Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 96.5%

Time: 7.4s

Alternatives: 14

Speedup: 0.9×

• 32.2% 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

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* t a) (+ x (* y z))) (* b (* z a)))))
   (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 = ((t * a) + (x + (y * z))) + (b * (z * a));
	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 = ((t * a) + (x + (y * z))) + (b * (z * a));
	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 = ((t * a) + (x + (y * z))) + (b * (z * a))
	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(t * a) + Float64(x + Float64(y * z))) + Float64(b * Float64(z * a)))
	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 = ((t * a) + (x + (y * z))) + (b * (z * a));
	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[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 98.4%

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

Alternative 2: 39.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{-74}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-95}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-208}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-294}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-35}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.6e+84)
   x
   (if (<= x -1.38e-74)
     (* y z)
     (if (<= x -1.9e-95)
       (* t a)
       (if (<= x -1.65e-208)
         (* y z)
         (if (<= x -2.1e-294)
           (* t a)
           (if (<= x 4.7e-306)
             (* y z)
             (if (<= x 1.12e-35) (* t a) (if (<= x 8.8e+77) (* y z) x)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+84) {
		tmp = x;
	} else if (x <= -1.38e-74) {
		tmp = y * z;
	} else if (x <= -1.9e-95) {
		tmp = t * a;
	} else if (x <= -1.65e-208) {
		tmp = y * z;
	} else if (x <= -2.1e-294) {
		tmp = t * a;
	} else if (x <= 4.7e-306) {
		tmp = y * z;
	} else if (x <= 1.12e-35) {
		tmp = t * a;
	} else if (x <= 8.8e+77) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.6d+84)) then
        tmp = x
    else if (x <= (-1.38d-74)) then
        tmp = y * z
    else if (x <= (-1.9d-95)) then
        tmp = t * a
    else if (x <= (-1.65d-208)) then
        tmp = y * z
    else if (x <= (-2.1d-294)) then
        tmp = t * a
    else if (x <= 4.7d-306) then
        tmp = y * z
    else if (x <= 1.12d-35) then
        tmp = t * a
    else if (x <= 8.8d+77) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+84) {
		tmp = x;
	} else if (x <= -1.38e-74) {
		tmp = y * z;
	} else if (x <= -1.9e-95) {
		tmp = t * a;
	} else if (x <= -1.65e-208) {
		tmp = y * z;
	} else if (x <= -2.1e-294) {
		tmp = t * a;
	} else if (x <= 4.7e-306) {
		tmp = y * z;
	} else if (x <= 1.12e-35) {
		tmp = t * a;
	} else if (x <= 8.8e+77) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.6e+84:
		tmp = x
	elif x <= -1.38e-74:
		tmp = y * z
	elif x <= -1.9e-95:
		tmp = t * a
	elif x <= -1.65e-208:
		tmp = y * z
	elif x <= -2.1e-294:
		tmp = t * a
	elif x <= 4.7e-306:
		tmp = y * z
	elif x <= 1.12e-35:
		tmp = t * a
	elif x <= 8.8e+77:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.6e+84)
		tmp = x;
	elseif (x <= -1.38e-74)
		tmp = Float64(y * z);
	elseif (x <= -1.9e-95)
		tmp = Float64(t * a);
	elseif (x <= -1.65e-208)
		tmp = Float64(y * z);
	elseif (x <= -2.1e-294)
		tmp = Float64(t * a);
	elseif (x <= 4.7e-306)
		tmp = Float64(y * z);
	elseif (x <= 1.12e-35)
		tmp = Float64(t * a);
	elseif (x <= 8.8e+77)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.6e+84)
		tmp = x;
	elseif (x <= -1.38e-74)
		tmp = y * z;
	elseif (x <= -1.9e-95)
		tmp = t * a;
	elseif (x <= -1.65e-208)
		tmp = y * z;
	elseif (x <= -2.1e-294)
		tmp = t * a;
	elseif (x <= 4.7e-306)
		tmp = y * z;
	elseif (x <= 1.12e-35)
		tmp = t * a;
	elseif (x <= 8.8e+77)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.6e+84], x, If[LessEqual[x, -1.38e-74], N[(y * z), $MachinePrecision], If[LessEqual[x, -1.9e-95], N[(t * a), $MachinePrecision], If[LessEqual[x, -1.65e-208], N[(y * z), $MachinePrecision], If[LessEqual[x, -2.1e-294], N[(t * a), $MachinePrecision], If[LessEqual[x, 4.7e-306], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.12e-35], N[(t * a), $MachinePrecision], If[LessEqual[x, 8.8e+77], N[(y * z), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5999999999999999e84 or 8.8000000000000002e77 < x

