Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.9% → 95.2%

Time: 12.6s

Alternatives: 14

Speedup: 0.4×

• 31.9% 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: 92.9% 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: 95.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;\left(t\_1 + a \cdot t\right) + b \cdot \left(z \cdot a\right) \leq \infty:\\ \;\;\;\;t\_1 + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   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* 33.3%

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

   3. Simplified 33.3%

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

      1. *-commutative 33.3%

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

      2. distribute-rgt-in 75.0%

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

      3. add-cube-cbrt 75.0%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 75.0%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 75.0%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 75.0%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 75.0%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 75.0%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in a around inf 84.2%

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

4. Final simplification 98.8%

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

Alternative 2: 94.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.0%

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

   1. associate-+l+ 94.0%

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

   2. +-commutative 94.0%

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

   3. fma-def 94.0%

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

   4. associate-*l* 96.4%

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

   5. *-commutative 96.4%

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

   6. *-commutative 96.4%

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

   7. distribute-rgt-out 98.4%

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

   8. *-commutative 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 39.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-274}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-71}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+76}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.2e+42)
   (* y z)
   (if (<= y -4.4e-184)
     x
     (if (<= y 5e-274)
       (* a t)
       (if (<= y 5.4e-104)
         x
         (if (<= y 3e-71)
           (* a t)
           (if (<= y 4.1e-22) x (if (<= y 1.4e+76) (* a t) (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.2e+42) {
		tmp = y * z;
	} else if (y <= -4.4e-184) {
		tmp = x;
	} else if (y <= 5e-274) {
		tmp = a * t;
	} else if (y <= 5.4e-104) {
		tmp = x;
	} else if (y <= 3e-71) {
		tmp = a * t;
	} else if (y <= 4.1e-22) {
		tmp = x;
	} else if (y <= 1.4e+76) {
		tmp = a * t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.2d+42)) then
        tmp = y * z
    else if (y <= (-4.4d-184)) then
        tmp = x
    else if (y <= 5d-274) then
        tmp = a * t
    else if (y <= 5.4d-104) then
        tmp = x
    else if (y <= 3d-71) then
        tmp = a * t
    else if (y <= 4.1d-22) then
        tmp = x
    else if (y <= 1.4d+76) then
        tmp = a * t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.2e+42) {
		tmp = y * z;
	} else if (y <= -4.4e-184) {
		tmp = x;
	} else if (y <= 5e-274) {
		tmp = a * t;
	} else if (y <= 5.4e-104) {
		tmp = x;
	} else if (y <= 3e-71) {
		tmp = a * t;
	} else if (y <= 4.1e-22) {
		tmp = x;
	} else if (y <= 1.4e+76) {
		tmp = a * t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.2e+42:
		tmp = y * z
	elif y <= -4.4e-184:
		tmp = x
	elif y <= 5e-274:
		tmp = a * t
	elif y <= 5.4e-104:
		tmp = x
	elif y <= 3e-71:
		tmp = a * t
	elif y <= 4.1e-22:
		tmp = x
	elif y <= 1.4e+76:
		tmp = a * t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.2e+42)
		tmp = Float64(y * z);
	elseif (y <= -4.4e-184)
		tmp = x;
	elseif (y <= 5e-274)
		tmp = Float64(a * t);
	elseif (y <= 5.4e-104)
		tmp = x;
	elseif (y <= 3e-71)
		tmp = Float64(a * t);
	elseif (y <= 4.1e-22)
		tmp = x;
	elseif (y <= 1.4e+76)
		tmp = Float64(a * t);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.2e+42)
		tmp = y * z;
	elseif (y <= -4.4e-184)
		tmp = x;
	elseif (y <= 5e-274)
		tmp = a * t;
	elseif (y <= 5.4e-104)
		tmp = x;
	elseif (y <= 3e-71)
		tmp = a * t;
	elseif (y <= 4.1e-22)
		tmp = x;
	elseif (y <= 1.4e+76)
		tmp = a * t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.2e+42], N[(y * z), $MachinePrecision], If[LessEqual[y, -4.4e-184], x, If[LessEqual[y, 5e-274], N[(a * t), $MachinePrecision], If[LessEqual[y, 5.4e-104], x, If[LessEqual[y, 3e-71], N[(a * t), $MachinePrecision], If[LessEqual[y, 4.1e-22], x, If[LessEqual[y, 1.4e+76], N[(a * t), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2000000000000002e42 or 1.3999999999999999e76 < y

