Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.6% → 96.5%

Time: 13.0s

Alternatives: 15

Speedup: 0.7×

• 31.4% 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: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, t \cdot a\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= (+ (+ (+ x (* y z)) (* t a)) t_1) INFINITY)
     (+ (fma 1.0 x (fma z y (* t a))) t_1)
     (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if ((((x + (y * z)) + (t * a)) + t_1) <= ((double) INFINITY)) {
		tmp = fma(1.0, x, fma(z, y, (t * a))) + t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + t_1) <= Inf)
		tmp = Float64(fma(1.0, x, fma(z, y, Float64(t * a))) + t_1);
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(N[(1.0 * x + N[(z * y + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. *-un-lft-identity 98.0%

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

      3. fma-define 98.0%

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

      4. *-commutative 98.0%

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

      5. fma-define 98.0%

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

      6. *-commutative 98.0%

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

   4. Applied egg-rr 98.0%

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

   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. Add Preprocessing
   3. 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-define 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-define 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%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in a around inf 91.7%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, t \cdot a\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 39.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-214}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-74}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1020000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+36} \lor \neg \left(t \leq 1.05 \cdot 10^{+55}\right) \land t \leq 3.6 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= t -2.3e+39)
     (* t a)
     (if (<= t -1.75e-205)
       t_1
       (if (<= t 1.12e-246)
         x
         (if (<= t 1.85e-214)
           (* y z)
           (if (<= t 2.6e-141)
             t_1
             (if (<= t 1e-74)
               (* y z)
               (if (<= t 1020000000000.0)
                 t_1
                 (if (or (<= t 9.5e+36)
                         (and (not (<= t 1.05e+55)) (<= t 3.6e+95)))
                   x
                   (* t a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -2.3e+39) {
		tmp = t * a;
	} else if (t <= -1.75e-205) {
		tmp = t_1;
	} else if (t <= 1.12e-246) {
		tmp = x;
	} else if (t <= 1.85e-214) {
		tmp = y * z;
	} else if (t <= 2.6e-141) {
		tmp = t_1;
	} else if (t <= 1e-74) {
		tmp = y * z;
	} else if (t <= 1020000000000.0) {
		tmp = t_1;
	} else if ((t <= 9.5e+36) || (!(t <= 1.05e+55) && (t <= 3.6e+95))) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (t <= (-2.3d+39)) then
        tmp = t * a
    else if (t <= (-1.75d-205)) then
        tmp = t_1
    else if (t <= 1.12d-246) then
        tmp = x
    else if (t <= 1.85d-214) then
        tmp = y * z
    else if (t <= 2.6d-141) then
        tmp = t_1
    else if (t <= 1d-74) then
        tmp = y * z
    else if (t <= 1020000000000.0d0) then
        tmp = t_1
    else if ((t <= 9.5d+36) .or. (.not. (t <= 1.05d+55)) .and. (t <= 3.6d+95)) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -2.3e+39) {
		tmp = t * a;
	} else if (t <= -1.75e-205) {
		tmp = t_1;
	} else if (t <= 1.12e-246) {
		tmp = x;
	} else if (t <= 1.85e-214) {
		tmp = y * z;
	} else if (t <= 2.6e-141) {
		tmp = t_1;
	} else if (t <= 1e-74) {
		tmp = y * z;
	} else if (t <= 1020000000000.0) {
		tmp = t_1;
	} else if ((t <= 9.5e+36) || (!(t <= 1.05e+55) && (t <= 3.6e+95))) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if t <= -2.3e+39:
		tmp = t * a
	elif t <= -1.75e-205:
		tmp = t_1
	elif t <= 1.12e-246:
		tmp = x
	elif t <= 1.85e-214:
		tmp = y * z
	elif t <= 2.6e-141:
		tmp = t_1
	elif t <= 1e-74:
		tmp = y * z
	elif t <= 1020000000000.0:
		tmp = t_1
	elif (t <= 9.5e+36) or (not (t <= 1.05e+55) and (t <= 3.6e+95)):
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (t <= -2.3e+39)
		tmp = Float64(t * a);
	elseif (t <= -1.75e-205)
		tmp = t_1;
	elseif (t <= 1.12e-246)
		tmp = x;
	elseif (t <= 1.85e-214)
		tmp = Float64(y * z);
	elseif (t <= 2.6e-141)
		tmp = t_1;
	elseif (t <= 1e-74)
		tmp = Float64(y * z);
	elseif (t <= 1020000000000.0)
		tmp = t_1;
	elseif ((t <= 9.5e+36) || (!(t <= 1.05e+55) && (t <= 3.6e+95)))
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (t <= -2.3e+39)
		tmp = t * a;
	elseif (t <= -1.75e-205)
		tmp = t_1;
	elseif (t <= 1.12e-246)
		tmp = x;
	elseif (t <= 1.85e-214)
		tmp = y * z;
	elseif (t <= 2.6e-141)
		tmp = t_1;
	elseif (t <= 1e-74)
		tmp = y * z;
	elseif (t <= 1020000000000.0)
		tmp = t_1;
	elseif ((t <= 9.5e+36) || (~((t <= 1.05e+55)) && (t <= 3.6e+95)))
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+39], N[(t * a), $MachinePrecision], If[LessEqual[t, -1.75e-205], t$95$1, If[LessEqual[t, 1.12e-246], x, If[LessEqual[t, 1.85e-214], N[(y * z), $MachinePrecision], If[LessEqual[t, 2.6e-141], t$95$1, If[LessEqual[t, 1e-74], N[(y * z), $MachinePrecision], If[LessEqual[t, 1020000000000.0], t$95$1, If[Or[LessEqual[t, 9.5e+36], And[N[Not[LessEqual[t, 1.05e+55]], $MachinePrecision], LessEqual[t, 3.6e+95]]], x, N[(t * a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.30000000000000012e39 or 9.49999999999999974e36 < t < 1.05e55 or 3.59999999999999978e95 < t