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around inf 65.3%

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

   if -3.5999999999999999e84 < x < -1.38e-74 or -1.8999999999999999e-95 < x < -1.65000000000000003e-208 or -2.09999999999999984e-294 < x < 4.7000000000000001e-306 or 1.12e-35 < x < 8.8000000000000002e77

   1. Initial program 95.1%

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

      1. associate-+l+ 95.1%

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

      2. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

   6. Simplified 51.8%

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

   if -1.38e-74 < x < -1.8999999999999999e-95 or -1.65000000000000003e-208 < x < -2.09999999999999984e-294 or 4.7000000000000001e-306 < x < 1.12e-35

   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* 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. Taylor expanded in t around inf 50.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{-74}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-95}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-208}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-294}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-35}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 410000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+128} \lor \neg \left(z \leq 2.6 \cdot 10^{+154}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -6.8e-35)
     t_2
     (if (<= z 6.6e-22)
       t_1
       (if (<= z 410000000.0)
         t_2
         (if (<= z 6.5e+59)
           t_1
           (if (or (<= z 9.5e+128) (not (<= z 2.6e+154)))
             t_2
             (+ x (* y z)))))))))

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 <= -6.8e-35) {
		tmp = t_2;
	} else if (z <= 6.6e-22) {
		tmp = t_1;
	} else if (z <= 410000000.0) {
		tmp = t_2;
	} else if (z <= 6.5e+59) {
		tmp = t_1;
	} else if ((z <= 9.5e+128) || !(z <= 2.6e+154)) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = z * (y + (a * b))
    if (z <= (-6.8d-35)) then
        tmp = t_2
    else if (z <= 6.6d-22) then
        tmp = t_1
    else if (z <= 410000000.0d0) then
        tmp = t_2
    else if (z <= 6.5d+59) then
        tmp = t_1
    else if ((z <= 9.5d+128) .or. (.not. (z <= 2.6d+154))) then
        tmp = t_2
    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 t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -6.8e-35) {
		tmp = t_2;
	} else if (z <= 6.6e-22) {
		tmp = t_1;
	} else if (z <= 410000000.0) {
		tmp = t_2;
	} else if (z <= 6.5e+59) {
		tmp = t_1;
	} else if ((z <= 9.5e+128) || !(z <= 2.6e+154)) {
		tmp = t_2;
	} else {
		tmp = x + (y * z);
	}
	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 <= -6.8e-35:
		tmp = t_2
	elif z <= 6.6e-22:
		tmp = t_1
	elif z <= 410000000.0:
		tmp = t_2
	elif z <= 6.5e+59:
		tmp = t_1
	elif (z <= 9.5e+128) or not (z <= 2.6e+154):
		tmp = t_2
	else:
		tmp = x + (y * z)
	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 <= -6.8e-35)
		tmp = t_2;
	elseif (z <= 6.6e-22)
		tmp = t_1;
	elseif (z <= 410000000.0)
		tmp = t_2;
	elseif (z <= 6.5e+59)
		tmp = t_1;
	elseif ((z <= 9.5e+128) || !(z <= 2.6e+154))
		tmp = t_2;
	else
		tmp = Float64(x + Float64(y * z));
	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 <= -6.8e-35)
		tmp = t_2;
	elseif (z <= 6.6e-22)
		tmp = t_1;
	elseif (z <= 410000000.0)
		tmp = t_2;
	elseif (z <= 6.5e+59)
		tmp = t_1;
	elseif ((z <= 9.5e+128) || ~((z <= 2.6e+154)))
		tmp = t_2;
	else
		tmp = x + (y * z);
	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, -6.8e-35], t$95$2, If[LessEqual[z, 6.6e-22], t$95$1, If[LessEqual[z, 410000000.0], t$95$2, If[LessEqual[z, 6.5e+59], t$95$1, If[Or[LessEqual[z, 9.5e+128], N[Not[LessEqual[z, 2.6e+154]], $MachinePrecision]], t$95$2, N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000005e-35 or 6.6000000000000002e-22 < z < 4.1e8 or 6.50000000000000021e59 < z < 9.50000000000000014e128 or 2.59999999999999989e154 < z

