Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.6% → 95.5%

Time: 9.8s

Alternatives: 14

Speedup: 0.5×

• 31.7% 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: 92.6% 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: 95.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= (+ (* b (* z a)) (+ t_1 (* a t))) INFINITY)
     (+ t_1 (+ (* a (* z b)) (* a t)))
     (* 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 (((b * (z * a)) + (t_1 + (a * t))) <= ((double) INFINITY)) {
		tmp = t_1 + ((a * (z * b)) + (a * t));
	} 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 (((b * (z * a)) + (t_1 + (a * t))) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + ((a * (z * b)) + (a * t));
	} 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 ((b * (z * a)) + (t_1 + (a * t))) <= math.inf:
		tmp = t_1 + ((a * (z * b)) + (a * t))
	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(b * Float64(z * a)) + Float64(t_1 + Float64(a * t))) <= Inf)
		tmp = Float64(t_1 + Float64(Float64(a * Float64(z * b)) + Float64(a * t)));
	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 (((b * (z * a)) + (t_1 + (a * t))) <= Inf)
		tmp = t_1 + ((a * (z * b)) + (a * t));
	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[(b * N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(a * t), $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 96.9%

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

      1. associate-+l+ 96.9%

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

      2. associate-*l* 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%

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

   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%

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

      2. *-un-lft-identity 0.0%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 0.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 0.0%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 0.0%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 0.0%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in a around inf 88.9%

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

4. Final simplification 97.7%

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

Alternative 2: 94.2% 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 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. +-commutative 93.5%

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

   3. fma-def 93.5%

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

   4. *-commutative 93.5%

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

   5. associate-*l* 94.9%

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

   6. *-commutative 94.9%

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

   7. distribute-lft-out 96.9%

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

   8. remove-double-neg 96.9%

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

   9. *-commutative 96.9%

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

   10. distribute-lft-neg-out 96.9%

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

   11. sub-neg 96.9%

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

   12. sub-neg 96.9%

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

   13. distribute-lft-neg-in 96.9%

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

   14. remove-double-neg 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 3: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2500000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-230}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 15500:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -7.2e+241)
     t_1
     (if (<= a -2.3e+154)
       (* a t)
       (if (<= a -6.5e+121)
         t_1
         (if (<= a -2500000000.0)
           (* a t)
           (if (<= a 9.5e-230)
             x
             (if (<= a 15500.0)
               (* y z)
               (if (<= a 2.3e+161) t_1 (* a t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -7.2e+241) {
		tmp = t_1;
	} else if (a <= -2.3e+154) {
		tmp = a * t;
	} else if (a <= -6.5e+121) {
		tmp = t_1;
	} else if (a <= -2500000000.0) {
		tmp = a * t;
	} else if (a <= 9.5e-230) {
		tmp = x;
	} else if (a <= 15500.0) {
		tmp = y * z;
	} else if (a <= 2.3e+161) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-7.2d+241)) then
        tmp = t_1
    else if (a <= (-2.3d+154)) then
        tmp = a * t
    else if (a <= (-6.5d+121)) then
        tmp = t_1
    else if (a <= (-2500000000.0d0)) then
        tmp = a * t
    else if (a <= 9.5d-230) then
        tmp = x
    else if (a <= 15500.0d0) then
        tmp = y * z
    else if (a <= 2.3d+161) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -7.2e+241) {
		tmp = t_1;
	} else if (a <= -2.3e+154) {
		tmp = a * t;
	} else if (a <= -6.5e+121) {
		tmp = t_1;
	} else if (a <= -2500000000.0) {
		tmp = a * t;
	} else if (a <= 9.5e-230) {
		tmp = x;
	} else if (a <= 15500.0) {
		tmp = y * z;
	} else if (a <= 2.3e+161) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -7.2e+241:
		tmp = t_1
	elif a <= -2.3e+154:
		tmp = a * t
	elif a <= -6.5e+121:
		tmp = t_1
	elif a <= -2500000000.0:
		tmp = a * t
	elif a <= 9.5e-230:
		tmp = x
	elif a <= 15500.0:
		tmp = y * z
	elif a <= 2.3e+161:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -7.2e+241)
		tmp = t_1;
	elseif (a <= -2.3e+154)
		tmp = Float64(a * t);
	elseif (a <= -6.5e+121)
		tmp = t_1;
	elseif (a <= -2500000000.0)
		tmp = Float64(a * t);
	elseif (a <= 9.5e-230)
		tmp = x;
	elseif (a <= 15500.0)
		tmp = Float64(y * z);
	elseif (a <= 2.3e+161)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -7.2e+241)
		tmp = t_1;
	elseif (a <= -2.3e+154)
		tmp = a * t;
	elseif (a <= -6.5e+121)
		tmp = t_1;
	elseif (a <= -2500000000.0)
		tmp = a * t;
	elseif (a <= 9.5e-230)
		tmp = x;
	elseif (a <= 15500.0)
		tmp = y * z;
	elseif (a <= 2.3e+161)
		tmp = t_1;
	else
		tmp = a * t;
	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[a, -7.2e+241], t$95$1, If[LessEqual[a, -2.3e+154], N[(a * t), $MachinePrecision], If[LessEqual[a, -6.5e+121], t$95$1, If[LessEqual[a, -2500000000.0], N[(a * t), $MachinePrecision], If[LessEqual[a, 9.5e-230], x, If[LessEqual[a, 15500.0], N[(y * z), $MachinePrecision], If[LessEqual[a, 2.3e+161], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.19999999999999966e241 or -2.3e154 < a < -6.50000000000000019e121 or 15500 < a < 2.2999999999999999e161