   1. Initial program 92.7%

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

      1. associate-+l+ 92.7%

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

      2. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   if -7.2000000000000002e42 < y < -4.39999999999999984e-184 or 5e-274 < y < 5.3999999999999997e-104 or 3.0000000000000001e-71 < y < 4.0999999999999999e-22

   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* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 42.5%

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

   if -4.39999999999999984e-184 < y < 5e-274 or 5.3999999999999997e-104 < y < 3.0000000000000001e-71 or 4.0999999999999999e-22 < y < 1.3999999999999999e76

   1. Initial program 93.5%

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

      1. associate-+l+ 93.5%

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

      2. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

      1. *-commutative 96.9%

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

      2. distribute-rgt-in 98.4%

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

      3. add-cube-cbrt 97.8%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 97.8%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 97.8%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 97.8%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 97.8%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 97.8%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in t around inf 44.6%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-274}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-71}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+76}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= y -1.02e-10)
     (* y z)
     (if (<= y -3.7e-289)
       t_1
       (if (<= y 3.2e-106)
         x
         (if (<= y 1.25e-79)
           t_1
           (if (<= y 2.35e-23) x (if (<= y 2.2e+81) (* a t) (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (y <= -1.02e-10) {
		tmp = y * z;
	} else if (y <= -3.7e-289) {
		tmp = t_1;
	} else if (y <= 3.2e-106) {
		tmp = x;
	} else if (y <= 1.25e-79) {
		tmp = t_1;
	} else if (y <= 2.35e-23) {
		tmp = x;
	} else if (y <= 2.2e+81) {
		tmp = a * t;
	} 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 = a * (z * b)
    if (y <= (-1.02d-10)) then
        tmp = y * z
    else if (y <= (-3.7d-289)) then
        tmp = t_1
    else if (y <= 3.2d-106) then
        tmp = x
    else if (y <= 1.25d-79) then
        tmp = t_1
    else if (y <= 2.35d-23) then
        tmp = x
    else if (y <= 2.2d+81) then
        tmp = a * t
    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 = a * (z * b);
	double tmp;
	if (y <= -1.02e-10) {
		tmp = y * z;
	} else if (y <= -3.7e-289) {
		tmp = t_1;
	} else if (y <= 3.2e-106) {
		tmp = x;
	} else if (y <= 1.25e-79) {
		tmp = t_1;
	} else if (y <= 2.35e-23) {
		tmp = x;
	} else if (y <= 2.2e+81) {
		tmp = a * t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if y <= -1.02e-10:
		tmp = y * z
	elif y <= -3.7e-289:
		tmp = t_1
	elif y <= 3.2e-106:
		tmp = x
	elif y <= 1.25e-79:
		tmp = t_1
	elif y <= 2.35e-23:
		tmp = x
	elif y <= 2.2e+81:
		tmp = a * t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (y <= -1.02e-10)
		tmp = Float64(y * z);
	elseif (y <= -3.7e-289)
		tmp = t_1;
	elseif (y <= 3.2e-106)
		tmp = x;
	elseif (y <= 1.25e-79)
		tmp = t_1;
	elseif (y <= 2.35e-23)
		tmp = x;
	elseif (y <= 2.2e+81)
		tmp = Float64(a * t);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (y <= -1.02e-10)
		tmp = y * z;
	elseif (y <= -3.7e-289)
		tmp = t_1;
	elseif (y <= 3.2e-106)
		tmp = x;
	elseif (y <= 1.25e-79)
		tmp = t_1;
	elseif (y <= 2.35e-23)
		tmp = x;
	elseif (y <= 2.2e+81)
		tmp = a * t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e-10], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.7e-289], t$95$1, If[LessEqual[y, 3.2e-106], x, If[LessEqual[y, 1.25e-79], t$95$1, If[LessEqual[y, 2.35e-23], x, If[LessEqual[y, 2.2e+81], N[(a * t), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.01999999999999997e-10 or 2.19999999999999987e81 < y

   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* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 60.1%

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

      1. *-commutative 60.1%

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

   7. Simplified 60.1%

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

   if -1.01999999999999997e-10 < y < -3.69999999999999989e-289 or 3.2e-106 < y < 1.25e-79

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

      1. *-commutative 94.2%

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

      2. distribute-rgt-in 98.4%

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

      3. add-cube-cbrt 97.7%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 97.7%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 97.7%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 97.7%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 97.7%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 97.7%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in b around inf 46.5%