   1. Initial program 87.2%

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

      1. associate-+l+ 87.2%

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

      2. associate-*l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in z around inf 81.7%

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

   if -6.8000000000000005e-35 < z < 6.6000000000000002e-22 or 4.1e8 < z < 6.50000000000000021e59

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 79.6%

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

   if 9.50000000000000014e128 < z < 2.59999999999999989e154

   1. Initial program 88.9%

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

      1. associate-+l+ 88.9%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around 0 88.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 410000000:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+59}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+128} \lor \neg \left(z \leq 2.6 \cdot 10^{+154}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 39.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-6}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= a -1.75e+99)
     t_1
     (if (<= a -4.4e-6)
       (* t a)
       (if (<= a -4.8e-123)
         (* y z)
         (if (<= a 9.5e-293)
           x
           (if (<= a 1.1e-36) (* y z) (if (<= a 7e+78) t_1 (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (a <= -1.75e+99) {
		tmp = t_1;
	} else if (a <= -4.4e-6) {
		tmp = t * a;
	} else if (a <= -4.8e-123) {
		tmp = y * z;
	} else if (a <= 9.5e-293) {
		tmp = x;
	} else if (a <= 1.1e-36) {
		tmp = y * z;
	} else if (a <= 7e+78) {
		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 = z * (a * b)
    if (a <= (-1.75d+99)) then
        tmp = t_1
    else if (a <= (-4.4d-6)) then
        tmp = t * a
    else if (a <= (-4.8d-123)) then
        tmp = y * z
    else if (a <= 9.5d-293) then
        tmp = x
    else if (a <= 1.1d-36) then
        tmp = y * z
    else if (a <= 7d+78) 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 = z * (a * b);
	double tmp;
	if (a <= -1.75e+99) {
		tmp = t_1;
	} else if (a <= -4.4e-6) {
		tmp = t * a;
	} else if (a <= -4.8e-123) {
		tmp = y * z;
	} else if (a <= 9.5e-293) {
		tmp = x;
	} else if (a <= 1.1e-36) {
		tmp = y * z;
	} else if (a <= 7e+78) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if a <= -1.75e+99:
		tmp = t_1
	elif a <= -4.4e-6:
		tmp = t * a
	elif a <= -4.8e-123:
		tmp = y * z
	elif a <= 9.5e-293:
		tmp = x
	elif a <= 1.1e-36:
		tmp = y * z
	elif a <= 7e+78:
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (a <= -1.75e+99)
		tmp = t_1;
	elseif (a <= -4.4e-6)
		tmp = Float64(t * a);
	elseif (a <= -4.8e-123)
		tmp = Float64(y * z);
	elseif (a <= 9.5e-293)
		tmp = x;
	elseif (a <= 1.1e-36)
		tmp = Float64(y * z);
	elseif (a <= 7e+78)
		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 = z * (a * b);
	tmp = 0.0;
	if (a <= -1.75e+99)
		tmp = t_1;
	elseif (a <= -4.4e-6)
		tmp = t * a;
	elseif (a <= -4.8e-123)
		tmp = y * z;
	elseif (a <= 9.5e-293)
		tmp = x;
	elseif (a <= 1.1e-36)
		tmp = y * z;
	elseif (a <= 7e+78)
		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[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+99], t$95$1, If[LessEqual[a, -4.4e-6], N[(t * a), $MachinePrecision], If[LessEqual[a, -4.8e-123], N[(y * z), $MachinePrecision], If[LessEqual[a, 9.5e-293], x, If[LessEqual[a, 1.1e-36], N[(y * z), $MachinePrecision], If[LessEqual[a, 7e+78], t$95$1, N[(t * a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7499999999999999e99 or 1.1e-36 < a < 7.0000000000000003e78

   1. Initial program 88.4%

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

      1. associate-+l+ 88.4%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around inf 61.0%

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

   5. Taylor expanded in a around inf 49.5%

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

      1. *-commutative 49.5%

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

   7. Simplified 49.5%

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

   if -1.7499999999999999e99 < a < -4.4000000000000002e-6 or 7.0000000000000003e78 < a