   1. Initial program 83.2%

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

      1. associate-+l+ 83.2%

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

      2. *-un-lft-identity 83.2%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 83.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 83.2%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 83.2%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 83.2%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]
   4. Step-by-step derivation

      1. fma-udef 83.2%

         \[\leadsto \color{blue}{\left(1 \cdot x + \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-un-lft-identity 83.2%

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

      3. +-commutative 83.2%

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

   5. Applied egg-rr 83.2%

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

   6. Taylor expanded in b around inf 62.9%

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

      1. *-commutative 62.9%

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

   8. Simplified 62.9%

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

   if -7.19999999999999966e241 < a < -2.3e154 or -6.50000000000000019e121 < a < -2.5e9 or 2.2999999999999999e161 < a

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. *-un-lft-identity 90.8%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in t around inf 62.5%

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

   if -2.5e9 < a < 9.5000000000000004e-230

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 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. Taylor expanded in x around inf 56.8%

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

   if 9.5000000000000004e-230 < a < 15500

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 93.8%

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

   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. Taylor expanded in y around inf 49.6%

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

      1. *-commutative 49.6%

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

   6. Simplified 49.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+241}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -2500000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-230}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 15500:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 4: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -5800000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6500:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -1.1e+243)
     t_1
     (if (<= a -4.3e+154)
       (* a t)
       (if (<= a -3.8e+120)
         (* b (* z a))
         (if (<= a -5800000000.0)
           (* a t)
           (if (<= a 2.6e-226)
             x
             (if (<= a 6500.0) (* y z) (if (<= a 3.6e+161) t_1 (* a t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -1.1e+243) {
		tmp = t_1;
	} else if (a <= -4.3e+154) {
		tmp = a * t;
	} else if (a <= -3.8e+120) {
		tmp = b * (z * a);
	} else if (a <= -5800000000.0) {
		tmp = a * t;
	} else if (a <= 2.6e-226) {
		tmp = x;
	} else if (a <= 6500.0) {
		tmp = y * z;
	} else if (a <= 3.6e+161) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-1.1d+243)) then
        tmp = t_1
    else if (a <= (-4.3d+154)) then
        tmp = a * t
    else if (a <= (-3.8d+120)) then
        tmp = b * (z * a)
    else if (a <= (-5800000000.0d0)) then
        tmp = a * t
    else if (a <= 2.6d-226) then
        tmp = x
    else if (a <= 6500.0d0) then
        tmp = y * z
    else if (a <= 3.6d+161) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -1.1e+243) {
		tmp = t_1;
	} else if (a <= -4.3e+154) {
		tmp = a * t;
	} else if (a <= -3.8e+120) {
		tmp = b * (z * a);
	} else if (a <= -5800000000.0) {
		tmp = a * t;
	} else if (a <= 2.6e-226) {
		tmp = x;
	} else if (a <= 6500.0) {
		tmp = y * z;
	} else if (a <= 3.6e+161) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -1.1e+243:
		tmp = t_1
	elif a <= -4.3e+154:
		tmp = a * t
