif (b <= 1.8e+170)
		tmp = t * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.6e+28], t$95$1, If[LessEqual[b, -13500.0], x, If[LessEqual[b, -7.4e-289], N[(t * a), $MachinePrecision], If[LessEqual[b, 4.7e-126], N[(y * z), $MachinePrecision], If[LessEqual[b, 1.8e+170], N[(t * a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.6e28 or 1.8e170 < b

   1. Initial program 89.6%

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

      1. associate-+l+ 89.6%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around inf 73.7%

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

   6. Taylor expanded in y around 0 56.2%

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

   if -6.6e28 < b < -13500

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 75.8%

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

   if -13500 < b < -7.39999999999999977e-289 or 4.70000000000000017e-126 < b < 1.8e170

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around inf 40.3%

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

   if -7.39999999999999977e-289 < b < 4.70000000000000017e-126

   1. Initial program 86.4%

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

      1. associate-+l+ 86.4%

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

      2. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   7. Simplified 59.3%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -13500:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-289}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-126}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+170}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+52} \lor \neg \left(a \leq -11500\right) \land \left(a \leq -5 \cdot 10^{-103} \lor \neg \left(a \leq 4 \cdot 10^{-48}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1e+52)
         (and (not (<= a -11500.0)) (or (<= a -5e-103) (not (<= a 4e-48)))))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+52) || (!(a <= -11500.0) && ((a <= -5e-103) || !(a <= 4e-48)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1d+52)) .or. (.not. (a <= (-11500.0d0))) .and. (a <= (-5d-103)) .or. (.not. (a <= 4d-48))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+52) || (!(a <= -11500.0) && ((a <= -5e-103) || !(a <= 4e-48)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1e+52) or (not (a <= -11500.0) and ((a <= -5e-103) or not (a <= 4e-48))):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1e+52) || (!(a <= -11500.0) && ((a <= -5e-103) || !(a <= 4e-48))))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1e+52) || (~((a <= -11500.0)) && ((a <= -5e-103) || ~((a <= 4e-48)))))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1e+52], And[N[Not[LessEqual[a, -11500.0]], $MachinePrecision], Or[LessEqual[a, -5e-103], N[Not[LessEqual[a, 4e-48]], $MachinePrecision]]]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.9999999999999999e51 or -11500 < a < -4.99999999999999966e-103 or 3.9999999999999999e-48 < a

   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. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in a around inf 77.5%

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

   if -9.9999999999999999e51 < a < -11500 or -4.99999999999999966e-103 < a < 3.9999999999999999e-48

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in a around 0 80.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+52} \lor \neg \left(a \leq -11500\right) \land \left(a \leq -5 \cdot 10^{-103} \lor \neg \left(a \leq 4 \cdot 10^{-48}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+35} \lor \neg \left(z \leq -4.5 \cdot 10^{-55} \lor \neg \left(z \leq -6.5 \cdot 10^{-99}\right) \land z \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.7e+35)
         (not (or (<= z -4.5e-55) (and (not (<= z -6.5e-99)) (<= z 2.3e+22)))))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+35) || !((z <= -4.5e-55) || (!(z <= -6.5e-99) && (z <= 2.3e+22)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.7d+35)) .or. (.not. (z <= (-4.5d-55)) .or. (.not. (z <= (-6.5d-99))) .and. (z <= 2.3d+22))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+35) || !((z <= -4.5e-55) || (!(z <= -6.5e-99) && (z <= 2.3e+22)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.7e+35) or not ((z <= -4.5e-55) or (not (z <= -6.5e-99) and (z <= 2.3e+22))):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.7e+35) || !((z <= -4.5e-55) || (!(z <= -6.5e-99) && (z <= 2.3e+22))))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.7e+35) || ~(((z <= -4.5e-55) || (~((z <= -6.5e-99)) && (z <= 2.3e+22)))))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.7e+35], N[Not[Or[LessEqual[z, -4.5e-55], And[N[Not[LessEqual[z, -6.5e-99]], $MachinePrecision], LessEqual[z, 2.3e+22]]]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000003e35 or -4.4999999999999997e-55 < z < -6.50000000000000033e-99 or 2.3000000000000002e22 < z