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

   if -3.69999999999999989e-289 < y < 3.2e-106 or 1.25e-79 < y < 2.35e-23

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf 48.0%

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

   if 2.35e-23 < y < 2.19999999999999987e81

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. add-cube-cbrt 99.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 99.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 99.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 99.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in t around inf 45.5%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-289}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-301}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+70}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e-11)
   (* y z)
   (if (<= y -7e-301)
     (* b (* z a))
     (if (<= y 2.1e-104)
       x
       (if (<= y 2.9e-79)
         (* a (* z b))
         (if (<= y 8e-23) x (if (<= y 6e+70) (* a t) (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-11) {
		tmp = y * z;
	} else if (y <= -7e-301) {
		tmp = b * (z * a);
	} else if (y <= 2.1e-104) {
		tmp = x;
	} else if (y <= 2.9e-79) {
		tmp = a * (z * b);
	} else if (y <= 8e-23) {
		tmp = x;
	} else if (y <= 6e+70) {
		tmp = a * t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d-11)) then
        tmp = y * z
    else if (y <= (-7d-301)) then
        tmp = b * (z * a)
    else if (y <= 2.1d-104) then
        tmp = x
    else if (y <= 2.9d-79) then
        tmp = a * (z * b)
    else if (y <= 8d-23) then
        tmp = x
    else if (y <= 6d+70) then
        tmp = a * t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-11) {
		tmp = y * z;
	} else if (y <= -7e-301) {
		tmp = b * (z * a);
	} else if (y <= 2.1e-104) {
		tmp = x;
	} else if (y <= 2.9e-79) {
		tmp = a * (z * b);
	} else if (y <= 8e-23) {
		tmp = x;
	} else if (y <= 6e+70) {
		tmp = a * t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e-11:
		tmp = y * z
	elif y <= -7e-301:
		tmp = b * (z * a)
	elif y <= 2.1e-104:
		tmp = x
	elif y <= 2.9e-79:
		tmp = a * (z * b)
	elif y <= 8e-23:
		tmp = x
	elif y <= 6e+70:
		tmp = a * t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e-11)
		tmp = Float64(y * z);
	elseif (y <= -7e-301)
		tmp = Float64(b * Float64(z * a));
	elseif (y <= 2.1e-104)
		tmp = x;
	elseif (y <= 2.9e-79)
		tmp = Float64(a * Float64(z * b));
	elseif (y <= 8e-23)
		tmp = x;
	elseif (y <= 6e+70)
		tmp = Float64(a * t);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e-11)
		tmp = y * z;
	elseif (y <= -7e-301)
		tmp = b * (z * a);
	elseif (y <= 2.1e-104)
		tmp = x;
	elseif (y <= 2.9e-79)
		tmp = a * (z * b);
	elseif (y <= 8e-23)
		tmp = x;
	elseif (y <= 6e+70)
		tmp = a * t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e-11], N[(y * z), $MachinePrecision], If[LessEqual[y, -7e-301], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-104], x, If[LessEqual[y, 2.9e-79], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-23], x, If[LessEqual[y, 6e+70], N[(a * t), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.99999999999999952e-11 or 5.99999999999999952e70 < y

   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* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 60.1%

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

      1. *-commutative 60.1%

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

   7. Simplified 60.1%

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

   if -7.99999999999999952e-11 < y < -6.99999999999999984e-301

   1. Initial program 95.0%

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

      1. associate-+l+ 95.0%

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

      2. associate-*l* 93.4%

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

   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. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 93.4%

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

      2. distribute-rgt-in 98.2%

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

      3. add-cube-cbrt 97.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 97.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 97.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 97.4%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 97.4%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 97.4%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in b around inf 45.0%

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

      1. associate-*r* 45.1%

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

      2. *-commutative 45.1%

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

   9. Simplified 45.1%

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

   10. Taylor expanded in z around 0 45.0%

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

       1. *-commutative 45.0%

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

       2. associate-*l* 46.6%

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

   12. Simplified 46.6%

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

   if -6.99999999999999984e-301 < y < 2.09999999999999999e-104 or 2.9000000000000001e-79 < y < 7.99999999999999968e-23

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf 48.0%

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

   if 2.09999999999999999e-104 < y < 2.9000000000000001e-79

   1. Initial program 88.7%

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

      1. associate-+l+ 88.7%

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

      2. associate-*l* 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. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. add-cube-cbrt 99.1%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 99.2%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 99.2%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 99.2%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 99.2%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 99.2%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in b around inf 56.4%