	elif a <= -3.8e+120:
		tmp = b * (z * a)
	elif a <= -5800000000.0:
		tmp = a * t
	elif a <= 2.6e-226:
		tmp = x
	elif a <= 6500.0:
		tmp = y * z
	elif a <= 3.6e+161:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -1.1e+243)
		tmp = t_1;
	elseif (a <= -4.3e+154)
		tmp = Float64(a * t);
	elseif (a <= -3.8e+120)
		tmp = Float64(b * Float64(z * a));
	elseif (a <= -5800000000.0)
		tmp = Float64(a * t);
	elseif (a <= 2.6e-226)
		tmp = x;
	elseif (a <= 6500.0)
		tmp = Float64(y * z);
	elseif (a <= 3.6e+161)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -1.1e+243)
		tmp = t_1;
	elseif (a <= -4.3e+154)
		tmp = a * t;
	elseif (a <= -3.8e+120)
		tmp = b * (z * a);
	elseif (a <= -5800000000.0)
		tmp = a * t;
	elseif (a <= 2.6e-226)
		tmp = x;
	elseif (a <= 6500.0)
		tmp = y * z;
	elseif (a <= 3.6e+161)
		tmp = t_1;
	else
		tmp = a * t;
	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[a, -1.1e+243], t$95$1, If[LessEqual[a, -4.3e+154], N[(a * t), $MachinePrecision], If[LessEqual[a, -3.8e+120], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5800000000.0], N[(a * t), $MachinePrecision], If[LessEqual[a, 2.6e-226], x, If[LessEqual[a, 6500.0], N[(y * z), $MachinePrecision], If[LessEqual[a, 3.6e+161], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.10000000000000004e243 or 6500 < a < 3.59999999999999984e161

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. *-un-lft-identity 82.1%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 82.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]
   4. Step-by-step derivation

      1. fma-udef 82.1%

         \[\leadsto \color{blue}{\left(1 \cdot x + \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-un-lft-identity 82.1%

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

      3. +-commutative 82.1%

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

   5. Applied egg-rr 82.1%

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

   6. Taylor expanded in b around inf 62.0%

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

      1. *-commutative 62.0%

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

   8. Simplified 62.0%

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

   if -1.10000000000000004e243 < a < -4.2999999999999998e154 or -3.7999999999999998e120 < a < -5.8e9 or 3.59999999999999984e161 < a

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. *-un-lft-identity 90.8%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in t around inf 62.5%

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

   if -4.2999999999999998e154 < a < -3.7999999999999998e120

   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%

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

      2. *-un-lft-identity 88.7%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 88.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 88.7%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 88.7%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 88.7%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]
   4. Step-by-step derivation

      1. fma-udef 88.7%

         \[\leadsto \color{blue}{\left(1 \cdot x + \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-un-lft-identity 88.7%

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

      3. +-commutative 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in b around inf 67.2%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 67.4%

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

   8. Simplified 67.4%

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

   if -5.8e9 < a < 2.5999999999999998e-226

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 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. Taylor expanded in x around inf 56.8%

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

   if 2.5999999999999998e-226 < a < 6500

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 93.8%

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

   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. Taylor expanded in y around inf 49.6%