   1. Initial program 82.9%

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

      1. associate-+l+ 82.9%

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

      2. associate-*l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 84.0%

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

   if -2.70000000000000003e35 < z < -4.4999999999999997e-55 or -6.50000000000000033e-99 < z < 2.3000000000000002e22

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+35} \lor \neg \left(z \leq -4.5 \cdot 10^{-55} \lor \neg \left(z \leq -6.5 \cdot 10^{-99}\right) \land z \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+107} \lor \neg \left(a \leq 1.7 \cdot 10^{+253}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.5e+102)
   (* z (* a b))
   (if (<= a 1.05e+65)
     (+ x (* y z))
     (if (or (<= a 2.65e+107) (not (<= a 1.7e+253))) (* t a) (* (* z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+102) {
		tmp = z * (a * b);
	} else if (a <= 1.05e+65) {
		tmp = x + (y * z);
	} else if ((a <= 2.65e+107) || !(a <= 1.7e+253)) {
		tmp = t * a;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.5d+102)) then
        tmp = z * (a * b)
    else if (a <= 1.05d+65) then
        tmp = x + (y * z)
    else if ((a <= 2.65d+107) .or. (.not. (a <= 1.7d+253))) then
        tmp = t * a
    else
        tmp = (z * a) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+102) {
		tmp = z * (a * b);
	} else if (a <= 1.05e+65) {
		tmp = x + (y * z);
	} else if ((a <= 2.65e+107) || !(a <= 1.7e+253)) {
		tmp = t * a;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.5e+102:
		tmp = z * (a * b)
	elif a <= 1.05e+65:
		tmp = x + (y * z)
	elif (a <= 2.65e+107) or not (a <= 1.7e+253):
		tmp = t * a
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.5e+102)
		tmp = Float64(z * Float64(a * b));
	elseif (a <= 1.05e+65)
		tmp = Float64(x + Float64(y * z));
	elseif ((a <= 2.65e+107) || !(a <= 1.7e+253))
		tmp = Float64(t * a);
	else
		tmp = Float64(Float64(z * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.5e+102)
		tmp = z * (a * b);
	elseif (a <= 1.05e+65)
		tmp = x + (y * z);
	elseif ((a <= 2.65e+107) || ~((a <= 1.7e+253)))
		tmp = t * a;
	else
		tmp = (z * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.5e+102], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+65], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.65e+107], N[Not[LessEqual[a, 1.7e+253]], $MachinePrecision]], N[(t * a), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.49999999999999981e102

   1. Initial program 79.5%

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

      1. associate-+l+ 79.5%

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

      2. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 65.4%

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

   6. Taylor expanded in y around 0 57.7%

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

   if -5.49999999999999981e102 < a < 1.04999999999999996e65

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around 0 67.7%

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

   if 1.04999999999999996e65 < a < 2.65e107 or 1.70000000000000009e253 < a

   1. Initial program 87.5%

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

      1. associate-+l+ 87.5%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 66.3%