   1. Initial program 89.1%

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

      1. associate-+l+ 89.1%

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

      2. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -4.4000000000000002e-6 < a < -4.8e-123 or 9.50000000000000049e-293 < a < 1.1e-36

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 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. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if -4.8e-123 < a < 9.50000000000000049e-293

   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. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around inf 57.3%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-6}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 5: 39.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -0.0016:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-124}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.3e+99)
   (* a (* z b))
   (if (<= a -0.0016)
     (* t a)
     (if (<= a -1.85e-124)
       (* y z)
       (if (<= a 9.2e-299)
         x
         (if (<= a 3.3e-37)
           (* y z)
           (if (<= a 9.6e+85) (* z (* a b)) (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.3e+99) {
		tmp = a * (z * b);
	} else if (a <= -0.0016) {
		tmp = t * a;
	} else if (a <= -1.85e-124) {
		tmp = y * z;
	} else if (a <= 9.2e-299) {
		tmp = x;
	} else if (a <= 3.3e-37) {
		tmp = y * z;
	} else if (a <= 9.6e+85) {
		tmp = z * (a * b);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.3d+99)) then
        tmp = a * (z * b)
    else if (a <= (-0.0016d0)) then
        tmp = t * a
    else if (a <= (-1.85d-124)) then
        tmp = y * z
    else if (a <= 9.2d-299) then
        tmp = x
    else if (a <= 3.3d-37) then
        tmp = y * z
    else if (a <= 9.6d+85) then
        tmp = z * (a * b)
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.3e+99) {
		tmp = a * (z * b);
	} else if (a <= -0.0016) {
		tmp = t * a;
	} else if (a <= -1.85e-124) {
		tmp = y * z;
	} else if (a <= 9.2e-299) {
		tmp = x;
	} else if (a <= 3.3e-37) {
		tmp = y * z;
	} else if (a <= 9.6e+85) {
		tmp = z * (a * b);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.3e+99:
		tmp = a * (z * b)
	elif a <= -0.0016:
		tmp = t * a
	elif a <= -1.85e-124:
		tmp = y * z
	elif a <= 9.2e-299:
		tmp = x
	elif a <= 3.3e-37:
		tmp = y * z
	elif a <= 9.6e+85:
		tmp = z * (a * b)
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.3e+99)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= -0.0016)
		tmp = Float64(t * a);
	elseif (a <= -1.85e-124)
		tmp = Float64(y * z);
	elseif (a <= 9.2e-299)
		tmp = x;
	elseif (a <= 3.3e-37)
		tmp = Float64(y * z);
	elseif (a <= 9.6e+85)
		tmp = Float64(z * Float64(a * b));
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.3e+99)
		tmp = a * (z * b);
	elseif (a <= -0.0016)
		tmp = t * a;
	elseif (a <= -1.85e-124)
		tmp = y * z;
	elseif (a <= 9.2e-299)
		tmp = x;
	elseif (a <= 3.3e-37)
		tmp = y * z;
	elseif (a <= 9.6e+85)
		tmp = z * (a * b);
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.3e+99], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.0016], N[(t * a), $MachinePrecision], If[LessEqual[a, -1.85e-124], N[(y * z), $MachinePrecision], If[LessEqual[a, 9.2e-299], x, If[LessEqual[a, 3.3e-37], N[(y * z), $MachinePrecision], If[LessEqual[a, 9.6e+85], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.30000000000000019e99

   1. Initial program 82.2%

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

      1. associate-+l+ 82.2%

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

      2. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in a around inf 71.1%

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

   5. Taylor expanded in t around 0 52.6%

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

   if -2.30000000000000019e99 < a < -0.00160000000000000008 or 9.59999999999999986e85 < a

   1. Initial program 89.1%

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

      1. associate-+l+ 89.1%

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

      2. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -0.00160000000000000008 < a < -1.84999999999999995e-124 or 9.2000000000000003e-299 < a < 3.29999999999999982e-37

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 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. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if -1.84999999999999995e-124 < a < 9.2000000000000003e-299

   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. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around inf 57.3%

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

   if 3.29999999999999982e-37 < a < 9.59999999999999986e85

   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. 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. Taylor expanded in z around inf 63.0%