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

      1. *-commutative 49.6%

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

   6. Simplified 49.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -5800000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6500:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 5: 38.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -64000000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1300:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -7e+243)
     t_1
     (if (<= a -2.7e+154)
       (* a t)
       (if (<= a -2.8e+121)
         (* z (* a b))
         (if (<= a -64000000000.0)
           (* a t)
           (if (<= a 3.8e-224)
             x
             (if (<= a 1300.0) (* y z) (if (<= a 6e+160) t_1 (* a t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -7e+243) {
		tmp = t_1;
	} else if (a <= -2.7e+154) {
		tmp = a * t;
	} else if (a <= -2.8e+121) {
		tmp = z * (a * b);
	} else if (a <= -64000000000.0) {
		tmp = a * t;
	} else if (a <= 3.8e-224) {
		tmp = x;
	} else if (a <= 1300.0) {
		tmp = y * z;
	} else if (a <= 6e+160) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-7d+243)) then
        tmp = t_1
    else if (a <= (-2.7d+154)) then
        tmp = a * t
    else if (a <= (-2.8d+121)) then
        tmp = z * (a * b)
    else if (a <= (-64000000000.0d0)) then
        tmp = a * t
    else if (a <= 3.8d-224) then
        tmp = x
    else if (a <= 1300.0d0) then
        tmp = y * z
    else if (a <= 6d+160) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -7e+243) {
		tmp = t_1;
	} else if (a <= -2.7e+154) {
		tmp = a * t;
	} else if (a <= -2.8e+121) {
		tmp = z * (a * b);
	} else if (a <= -64000000000.0) {
		tmp = a * t;
	} else if (a <= 3.8e-224) {
		tmp = x;
	} else if (a <= 1300.0) {
		tmp = y * z;
	} else if (a <= 6e+160) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -7e+243:
		tmp = t_1
	elif a <= -2.7e+154:
		tmp = a * t
	elif a <= -2.8e+121:
		tmp = z * (a * b)
	elif a <= -64000000000.0:
		tmp = a * t
	elif a <= 3.8e-224:
		tmp = x
	elif a <= 1300.0:
		tmp = y * z
	elif a <= 6e+160:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -7e+243)
		tmp = t_1;
	elseif (a <= -2.7e+154)
		tmp = Float64(a * t);
	elseif (a <= -2.8e+121)
		tmp = Float64(z * Float64(a * b));
	elseif (a <= -64000000000.0)
		tmp = Float64(a * t);
	elseif (a <= 3.8e-224)
		tmp = x;
	elseif (a <= 1300.0)
		tmp = Float64(y * z);
	elseif (a <= 6e+160)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -7e+243)
		tmp = t_1;
	elseif (a <= -2.7e+154)
		tmp = a * t;
	elseif (a <= -2.8e+121)
		tmp = z * (a * b);
	elseif (a <= -64000000000.0)
		tmp = a * t;
	elseif (a <= 3.8e-224)
		tmp = x;
	elseif (a <= 1300.0)
		tmp = y * z;
	elseif (a <= 6e+160)
		tmp = t_1;
	else
		tmp = a * t;
	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[a, -7e+243], t$95$1, If[LessEqual[a, -2.7e+154], N[(a * t), $MachinePrecision], If[LessEqual[a, -2.8e+121], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -64000000000.0], N[(a * t), $MachinePrecision], If[LessEqual[a, 3.8e-224], x, If[LessEqual[a, 1300.0], N[(y * z), $MachinePrecision], If[LessEqual[a, 6e+160], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.99999999999999976e243 or 1300 < a < 5.9999999999999997e160

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. *-un-lft-identity 82.1%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 82.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]
   4. Step-by-step derivation

      1. fma-udef 82.1%

         \[\leadsto \color{blue}{\left(1 \cdot x + \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-un-lft-identity 82.1%

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

      3. +-commutative 82.1%

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

   5. Applied egg-rr 82.1%

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

   6. Taylor expanded in b around inf 62.0%

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

      1. *-commutative 62.0%

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

   8. Simplified 62.0%

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

   if -6.99999999999999976e243 < a < -2.70000000000000006e154 or -2.80000000000000006e121 < a < -6.4e10 or 5.9999999999999997e160 < a

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. *-un-lft-identity 90.8%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in t around inf 62.5%

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

   if -2.70000000000000006e154 < a < -2.80000000000000006e121

   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* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around inf 78.6%

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

   5. Taylor expanded in y around 0 67.7%

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

   if -6.4e10 < a < 3.80000000000000002e-224

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 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. Taylor expanded in x around inf 56.8%

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

   if 3.80000000000000002e-224 < a < 1300

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 93.8%

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

   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. Taylor expanded in y around inf 49.6%