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

   if 2.65e107 < a < 1.70000000000000009e253

   1. Initial program 73.3%

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

      1. associate-+l+ 73.3%

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

      2. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 59.1%

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

   6. Taylor expanded in y around 0 56.5%

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

      1. associate-*r* 49.3%

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

      2. *-commutative 49.3%

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

      3. associate-*r* 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+107} \lor \neg \left(a \leq 1.7 \cdot 10^{+253}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := x + y \cdot z\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (+ x (* y z))))
   (if (<= y -7.5e+90)
     t_2
     (if (<= y -1.4e-159)
       t_1
       (if (<= y -3.6e-200) (* z (* a b)) (if (<= y 2.55e-11) 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 = x + (y * z);
	double tmp;
	if (y <= -7.5e+90) {
		tmp = t_2;
	} else if (y <= -1.4e-159) {
		tmp = t_1;
	} else if (y <= -3.6e-200) {
		tmp = z * (a * b);
	} else if (y <= 2.55e-11) {
		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 = x + (y * z)
    if (y <= (-7.5d+90)) then
        tmp = t_2
    else if (y <= (-1.4d-159)) then
        tmp = t_1
    else if (y <= (-3.6d-200)) then
        tmp = z * (a * b)
    else if (y <= 2.55d-11) 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 = x + (y * z);
	double tmp;
	if (y <= -7.5e+90) {
		tmp = t_2;
	} else if (y <= -1.4e-159) {
		tmp = t_1;
	} else if (y <= -3.6e-200) {
		tmp = z * (a * b);
	} else if (y <= 2.55e-11) {
		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 = x + (y * z)
	tmp = 0
	if y <= -7.5e+90:
		tmp = t_2
	elif y <= -1.4e-159:
		tmp = t_1
	elif y <= -3.6e-200:
		tmp = z * (a * b)
	elif y <= 2.55e-11:
		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(x + Float64(y * z))
	tmp = 0.0
	if (y <= -7.5e+90)
		tmp = t_2;
	elseif (y <= -1.4e-159)
		tmp = t_1;
	elseif (y <= -3.6e-200)
		tmp = Float64(z * Float64(a * b));
	elseif (y <= 2.55e-11)
		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 = x + (y * z);
	tmp = 0.0;
	if (y <= -7.5e+90)
		tmp = t_2;
	elseif (y <= -1.4e-159)
		tmp = t_1;
	elseif (y <= -3.6e-200)
		tmp = z * (a * b);
	elseif (y <= 2.55e-11)
		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[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+90], t$95$2, If[LessEqual[y, -1.4e-159], t$95$1, If[LessEqual[y, -3.6e-200], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e-11], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000014e90 or 2.54999999999999992e-11 < y

   1. Initial program 84.6%

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

      1. associate-+l+ 84.6%

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

      2. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around 0 70.9%

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

   if -7.50000000000000014e90 < y < -1.4000000000000001e-159 or -3.6000000000000002e-200 < y < 2.54999999999999992e-11

   1. Initial program 95.6%

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

      1. associate-+l+ 95.6%

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

      2. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. +-commutative 65.6%

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

   7. Simplified 65.6%

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

   if -1.4000000000000001e-159 < y < -3.6000000000000002e-200

   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. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf 80.3%

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

   6. Taylor expanded in y around 0 80.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-159}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.9e+161)
     t_1
     (if (<= z 5.2e+95)
       (+ (+ x (* y z)) (+ (* a (* z b)) (* t a)))
       (+ x 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 <= -1.9e+161) {
		tmp = t_1;
	} else if (z <= 5.2e+95) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	} else {
		tmp = x + 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 <= (-1.9d+161)) then
        tmp = t_1
    else if (z <= 5.2d+95) then
        tmp = (x + (y * z)) + ((a * (z * b)) + (t * a))
    else
        tmp = x + 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 <= -1.9e+161) {
		tmp = t_1;
	} else if (z <= 5.2e+95) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -1.9e+161:
		tmp = t_1
	elif z <= 5.2e+95:
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a))
	else:
		tmp = x + 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 <= -1.9e+161)
		tmp = t_1;
	elseif (z <= 5.2e+95)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(a * Float64(z * b)) + Float64(t * a)));
	else
		tmp = Float64(x + 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 <= -1.9e+161)
		tmp = t_1;
	elseif (z <= 5.2e+95)
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	else
		tmp = x + 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, -1.9e+161], t$95$1, If[LessEqual[z, 5.2e+95], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9000000000000001e161

   1. Initial program 68.6%

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

      1. associate-+l+ 68.6%

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

      2. associate-*l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 91.5%

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

   if -1.9000000000000001e161 < z < 5.19999999999999981e95

   1. Initial program 97.2%

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

      1. associate-+l+ 97.2%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   if 5.19999999999999981e95 < z