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

   5. Taylor expanded in a around inf 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -0.0016:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-124}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 6: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 245000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+153}:\\ \;\;\;\;x + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -8e-35)
     t_2
     (if (<= z 5.5e-26)
       t_1
       (if (<= z 245000000.0)
         t_2
         (if (<= z 1.9e+42)
           t_1
           (if (<= z 8e+153) (+ x (* b (* z a))) 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 <= -8e-35) {
		tmp = t_2;
	} else if (z <= 5.5e-26) {
		tmp = t_1;
	} else if (z <= 245000000.0) {
		tmp = t_2;
	} else if (z <= 1.9e+42) {
		tmp = t_1;
	} else if (z <= 8e+153) {
		tmp = x + (b * (z * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = z * (y + (a * b))
    if (z <= (-8d-35)) then
        tmp = t_2
    else if (z <= 5.5d-26) then
        tmp = t_1
    else if (z <= 245000000.0d0) then
        tmp = t_2
    else if (z <= 1.9d+42) then
        tmp = t_1
    else if (z <= 8d+153) then
        tmp = x + (b * (z * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -8e-35) {
		tmp = t_2;
	} else if (z <= 5.5e-26) {
		tmp = t_1;
	} else if (z <= 245000000.0) {
		tmp = t_2;
	} else if (z <= 1.9e+42) {
		tmp = t_1;
	} else if (z <= 8e+153) {
		tmp = x + (b * (z * a));
	} 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 <= -8e-35:
		tmp = t_2
	elif z <= 5.5e-26:
		tmp = t_1
	elif z <= 245000000.0:
		tmp = t_2
	elif z <= 1.9e+42:
		tmp = t_1
	elif z <= 8e+153:
		tmp = x + (b * (z * a))
	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 <= -8e-35)
		tmp = t_2;
	elseif (z <= 5.5e-26)
		tmp = t_1;
	elseif (z <= 245000000.0)
		tmp = t_2;
	elseif (z <= 1.9e+42)
		tmp = t_1;
	elseif (z <= 8e+153)
		tmp = Float64(x + Float64(b * Float64(z * a)));
	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 <= -8e-35)
		tmp = t_2;
	elseif (z <= 5.5e-26)
		tmp = t_1;
	elseif (z <= 245000000.0)
		tmp = t_2;
	elseif (z <= 1.9e+42)
		tmp = t_1;
	elseif (z <= 8e+153)
		tmp = x + (b * (z * a));
	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, -8e-35], t$95$2, If[LessEqual[z, 5.5e-26], t$95$1, If[LessEqual[z, 245000000.0], t$95$2, If[LessEqual[z, 1.9e+42], t$95$1, If[LessEqual[z, 8e+153], N[(x + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000006e-35 or 5.5000000000000005e-26 < z < 2.45e8 or 8e153 < z

   1. Initial program 86.4%

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

      1. associate-+l+ 86.4%

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

      2. associate-*l* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in z around inf 83.3%

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

   if -8.00000000000000006e-35 < z < 5.5000000000000005e-26 or 2.45e8 < z < 1.8999999999999999e42

   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. 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. Taylor expanded in z around 0 79.9%

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

   if 1.8999999999999999e42 < z < 8e153

   1. Initial program 92.2%

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

      1. associate-+l+ 92.2%

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

      2. +-commutative 92.2%

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

      3. *-commutative 92.2%

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

      4. associate-*l* 84.9%

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

      5. distribute-lft-out 88.7%

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

      6. fma-def 88.7%

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

      7. +-commutative 88.7%

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

      8. fma-def 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in y around 0 73.2%