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

      1. *-commutative 49.6%

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

   6. Simplified 49.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -64000000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1300:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 6: 57.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -320000000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 9600:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -2.5e+244)
     t_1
     (if (<= a -4.8e+154)
       (* a t)
       (if (<= a -2.35e+117)
         (* z (* a b))
         (if (<= a -320000000000.0)
           (* a t)
           (if (<= a 9600.0)
             (+ x (* y z))
             (if (<= a 8e+160) t_1 (* a t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.5e+244) {
		tmp = t_1;
	} else if (a <= -4.8e+154) {
		tmp = a * t;
	} else if (a <= -2.35e+117) {
		tmp = z * (a * b);
	} else if (a <= -320000000000.0) {
		tmp = a * t;
	} else if (a <= 9600.0) {
		tmp = x + (y * z);
	} else if (a <= 8e+160) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-2.5d+244)) then
        tmp = t_1
    else if (a <= (-4.8d+154)) then
        tmp = a * t
    else if (a <= (-2.35d+117)) then
        tmp = z * (a * b)
    else if (a <= (-320000000000.0d0)) then
        tmp = a * t
    else if (a <= 9600.0d0) then
        tmp = x + (y * z)
    else if (a <= 8d+160) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.5e+244) {
		tmp = t_1;
	} else if (a <= -4.8e+154) {
		tmp = a * t;
	} else if (a <= -2.35e+117) {
		tmp = z * (a * b);
	} else if (a <= -320000000000.0) {
		tmp = a * t;
	} else if (a <= 9600.0) {
		tmp = x + (y * z);
	} else if (a <= 8e+160) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -2.5e+244:
		tmp = t_1
	elif a <= -4.8e+154:
		tmp = a * t
	elif a <= -2.35e+117:
		tmp = z * (a * b)
	elif a <= -320000000000.0:
		tmp = a * t
	elif a <= 9600.0:
		tmp = x + (y * z)
	elif a <= 8e+160:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -2.5e+244)
		tmp = t_1;
	elseif (a <= -4.8e+154)
		tmp = Float64(a * t);
	elseif (a <= -2.35e+117)
		tmp = Float64(z * Float64(a * b));
	elseif (a <= -320000000000.0)
		tmp = Float64(a * t);
	elseif (a <= 9600.0)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 8e+160)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -2.5e+244)
		tmp = t_1;
	elseif (a <= -4.8e+154)
		tmp = a * t;
	elseif (a <= -2.35e+117)
		tmp = z * (a * b);
	elseif (a <= -320000000000.0)
		tmp = a * t;
	elseif (a <= 9600.0)
		tmp = x + (y * z);
	elseif (a <= 8e+160)
		tmp = t_1;
	else
		tmp = a * t;
	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[a, -2.5e+244], t$95$1, If[LessEqual[a, -4.8e+154], N[(a * t), $MachinePrecision], If[LessEqual[a, -2.35e+117], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -320000000000.0], N[(a * t), $MachinePrecision], If[LessEqual[a, 9600.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+160], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.50000000000000011e244 or 9600 < a < 8.00000000000000005e160

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. *-un-lft-identity 82.1%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 82.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]
   4. Step-by-step derivation

      1. fma-udef 82.1%

         \[\leadsto \color{blue}{\left(1 \cdot x + \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-un-lft-identity 82.1%

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

      3. +-commutative 82.1%

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

   5. Applied egg-rr 82.1%

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

   6. Taylor expanded in b around inf 62.0%

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

      1. *-commutative 62.0%

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

   8. Simplified 62.0%

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

   if -2.50000000000000011e244 < a < -4.8000000000000003e154 or -2.35000000000000003e117 < a < -3.2e11 or 8.00000000000000005e160 < a

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. *-un-lft-identity 90.8%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 90.9%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in t around inf 62.5%

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

   if -4.8000000000000003e154 < a < -2.35000000000000003e117

   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* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around inf 78.6%