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

   if 7.99999999999999968e-23 < y < 5.99999999999999952e70

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. add-cube-cbrt 99.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 99.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 99.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 99.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in t around inf 45.5%

      \[\leadsto \color{blue}{a \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-301}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+70}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot t + y \cdot z\\ t_2 := x + y \cdot z\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+149}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a t) (* y z))) (t_2 (+ x (* y z))))
   (if (<= y -1.02e+86)
     t_1
     (if (<= y 1.8e+85)
       (+ x (* a (+ t (* z b))))
       (if (<= y 2.6e+143)
         t_2
         (if (<= y 2.2e+149) (+ x (* a t)) (if (<= y 7.5e+248) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * t) + (y * z);
	double t_2 = x + (y * z);
	double tmp;
	if (y <= -1.02e+86) {
		tmp = t_1;
	} else if (y <= 1.8e+85) {
		tmp = x + (a * (t + (z * b)));
	} else if (y <= 2.6e+143) {
		tmp = t_2;
	} else if (y <= 2.2e+149) {
		tmp = x + (a * t);
	} else if (y <= 7.5e+248) {
		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 = (a * t) + (y * z)
    t_2 = x + (y * z)
    if (y <= (-1.02d+86)) then
        tmp = t_1
    else if (y <= 1.8d+85) then
        tmp = x + (a * (t + (z * b)))
    else if (y <= 2.6d+143) then
        tmp = t_2
    else if (y <= 2.2d+149) then
        tmp = x + (a * t)
    else if (y <= 7.5d+248) 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 = (a * t) + (y * z);
	double t_2 = x + (y * z);
	double tmp;
	if (y <= -1.02e+86) {
		tmp = t_1;
	} else if (y <= 1.8e+85) {
		tmp = x + (a * (t + (z * b)));
	} else if (y <= 2.6e+143) {
		tmp = t_2;
	} else if (y <= 2.2e+149) {
		tmp = x + (a * t);
	} else if (y <= 7.5e+248) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * t) + (y * z)
	t_2 = x + (y * z)
	tmp = 0
	if y <= -1.02e+86:
		tmp = t_1
	elif y <= 1.8e+85:
		tmp = x + (a * (t + (z * b)))
	elif y <= 2.6e+143:
		tmp = t_2
	elif y <= 2.2e+149:
		tmp = x + (a * t)
	elif y <= 7.5e+248:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * t) + Float64(y * z))
	t_2 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (y <= -1.02e+86)
		tmp = t_1;
	elseif (y <= 1.8e+85)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (y <= 2.6e+143)
		tmp = t_2;
	elseif (y <= 2.2e+149)
		tmp = Float64(x + Float64(a * t));
	elseif (y <= 7.5e+248)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * t) + (y * z);
	t_2 = x + (y * z);
	tmp = 0.0;
	if (y <= -1.02e+86)
		tmp = t_1;
	elseif (y <= 1.8e+85)
		tmp = x + (a * (t + (z * b)));
	elseif (y <= 2.6e+143)
		tmp = t_2;
	elseif (y <= 2.2e+149)
		tmp = x + (a * t);
	elseif (y <= 7.5e+248)
		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[(N[(a * t), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+86], t$95$1, If[LessEqual[y, 1.8e+85], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+143], t$95$2, If[LessEqual[y, 2.2e+149], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+248], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.01999999999999996e86 or 2.2e149 < y < 7.5000000000000004e248

   1. Initial program 90.3%

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

      1. associate-+l+ 90.3%

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

      2. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around inf 93.6%

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

   6. Taylor expanded in x around 0 84.3%

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

   if -1.01999999999999996e86 < y < 1.7999999999999999e85

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. +-commutative 94.3%

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

      3. fma-def 94.3%

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

      4. associate-*l* 96.9%

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

      5. *-commutative 96.9%

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

      6. *-commutative 96.9%

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

      7. distribute-rgt-out 99.3%

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

      8. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 89.2%

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

   if 1.7999999999999999e85 < y < 2.5999999999999999e143 or 7.5000000000000004e248 < y

   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* 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 a around 0 89.3%