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

   5. Taylor expanded in z around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-*l* 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 245000000:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+42}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+153}:\\ \;\;\;\;x + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 7: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(z \cdot b\right) + \left(x + y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.25e-80)
   (+ (* a (* z b)) (+ x (* y z)))
   (if (<= x 1.6e+16)
     (+ (* b (* z a)) (+ (* t a) (* y z)))
     (+ x (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e-80) {
		tmp = (a * (z * b)) + (x + (y * z));
	} else if (x <= 1.6e+16) {
		tmp = (b * (z * a)) + ((t * a) + (y * z));
	} 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 (x <= (-1.25d-80)) then
        tmp = (a * (z * b)) + (x + (y * z))
    else if (x <= 1.6d+16) then
        tmp = (b * (z * a)) + ((t * a) + (y * z))
    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 (x <= -1.25e-80) {
		tmp = (a * (z * b)) + (x + (y * z));
	} else if (x <= 1.6e+16) {
		tmp = (b * (z * a)) + ((t * a) + (y * z));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.25e-80:
		tmp = (a * (z * b)) + (x + (y * z))
	elif x <= 1.6e+16:
		tmp = (b * (z * a)) + ((t * a) + (y * z))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.25e-80)
		tmp = Float64(Float64(a * Float64(z * b)) + Float64(x + Float64(y * z)));
	elseif (x <= 1.6e+16)
		tmp = Float64(Float64(b * Float64(z * a)) + Float64(Float64(t * a) + Float64(y * z)));
	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 (x <= -1.25e-80)
		tmp = (a * (z * b)) + (x + (y * z));
	elseif (x <= 1.6e+16)
		tmp = (b * (z * a)) + ((t * a) + (y * z));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.25e-80], N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+16], N[(N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e-80

   1. Initial program 94.7%

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

      1. associate-+l+ 94.7%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around 0 83.6%

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

   if -1.25e-80 < x < 1.6e16

   1. Initial program 93.3%

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

   2. Taylor expanded in x around 0 89.3%

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

   if 1.6e16 < x

   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%

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

      3. *-commutative 90.2%

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

      4. associate-*l* 85.5%

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

      5. distribute-lft-out 85.5%

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

      6. fma-def 87.1%

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

      7. +-commutative 87.1%

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

      8. fma-def 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around 0 80.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(z \cdot b\right) + \left(x + y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8: 92.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+154}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 7.6e+154)
   (+ (+ (* a (* z b)) (* t a)) (+ x (* y z)))
   (* z (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 7.6e+154) {
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 7.6d+154) then
        tmp = ((a * (z * b)) + (t * a)) + (x + (y * z))
    else
        tmp = z * (y + (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 7.6e+154) {
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 7.6e+154:
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z))
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 7.6e+154)
		tmp = Float64(Float64(Float64(a * Float64(z * b)) + Float64(t * a)) + Float64(x + Float64(y * z)));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 7.6e+154)
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 7.6e+154], N[(N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.5999999999999996e154

   1. Initial program 95.2%

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

      1. associate-+l+ 95.2%

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

      2. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   if 7.5999999999999996e154 < z

   1. Initial program 75.0%

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

      1. associate-+l+ 75.0%

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

      2. associate-*l* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+154}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 9: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -0.00085:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))))
   (if (<= a -1.25e+265)
     t_1
     (if (<= a -1.35e+167)
       (* a (* z b))
       (if (<= a -0.00085)
         t_1
         (if (<= a 1.2e+50)
           (+ x (* y z))
           (if (<= a 3.8e+78) (* z (* a b)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double tmp;
	if (a <= -1.25e+265) {
		tmp = t_1;
	} else if (a <= -1.35e+167) {
		tmp = a * (z * b);
	} else if (a <= -0.00085) {
		tmp = t_1;
	} else if (a <= 1.2e+50) {
		tmp = x + (y * z);
	} else if (a <= 3.8e+78) {
		tmp = z * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * a)
    if (a <= (-1.25d+265)) then
        tmp = t_1
    else if (a <= (-1.35d+167)) then
        tmp = a * (z * b)
    else if (a <= (-0.00085d0)) then
        tmp = t_1
    else if (a <= 1.2d+50) then
        tmp = x + (y * z)
    else if (a <= 3.8d+78) then
        tmp = z * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double tmp;
	if (a <= -1.25e+265) {
		tmp = t_1;
	} else if (a <= -1.35e+167) {
		tmp = a * (z * b);
	} else if (a <= -0.00085) {
		tmp = t_1;
	} else if (a <= 1.2e+50) {
		tmp = x + (y * z);
	} else if (a <= 3.8e+78) {
		tmp = z * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	tmp = 0
	if a <= -1.25e+265:
		tmp = t_1
	elif a <= -1.35e+167:
		tmp = a * (z * b)
	elif a <= -0.00085:
		tmp = t_1
	elif a <= 1.2e+50:
		tmp = x + (y * z)
	elif a <= 3.8e+78:
		tmp = z * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	tmp = 0.0
	if (a <= -1.25e+265)
		tmp = t_1;
	elseif (a <= -1.35e+167)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= -0.00085)
		tmp = t_1;
	elseif (a <= 1.2e+50)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 3.8e+78)
		tmp = Float64(z * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	tmp = 0.0;
	if (a <= -1.25e+265)
		tmp = t_1;
	elseif (a <= -1.35e+167)
		tmp = a * (z * b);
	elseif (a <= -0.00085)
		tmp = t_1;
	elseif (a <= 1.2e+50)
		tmp = x + (y * z);
	elseif (a <= 3.8e+78)
		tmp = z * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+265], t$95$1, If[LessEqual[a, -1.35e+167], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.00085], t$95$1, If[LessEqual[a, 1.2e+50], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+78], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.25e265 or -1.35000000000000003e167 < a < -8.49999999999999953e-4 or 3.7999999999999999e78 < a