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

   5. Taylor expanded in y around 0 67.7%

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

   if -3.2e11 < a < 9600

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 82.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+244}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+154}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -320000000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 9600:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 7: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;a \leq 13500:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -6.4e+32)
     (+ x t_1)
     (if (<= a 13500.0) (+ (+ x (* y z)) (* a t)) (+ t_1 (* 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 <= -6.4e+32) {
		tmp = x + t_1;
	} else if (a <= 13500.0) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = t_1 + (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 <= (-6.4d+32)) then
        tmp = x + t_1
    else if (a <= 13500.0d0) then
        tmp = (x + (y * z)) + (a * t)
    else
        tmp = t_1 + (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 <= -6.4e+32) {
		tmp = x + t_1;
	} else if (a <= 13500.0) {
		tmp = (x + (y * z)) + (a * t);
	} else {
		tmp = t_1 + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -6.4e+32:
		tmp = x + t_1
	elif a <= 13500.0:
		tmp = (x + (y * z)) + (a * t)
	else:
		tmp = t_1 + (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 <= -6.4e+32)
		tmp = Float64(x + t_1);
	elseif (a <= 13500.0)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(a * t));
	else
		tmp = Float64(t_1 + 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 <= -6.4e+32)
		tmp = x + t_1;
	elseif (a <= 13500.0)
		tmp = (x + (y * z)) + (a * t);
	else
		tmp = t_1 + (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, -6.4e+32], N[(x + t$95$1), $MachinePrecision], If[LessEqual[a, 13500.0], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.3999999999999998e32

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. +-commutative 90.9%

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

      3. fma-def 90.9%

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

      4. *-commutative 90.9%

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

      5. associate-*l* 94.4%

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

      6. *-commutative 94.4%

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

      7. distribute-lft-out 98.1%

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

      8. remove-double-neg 98.1%

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

      9. *-commutative 98.1%

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

      10. distribute-lft-neg-out 98.1%

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

      11. sub-neg 98.1%

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

      12. sub-neg 98.1%

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

      13. distribute-lft-neg-in 98.1%

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

      14. remove-double-neg 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around 0 93.1%

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

   if -6.3999999999999998e32 < a < 13500

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around inf 91.5%

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

   if 13500 < a

   1. Initial program 83.7%

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

      1. associate-+l+ 83.7%

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

      2. +-commutative 83.7%

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

      3. fma-def 83.7%

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

      4. *-commutative 83.7%

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

      5. associate-*l* 93.9%

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

      6. *-commutative 93.9%

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

      7. distribute-lft-out 98.4%

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

      8. remove-double-neg 98.4%

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

      9. *-commutative 98.4%

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

      10. distribute-lft-neg-out 98.4%

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

      11. sub-neg 98.4%

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

      12. sub-neg 98.4%

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

      13. distribute-lft-neg-in 98.4%

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

      14. remove-double-neg 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. Taylor expanded in x around 0 92.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 13500:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + y \cdot z\\ \end{array} \]

Alternative 8: 82.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-58} \lor \neg \left(a \leq 8.4 \cdot 10^{-70}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.2e-58) (not (<= a 8.4e-70)))
   (+ x (* a (+ t (* z b))))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.2e-58) || !(a <= 8.4e-70)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4.2d-58)) .or. (.not. (a <= 8.4d-70))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.2e-58) || !(a <= 8.4e-70)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.2e-58) or not (a <= 8.4e-70):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.2e-58) || !(a <= 8.4e-70))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.2e-58) || ~((a <= 8.4e-70)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.2e-58], N[Not[LessEqual[a, 8.4e-70]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.19999999999999975e-58 or 8.4000000000000004e-70 < a

   1. Initial program 89.5%

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

      1. associate-+l+ 89.5%

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

      2. +-commutative 89.5%

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

      3. fma-def 89.6%

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

      4. *-commutative 89.6%

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

      5. associate-*l* 95.3%

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

      6. *-commutative 95.3%

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

      7. distribute-lft-out 98.6%

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

      8. remove-double-neg 98.6%

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

      9. *-commutative 98.6%

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

      10. distribute-lft-neg-out 98.6%

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

      11. sub-neg 98.6%

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

      12. sub-neg 98.6%

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

      13. distribute-lft-neg-in 98.6%

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

      14. remove-double-neg 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 88.5%

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

   if -4.19999999999999975e-58 < a < 8.4000000000000004e-70

   1. Initial program 99.0%

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

      1. associate-+l+ 99.0%

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

      2. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in a around 0 86.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-58} \lor \neg \left(a \leq 8.4 \cdot 10^{-70}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 9: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+32} \lor \neg \left(a \leq 3.8 \cdot 10^{-6}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1e+32) (not (<= a 3.8e-6)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* y z)) (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+32) || !(a <= 3.8e-6)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1d+32)) .or. (.not. (a <= 3.8d-6))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (y * z)) + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+32) || !(a <= 3.8e-6)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1e+32) or not (a <= 3.8e-6):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (y * z)) + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1e+32) || !(a <= 3.8e-6))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1e+32) || ~((a <= 3.8e-6)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (y * z)) + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1e+32], N[Not[LessEqual[a, 3.8e-6]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000005e32 or 3.8e-6 < a