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

   if 2.5999999999999999e143 < y < 2.2e149

   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 z around 0 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+143}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+149}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+248}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{+24} \lor \neg \left(a \leq 52000000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -8e+168)
     t_1
     (if (<= a -3.4e+69)
       (+ x (* a t))
       (if (or (<= a -3.6e+24) (not (<= a 52000000000.0)))
         t_1
         (+ x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -8e+168) {
		tmp = t_1;
	} else if (a <= -3.4e+69) {
		tmp = x + (a * t);
	} else if ((a <= -3.6e+24) || !(a <= 52000000000.0)) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-8d+168)) then
        tmp = t_1
    else if (a <= (-3.4d+69)) then
        tmp = x + (a * t)
    else if ((a <= (-3.6d+24)) .or. (.not. (a <= 52000000000.0d0))) then
        tmp = t_1
    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 = a * (t + (z * b));
	double tmp;
	if (a <= -8e+168) {
		tmp = t_1;
	} else if (a <= -3.4e+69) {
		tmp = x + (a * t);
	} else if ((a <= -3.6e+24) || !(a <= 52000000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -8e+168:
		tmp = t_1
	elif a <= -3.4e+69:
		tmp = x + (a * t)
	elif (a <= -3.6e+24) or not (a <= 52000000000.0):
		tmp = t_1
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -8e+168)
		tmp = t_1;
	elseif (a <= -3.4e+69)
		tmp = Float64(x + Float64(a * t));
	elseif ((a <= -3.6e+24) || !(a <= 52000000000.0))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -8e+168)
		tmp = t_1;
	elseif (a <= -3.4e+69)
		tmp = x + (a * t);
	elseif ((a <= -3.6e+24) || ~((a <= 52000000000.0)))
		tmp = t_1;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+168], t$95$1, If[LessEqual[a, -3.4e+69], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3.6e+24], N[Not[LessEqual[a, 52000000000.0]], $MachinePrecision]], t$95$1, N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.9999999999999995e168 or -3.39999999999999986e69 < a < -3.59999999999999983e24 or 5.2e10 < 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* 93.7%

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

   3. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. distribute-rgt-in 97.9%

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

      3. add-cube-cbrt 97.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 97.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 97.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 97.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 97.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 97.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in a around inf 79.2%

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

   if -7.9999999999999995e168 < a < -3.39999999999999986e69

   1. Initial program 82.4%

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

      1. associate-+l+ 82.4%

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

      2. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

   7. Simplified 74.1%

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

   if -3.59999999999999983e24 < a < 5.2e10

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-*l* 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 a around 0 74.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+168}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{+24} \lor \neg \left(a \leq 52000000000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -50000000000:\\ \;\;\;\;x + b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-101}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;a \leq 70000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -7.2e+132)
     t_1
     (if (<= a -50000000000.0)
       (+ x (* b (* z a)))
       (if (<= a -4.1e-101)
         (+ (* a t) (* y z))
         (if (<= a 70000000.0) (+ x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -7.2e+132) {
		tmp = t_1;
	} else if (a <= -50000000000.0) {
		tmp = x + (b * (z * a));
	} else if (a <= -4.1e-101) {
		tmp = (a * t) + (y * z);
	} else if (a <= 70000000.0) {
		tmp = x + (y * z);
	} 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 = a * (t + (z * b))
    if (a <= (-7.2d+132)) then
        tmp = t_1
    else if (a <= (-50000000000.0d0)) then
        tmp = x + (b * (z * a))
    else if (a <= (-4.1d-101)) then
        tmp = (a * t) + (y * z)
    else if (a <= 70000000.0d0) then
        tmp = x + (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -7.2e+132) {
		tmp = t_1;
	} else if (a <= -50000000000.0) {
		tmp = x + (b * (z * a));
	} else if (a <= -4.1e-101) {
		tmp = (a * t) + (y * z);
	} else if (a <= 70000000.0) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -7.2e+132:
		tmp = t_1
	elif a <= -50000000000.0:
		tmp = x + (b * (z * a))
	elif a <= -4.1e-101:
		tmp = (a * t) + (y * z)
	elif a <= 70000000.0:
		tmp = x + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -7.2e+132)
		tmp = t_1;
	elseif (a <= -50000000000.0)
		tmp = Float64(x + Float64(b * Float64(z * a)));
	elseif (a <= -4.1e-101)
		tmp = Float64(Float64(a * t) + Float64(y * z));
	elseif (a <= 70000000.0)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -7.2e+132)
		tmp = t_1;
	elseif (a <= -50000000000.0)
		tmp = x + (b * (z * a));
	elseif (a <= -4.1e-101)
		tmp = (a * t) + (y * z);
	elseif (a <= 70000000.0)
		tmp = x + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+132], t$95$1, If[LessEqual[a, -50000000000.0], N[(x + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e-101], N[(N[(a * t), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 70000000.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.20000000000000031e132 or 7e7 < a