   1. Initial program 85.9%

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

      1. associate-+l+ 85.9%

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

      2. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around 0 68.5%

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

   if -1.25e265 < a < -1.35000000000000003e167

   1. Initial program 87.4%

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

      1. associate-+l+ 87.4%

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

      2. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in a around inf 78.6%

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

   5. Taylor expanded in t around 0 67.5%

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

   if -8.49999999999999953e-4 < a < 1.2000000000000001e50

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in a around 0 79.4%

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

   if 1.2000000000000001e50 < a < 3.7999999999999999e78

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 87.9%

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

   5. Taylor expanded in a around inf 87.9%

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

      1. *-commutative 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+265}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -0.00085:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 10: 57.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+89}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+154}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -2.7e+89)
     (* y z)
     (if (<= z -6.2e+34)
       t_1
       (if (<= z -8e-35) (* y z) (if (<= z 2.8e+154) (+ x (* 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 (z <= -2.7e+89) {
		tmp = y * z;
	} else if (z <= -6.2e+34) {
		tmp = t_1;
	} else if (z <= -8e-35) {
		tmp = y * z;
	} else if (z <= 2.8e+154) {
		tmp = x + (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 (z <= (-2.7d+89)) then
        tmp = y * z
    else if (z <= (-6.2d+34)) then
        tmp = t_1
    else if (z <= (-8d-35)) then
        tmp = y * z
    else if (z <= 2.8d+154) then
        tmp = x + (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 (z <= -2.7e+89) {
		tmp = y * z;
	} else if (z <= -6.2e+34) {
		tmp = t_1;
	} else if (z <= -8e-35) {
		tmp = y * z;
	} else if (z <= 2.8e+154) {
		tmp = x + (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 z <= -2.7e+89:
		tmp = y * z
	elif z <= -6.2e+34:
		tmp = t_1
	elif z <= -8e-35:
		tmp = y * z
	elif z <= 2.8e+154:
		tmp = x + (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 (z <= -2.7e+89)
		tmp = Float64(y * z);
	elseif (z <= -6.2e+34)
		tmp = t_1;
	elseif (z <= -8e-35)
		tmp = Float64(y * z);
	elseif (z <= 2.8e+154)
		tmp = Float64(x + 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 (z <= -2.7e+89)
		tmp = y * z;
	elseif (z <= -6.2e+34)
		tmp = t_1;
	elseif (z <= -8e-35)
		tmp = y * z;
	elseif (z <= 2.8e+154)
		tmp = x + (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[z, -2.7e+89], N[(y * z), $MachinePrecision], If[LessEqual[z, -6.2e+34], t$95$1, If[LessEqual[z, -8e-35], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.8e+154], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e89 or -6.19999999999999955e34 < z < -8.00000000000000006e-35

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if -2.7e89 < z < -6.19999999999999955e34 or 2.7999999999999999e154 < z

   1. Initial program 78.0%

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

      1. associate-+l+ 78.0%

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

      2. associate-*l* 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around inf 90.6%