   1. Initial program 87.2%

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

      1. associate-+l+ 87.2%

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

      2. +-commutative 87.2%

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

      3. fma-def 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-*l* 94.2%

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

      6. *-commutative 94.2%

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

      7. distribute-lft-out 98.3%

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

      8. remove-double-neg 98.3%

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

      9. *-commutative 98.3%

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

      10. distribute-lft-neg-out 98.3%

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

      11. sub-neg 98.3%

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

      12. sub-neg 98.3%

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

      13. distribute-lft-neg-in 98.3%

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

      14. remove-double-neg 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around 0 93.0%

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

   if -1.00000000000000005e32 < a < 3.8e-6

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 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. Taylor expanded in t around inf 91.4%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+32} \lor \neg \left(a \leq 3.8 \cdot 10^{-6}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot t\\ \end{array} \]

Alternative 10: 61.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot t\\ \mathbf{if}\;a \leq -5000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9600:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a t))))
   (if (<= a -5000000000.0)
     t_1
     (if (<= a 9600.0) (+ x (* y z)) (if (<= a 2e+161) (* a (* z b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double tmp;
	if (a <= -5000000000.0) {
		tmp = t_1;
	} else if (a <= 9600.0) {
		tmp = x + (y * z);
	} else if (a <= 2e+161) {
		tmp = a * (z * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * t)
    if (a <= (-5000000000.0d0)) then
        tmp = t_1
    else if (a <= 9600.0d0) then
        tmp = x + (y * z)
    else if (a <= 2d+161) then
        tmp = a * (z * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double tmp;
	if (a <= -5000000000.0) {
		tmp = t_1;
	} else if (a <= 9600.0) {
		tmp = x + (y * z);
	} else if (a <= 2e+161) {
		tmp = a * (z * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * t)
	tmp = 0
	if a <= -5000000000.0:
		tmp = t_1
	elif a <= 9600.0:
		tmp = x + (y * z)
	elif a <= 2e+161:
		tmp = a * (z * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * t))
	tmp = 0.0
	if (a <= -5000000000.0)
		tmp = t_1;
	elseif (a <= 9600.0)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 2e+161)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * t);
	tmp = 0.0;
	if (a <= -5000000000.0)
		tmp = t_1;
	elseif (a <= 9600.0)
		tmp = x + (y * z);
	elseif (a <= 2e+161)
		tmp = a * (z * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5000000000.0], t$95$1, If[LessEqual[a, 9600.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+161], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5e9 or 2.0000000000000001e161 < a

   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* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 64.3%

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

      1. +-commutative 64.3%

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

   6. Simplified 64.3%

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

   if -5e9 < a < 9600

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 82.6%

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

   if 9600 < a < 2.0000000000000001e161

   1. Initial program 82.2%

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

      1. associate-+l+ 82.2%

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

      2. *-un-lft-identity 82.2%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 82.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 82.2%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]
   4. Step-by-step derivation

      1. fma-udef 82.2%

         \[\leadsto \color{blue}{\left(1 \cdot x + \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-un-lft-identity 82.2%

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

      3. +-commutative 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in b around inf 58.4%

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

      1. *-commutative 58.4%

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

   8. Simplified 58.4%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5000000000:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 9600:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+161}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 11: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -550000000000 \lor \neg \left(a \leq 122\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -550000000000.0) (not (<= a 122.0)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -550000000000.0) || !(a <= 122.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-550000000000.0d0)) .or. (.not. (a <= 122.0d0))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -550000000000.0) || !(a <= 122.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -550000000000.0) or not (a <= 122.0):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -550000000000.0) || !(a <= 122.0))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -550000000000.0) || ~((a <= 122.0)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -550000000000.0], N[Not[LessEqual[a, 122.0]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e11 or 122 < a

   1. Initial program 87.7%

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

      1. associate-+l+ 87.7%

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

      2. *-un-lft-identity 87.7%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 87.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 87.7%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in a around inf 82.9%