   1. Initial program 84.5%

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

      1. associate-+l+ 84.5%

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

      2. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

      1. *-commutative 91.6%

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

      2. distribute-rgt-in 96.8%

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

      3. add-cube-cbrt 96.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 96.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 96.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 96.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 96.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 96.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in a around inf 77.6%

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

   if -7.20000000000000031e132 < a < -5e10

   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* 99.9%

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

   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 t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. +-commutative 84.3%

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

      3. associate-*r* 79.1%

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

      4. distribute-rgt-in 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in y around 0 69.4%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. *-commutative 33.2%

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

       2. associate-*l* 38.0%

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

   11. Simplified 79.4%

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

   if -5e10 < a < -4.10000000000000026e-101

   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. Add Preprocessing

   5. Taylor expanded in t around inf 88.8%

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

   6. Taylor expanded in x around 0 73.7%

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

   if -4.10000000000000026e-101 < a < 7e7

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in a around 0 77.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -50000000000:\\ \;\;\;\;x + b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-101}:\\ \;\;\;\;a \cdot t + y \cdot z\\ \mathbf{elif}\;a \leq 70000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+78} \lor \neg \left(y \leq 4 \cdot 10^{+68}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.5e+78) (not (<= y 4e+68)))
   (+ x (* 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 ((y <= -6.5e+78) || !(y <= 4e+68)) {
		tmp = x + (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 ((y <= (-6.5d+78)) .or. (.not. (y <= 4d+68))) then
        tmp = x + (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 ((y <= -6.5e+78) || !(y <= 4e+68)) {
		tmp = x + (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 (y <= -6.5e+78) or not (y <= 4e+68):
		tmp = x + (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 ((y <= -6.5e+78) || !(y <= 4e+68))
		tmp = Float64(x + 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 ((y <= -6.5e+78) || ~((y <= 4e+68)))
		tmp = x + (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[y, -6.5e+78], N[Not[LessEqual[y, 4e+68]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $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 y < -6.50000000000000036e78 or 3.99999999999999981e68 < y

   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* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. +-commutative 84.4%

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

      3. associate-*r* 84.5%

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

      4. distribute-rgt-in 86.7%

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

   7. Simplified 86.7%

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

   if -6.50000000000000036e78 < y < 3.99999999999999981e68

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. +-commutative 94.3%

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

      3. fma-def 94.3%

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

      4. associate-*l* 96.9%

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

      5. *-commutative 96.9%

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

      6. *-commutative 96.9%

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

      7. distribute-rgt-out 99.3%

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

      8. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 89.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+78} \lor \neg \left(y \leq 4 \cdot 10^{+68}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-31} \lor \neg \left(y \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e-31) (not (<= y 6.5e-6)))
   (+ (+ x (* y z)) (* a t))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e-31) || !(y <= 6.5e-6)) {
		tmp = (x + (y * z)) + (a * t);
	} 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 ((y <= (-1d-31)) .or. (.not. (y <= 6.5d-6))) then
        tmp = (x + (y * z)) + (a * t)
    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 ((y <= -1e-31) || !(y <= 6.5e-6)) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e-31) or not (y <= 6.5e-6):
		tmp = (x + (y * z)) + (a * t)
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e-31) || !(y <= 6.5e-6))
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(a * t));
	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 ((y <= -1e-31) || ~((y <= 6.5e-6)))
		tmp = (x + (y * z)) + (a * t);
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e-31], N[Not[LessEqual[y, 6.5e-6]], $MachinePrecision]], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e-31 or 6.4999999999999996e-6 < y