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

   5. Taylor expanded in a around inf 57.3%

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

      1. *-commutative 57.3%

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

   7. Simplified 57.3%

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

   if -8.00000000000000006e-35 < z < 2.7999999999999999e154

   1. Initial program 96.9%

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

      1. associate-+l+ 96.9%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 72.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+89}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+154}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 11: 80.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-35} \lor \neg \left(z \leq 8 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e-35) (not (<= z 8e+153)))
   (* 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 <= -8e-35) || !(z <= 8e+153)) {
		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 <= (-8d-35)) .or. (.not. (z <= 8d+153))) 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 <= -8e-35) || !(z <= 8e+153)) {
		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 <= -8e-35) or not (z <= 8e+153):
		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 <= -8e-35) || !(z <= 8e+153))
		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 <= -8e-35) || ~((z <= 8e+153)))
		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, -8e-35], N[Not[LessEqual[z, 8e+153]], $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 < -8.00000000000000006e-35 or 8e153 < z

   1. Initial program 86.3%

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

      1. associate-+l+ 86.3%

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

      2. associate-*l* 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in z around inf 83.6%

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

   if -8.00000000000000006e-35 < z < 8e153

   1. Initial program 96.9%

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

      1. associate-+l+ 96.9%

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

      2. +-commutative 96.9%

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

      3. *-commutative 96.9%

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

      4. associate-*l* 96.3%

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

      5. distribute-lft-out 98.1%

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

      6. fma-def 98.1%

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

      7. +-commutative 98.1%

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

      8. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around 0 84.7%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-35} \lor \neg \left(z \leq 8 \cdot 10^{+153}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 12: 81.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(z \cdot b\right) + \left(x + y \cdot z\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+153}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.25e-37)
   (+ (* a (* z b)) (+ x (* y z)))
   (if (<= z 8e+153) (+ x (* a (+ t (* z b)))) (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e-37) {
		tmp = (a * (z * b)) + (x + (y * z));
	} else if (z <= 8e+153) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.25d-37)) then
        tmp = (a * (z * b)) + (x + (y * z))
    else if (z <= 8d+153) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = z * (y + (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e-37) {
		tmp = (a * (z * b)) + (x + (y * z));
	} else if (z <= 8e+153) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.25e-37:
		tmp = (a * (z * b)) + (x + (y * z))
	elif z <= 8e+153:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.25e-37)
		tmp = Float64(Float64(a * Float64(z * b)) + Float64(x + Float64(y * z)));
	elseif (z <= 8e+153)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.25e-37)
		tmp = (a * (z * b)) + (x + (y * z));
	elseif (z <= 8e+153)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.25e-37], N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+153], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2499999999999999e-37

   1. Initial program 91.0%

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

      1. associate-+l+ 91.0%

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

      2. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in t around 0 80.0%

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

   if -1.2499999999999999e-37 < z < 8e153

   1. Initial program 96.9%

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

      1. associate-+l+ 96.9%

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

      2. +-commutative 96.9%

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

      3. *-commutative 96.9%

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

      4. associate-*l* 96.3%

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

      5. distribute-lft-out 98.1%

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

      6. fma-def 98.1%

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

      7. +-commutative 98.1%

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

      8. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around 0 84.7%

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

   if 8e153 < z

   1. Initial program 75.0%

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

      1. associate-+l+ 75.0%

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

      2. associate-*l* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(z \cdot b\right) + \left(x + y \cdot z\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+153}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 13: 38.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3e-74) x (if (<= x 3.6e+14) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e-74) {
		tmp = x;
	} else if (x <= 3.6e+14) {
		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 (x <= (-3d-74)) then
        tmp = x
    else if (x <= 3.6d+14) 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 (x <= -3e-74) {
		tmp = x;
	} else if (x <= 3.6e+14) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3e-74:
		tmp = x
	elif x <= 3.6e+14:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3e-74)
		tmp = x;
	elseif (x <= 3.6e+14)
		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 (x <= -3e-74)
		tmp = x;
	elseif (x <= 3.6e+14)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3e-74], x, If[LessEqual[x, 3.6e+14], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000007e-74 or 3.6e14 < x

   1. Initial program 93.4%

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

      1. associate-+l+ 93.4%

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

      2. associate-*l* 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. Taylor expanded in x around inf 50.1%

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

   if -3.00000000000000007e-74 < x < 3.6e14

   1. Initial program 92.5%

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

      1. associate-+l+ 92.5%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around inf 40.2%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 26.1% 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. associate-*l* 90.3%

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

3. Simplified 90.3%

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

4. Taylor expanded in x around inf 29.6%

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

5. Final simplification 29.6%

   \[\leadsto x \]

Developer target: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023224 
(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)))