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

   if -5.5e11 < a < 122

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 82.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -550000000000 \lor \neg \left(a \leq 122\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 12: 38.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2050000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2050000000.0)
   (* a t)
   (if (<= a 2.8e-223) x (if (<= a 1.45e+79) (* y z) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2050000000.0) {
		tmp = a * t;
	} else if (a <= 2.8e-223) {
		tmp = x;
	} else if (a <= 1.45e+79) {
		tmp = y * z;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2050000000.0d0)) then
        tmp = a * t
    else if (a <= 2.8d-223) then
        tmp = x
    else if (a <= 1.45d+79) then
        tmp = y * z
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2050000000.0) {
		tmp = a * t;
	} else if (a <= 2.8e-223) {
		tmp = x;
	} else if (a <= 1.45e+79) {
		tmp = y * z;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2050000000.0:
		tmp = a * t
	elif a <= 2.8e-223:
		tmp = x
	elif a <= 1.45e+79:
		tmp = y * z
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2050000000.0)
		tmp = Float64(a * t);
	elseif (a <= 2.8e-223)
		tmp = x;
	elseif (a <= 1.45e+79)
		tmp = Float64(y * z);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2050000000.0)
		tmp = a * t;
	elseif (a <= 2.8e-223)
		tmp = x;
	elseif (a <= 1.45e+79)
		tmp = y * z;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2050000000.0], N[(a * t), $MachinePrecision], If[LessEqual[a, 2.8e-223], x, If[LessEqual[a, 1.45e+79], N[(y * z), $MachinePrecision], N[(a * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.05e9 or 1.44999999999999996e79 < a

   1. Initial program 86.3%

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

      1. associate-+l+ 86.3%

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

      2. *-un-lft-identity 86.3%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 86.3%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in t around inf 51.7%

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

   if -2.05e9 < a < 2.80000000000000015e-223

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 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. Taylor expanded in x around inf 56.8%

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

   if 2.80000000000000015e-223 < a < 1.44999999999999996e79

   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* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 45.9%

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

      1. *-commutative 45.9%

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

   6. Simplified 45.9%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2050000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 13: 38.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1060000000 \lor \neg \left(a \leq 5.6 \cdot 10^{+53}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1060000000.0) (not (<= a 5.6e+53))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1060000000.0) || !(a <= 5.6e+53)) {
		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 ((a <= (-1060000000.0d0)) .or. (.not. (a <= 5.6d+53))) 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 ((a <= -1060000000.0) || !(a <= 5.6e+53)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1060000000.0) or not (a <= 5.6e+53):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1060000000.0) || !(a <= 5.6e+53))
		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 ((a <= -1060000000.0) || ~((a <= 5.6e+53)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1060000000.0], N[Not[LessEqual[a, 5.6e+53]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.06e9 or 5.6e53 < a

   1. Initial program 86.9%

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

      1. associate-+l+ 86.9%

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

      2. *-un-lft-identity 86.9%

         \[\leadsto \left(\color{blue}{1 \cdot x} + \left(y \cdot z + t \cdot a\right)\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 86.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, y \cdot z + t \cdot a\right)} + \left(a \cdot z\right) \cdot b \]

      4. *-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{z \cdot y} + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

      5. fma-def 87.0%

         \[\leadsto \mathsf{fma}\left(1, x, \color{blue}{\mathsf{fma}\left(z, y, t \cdot a\right)}\right) + \left(a \cdot z\right) \cdot b \]

      6. *-commutative 87.0%

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, \color{blue}{a \cdot t}\right)\right) + \left(a \cdot z\right) \cdot b \]

   3. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, a \cdot t\right)\right)} + \left(a \cdot z\right) \cdot b \]

   4. Taylor expanded in t around inf 50.2%

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

   if -1.06e9 < a < 5.6e53

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 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. Taylor expanded in x around inf 43.5%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1060000000 \lor \neg \left(a \leq 5.6 \cdot 10^{+53}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 26.8% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

   \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
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* 94.9%

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

3. Simplified 94.9%

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

4. Taylor expanded in x around inf 28.2%

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

5. Final simplification 28.2%

   \[\leadsto x \]

Developer target: 97.5% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023322 
(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)))