   1. Initial program 81.4%

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

      1. associate-+l+ 81.4%

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

      2. associate-*l* 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in t around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. +-commutative 71.3%

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

      3. associate-*r* 82.0%

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

      4. distribute-rgt-in 91.5%

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

   7. Simplified 91.5%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+100} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+100) (not (<= z 1.35e+25)))
   (* z (+ y (* a b)))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+100) || !(z <= 1.35e+25)) {
		tmp = z * (y + (a * 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 ((z <= (-1.4d+100)) .or. (.not. (z <= 1.35d+25))) then
        tmp = z * (y + (a * 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 ((z <= -1.4e+100) || !(z <= 1.35e+25)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+100) or not (z <= 1.35e+25):
		tmp = z * (y + (a * b))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+100) || !(z <= 1.35e+25))
		tmp = Float64(z * Float64(y + Float64(a * 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 ((z <= -1.4e+100) || ~((z <= 1.35e+25)))
		tmp = z * (y + (a * b));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+100], N[Not[LessEqual[z, 1.35e+25]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $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 z < -1.3999999999999999e100 or 1.35e25 < z

   1. Initial program 80.1%

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

      1. associate-+l+ 80.1%

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

      2. associate-*l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around inf 85.6%

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

   if -1.3999999999999999e100 < z < 1.35e25

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in b around 0 90.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+100} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+35} \lor \neg \left(z \leq 9.2 \cdot 10^{+21}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.1e+35) (not (<= z 9.2e+21)))
   (+ x (* z (+ y (* a b))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+35) || !(z <= 9.2e+21)) {
		tmp = x + (z * (y + (a * 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 ((z <= (-3.1d+35)) .or. (.not. (z <= 9.2d+21))) then
        tmp = x + (z * (y + (a * 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 ((z <= -3.1e+35) || !(z <= 9.2e+21)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.1e+35) or not (z <= 9.2e+21):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.1e+35) || !(z <= 9.2e+21))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * 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 ((z <= -3.1e+35) || ~((z <= 9.2e+21)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.1e+35], N[Not[LessEqual[z, 9.2e+21]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * 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 z < -3.09999999999999987e35 or 9.2e21 < z

   1. Initial program 82.3%

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

      1. associate-+l+ 82.3%

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

      2. associate-*l* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in t around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. +-commutative 73.8%

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

      3. associate-*r* 81.7%

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

      4. distribute-rgt-in 89.5%

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

   7. Simplified 89.5%

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

   if -3.09999999999999987e35 < z < 9.2e21

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in b around 0 93.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+35} \lor \neg \left(z \leq 9.2 \cdot 10^{+21}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+104} \lor \neg \left(a \leq 2.6 \cdot 10^{-129}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.5e+104) (not (<= a 2.6e-129))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.5e+104) || !(a <= 2.6e-129)) {
		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 ((a <= (-7.5d+104)) .or. (.not. (a <= 2.6d-129))) 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 ((a <= -7.5e+104) || !(a <= 2.6e-129)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.5e+104) or not (a <= 2.6e-129):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.5e+104) || !(a <= 2.6e-129))
		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 ((a <= -7.5e+104) || ~((a <= 2.6e-129)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.5e+104], N[Not[LessEqual[a, 2.6e-129]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -7.5000000000000002e104 or 2.6000000000000001e-129 < a

   1. Initial program 82.6%

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

      1. associate-+l+ 82.6%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around inf 43.6%

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

   if -7.5000000000000002e104 < a < 2.6000000000000001e-129

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 38.5%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+104} \lor \neg \left(a \leq 2.6 \cdot 10^{-129}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.3% 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 90.7%

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

   1. associate-+l+ 90.7%

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

   2. associate-*l* 90.5%

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

3. Simplified 90.5%

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

5. Taylor expanded in x around inf 22.9%

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

6. Final simplification 22.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.4% accurate, 0.7× 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 2024039 
(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)))