   1. Initial program 94.4%

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

      1. associate-+l+ 94.4%

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

      2. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 91.8%

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

   if -1e-31 < y < 6.4999999999999996e-6

   1. Initial program 93.6%

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

      1. associate-+l+ 93.6%

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

      2. +-commutative 93.6%

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

      3. fma-def 93.6%

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

      4. associate-*l* 96.1%

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

      5. *-commutative 96.1%

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

      6. *-commutative 96.1%

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

      7. distribute-rgt-out 99.1%

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

      8. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 92.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-31} \lor \neg \left(y \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-85} \lor \neg \left(y \leq 3.5 \cdot 10^{+68}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.8e-85) (not (<= y 3.5e+68))) (+ x (* y z)) (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.8e-85) || !(y <= 3.5e+68)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.8d-85)) .or. (.not. (y <= 3.5d+68))) then
        tmp = x + (y * z)
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.8e-85) || !(y <= 3.5e+68)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.8e-85) or not (y <= 3.5e+68):
		tmp = x + (y * z)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.8e-85) || !(y <= 3.5e+68))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.8e-85) || ~((y <= 3.5e+68)))
		tmp = x + (y * z);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.8e-85], N[Not[LessEqual[y, 3.5e+68]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8e-85 or 3.49999999999999977e68 < y

   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* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in a around 0 73.7%

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

   if -8.8e-85 < y < 3.49999999999999977e68

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 61.5%

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

      1. +-commutative 61.5%

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

   7. Simplified 61.5%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-85} \lor \neg \left(y \leq 3.5 \cdot 10^{+68}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.4e+187)
   (* z (* a b))
   (if (<= b 5.8e+84) (+ x (* y z)) (* a (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.4e+187) {
		tmp = z * (a * b);
	} else if (b <= 5.8e+84) {
		tmp = x + (y * z);
	} else {
		tmp = a * (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 (b <= (-9.4d+187)) then
        tmp = z * (a * b)
    else if (b <= 5.8d+84) then
        tmp = x + (y * z)
    else
        tmp = a * (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 (b <= -9.4e+187) {
		tmp = z * (a * b);
	} else if (b <= 5.8e+84) {
		tmp = x + (y * z);
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.4e+187:
		tmp = z * (a * b)
	elif b <= 5.8e+84:
		tmp = x + (y * z)
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.4e+187)
		tmp = Float64(z * Float64(a * b));
	elseif (b <= 5.8e+84)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(a * Float64(z * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.4e+187)
		tmp = z * (a * b);
	elseif (b <= 5.8e+84)
		tmp = x + (y * z);
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.4e+187], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+84], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.39999999999999978e187

   1. Initial program 91.8%

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

      1. associate-+l+ 91.8%

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

      2. associate-*l* 93.8%

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

   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. Step-by-step derivation

      1. *-commutative 93.8%

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

      2. distribute-rgt-in 99.7%

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

      3. add-cube-cbrt 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 99.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 99.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 99.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 99.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in b around inf 66.1%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   9. Simplified 71.8%

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

   if -9.39999999999999978e187 < b < 5.79999999999999977e84

   1. Initial program 95.0%

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

      1. associate-+l+ 95.0%

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

      2. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in a around 0 61.8%

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

   if 5.79999999999999977e84 < 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* 89.6%

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

   3. Simplified 89.6%

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

      1. *-commutative 89.6%

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

      2. distribute-rgt-in 99.8%

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

      3. add-cube-cbrt 99.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 99.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 99.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 99.5%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 99.5%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 99.5%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in b around inf 69.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+137} \lor \neg \left(t \leq 2.2 \cdot 10^{-27}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.5e+137) (not (<= t 2.2e-27))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.5e+137) || !(t <= 2.2e-27)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-8.5d+137)) .or. (.not. (t <= 2.2d-27))) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.5e+137) || !(t <= 2.2e-27)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.5e+137) or not (t <= 2.2e-27):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.5e+137) || !(t <= 2.2e-27))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8.5e+137) || ~((t <= 2.2e-27)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.5e+137], N[Not[LessEqual[t, 2.2e-27]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000028e137 or 2.19999999999999987e-27 < t

   1. Initial program 92.0%

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

      1. associate-+l+ 92.0%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

      1. *-commutative 95.0%

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

      2. distribute-rgt-in 98.0%

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

      3. add-cube-cbrt 97.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 97.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 97.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 97.5%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-def 97.5%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 97.5%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in t around inf 48.5%

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

   if -8.50000000000000028e137 < t < 2.19999999999999987e-27

   1. Initial program 95.3%

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

      1. associate-+l+ 95.3%

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

      2. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 33.9%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+137} \lor \neg \left(t \leq 2.2 \cdot 10^{-27}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 94.0%

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

   1. associate-+l+ 94.0%

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

   2. associate-*l* 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in x around inf 25.6%

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

6. Final simplification 25.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.6% 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 2024033 
(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)))