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. *-un-lft-identity 93.0%

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

      3. fma-define 93.0%

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

      4. *-commutative 93.0%

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

      5. fma-define 93.1%

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

      6. *-commutative 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around inf 60.9%

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

   if -2.30000000000000012e39 < t < -1.75e-205 or 1.8500000000000001e-214 < t < 2.60000000000000011e-141 or 9.99999999999999958e-75 < t < 1.02e12

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. +-commutative 83.4%

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

      3. associate-*r* 83.3%

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

      4. distribute-rgt-in 88.2%

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

   7. Simplified 88.2%

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

   8. Taylor expanded in y around 0 74.0%

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

   9. Taylor expanded in x around 0 49.5%

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

       1. *-commutative 49.5%

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

   11. Simplified 49.5%

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

   if -1.75e-205 < t < 1.11999999999999995e-246 or 1.02e12 < t < 9.49999999999999974e36 or 1.05e55 < t < 3.59999999999999978e95

   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* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 54.0%

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

   if 1.11999999999999995e-246 < t < 1.8500000000000001e-214 or 2.60000000000000011e-141 < t < 9.99999999999999958e-75

   1. Initial program 89.2%

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

      1. associate-+l+ 89.2%

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

      2. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in y around inf 78.1%

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

      1. *-commutative 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-214}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 10^{-74}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1020000000000:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+36} \lor \neg \left(t \leq 1.05 \cdot 10^{+55}\right) \land t \leq 3.6 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+39}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-212}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 2100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+37} \lor \neg \left(t \leq 1.65 \cdot 10^{+55}\right) \land t \leq 5 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= t -1.02e+39)
     (* t a)
     (if (<= t -1.55e-204)
       t_1
       (if (<= t 5.1e-248)
         x
         (if (<= t 1.9e-212)
           (* y z)
           (if (<= t 1.3e-141)
             (* a (* z b))
             (if (<= t 1.15e-76)
               (* y z)
               (if (<= t 2100.0)
                 t_1
                 (if (or (<= t 3e+37) (and (not (<= t 1.65e+55)) (<= t 5e+93)))
                   x
                   (* t a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (t <= -1.02e+39) {
		tmp = t * a;
	} else if (t <= -1.55e-204) {
		tmp = t_1;
	} else if (t <= 5.1e-248) {
		tmp = x;
	} else if (t <= 1.9e-212) {
		tmp = y * z;
	} else if (t <= 1.3e-141) {
		tmp = a * (z * b);
	} else if (t <= 1.15e-76) {
		tmp = y * z;
	} else if (t <= 2100.0) {
		tmp = t_1;
	} else if ((t <= 3e+37) || (!(t <= 1.65e+55) && (t <= 5e+93))) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * a) * b
    if (t <= (-1.02d+39)) then
        tmp = t * a
    else if (t <= (-1.55d-204)) then
        tmp = t_1
    else if (t <= 5.1d-248) then
        tmp = x
    else if (t <= 1.9d-212) then
        tmp = y * z
    else if (t <= 1.3d-141) then
        tmp = a * (z * b)
    else if (t <= 1.15d-76) then
        tmp = y * z
    else if (t <= 2100.0d0) then
        tmp = t_1
    else if ((t <= 3d+37) .or. (.not. (t <= 1.65d+55)) .and. (t <= 5d+93)) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (t <= -1.02e+39) {
		tmp = t * a;
	} else if (t <= -1.55e-204) {
		tmp = t_1;
	} else if (t <= 5.1e-248) {
		tmp = x;
	} else if (t <= 1.9e-212) {
		tmp = y * z;
	} else if (t <= 1.3e-141) {
		tmp = a * (z * b);
	} else if (t <= 1.15e-76) {
		tmp = y * z;
	} else if (t <= 2100.0) {
		tmp = t_1;
	} else if ((t <= 3e+37) || (!(t <= 1.65e+55) && (t <= 5e+93))) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if t <= -1.02e+39:
		tmp = t * a
	elif t <= -1.55e-204:
		tmp = t_1
	elif t <= 5.1e-248:
		tmp = x
	elif t <= 1.9e-212:
		tmp = y * z
	elif t <= 1.3e-141:
		tmp = a * (z * b)
	elif t <= 1.15e-76:
		tmp = y * z
	elif t <= 2100.0:
		tmp = t_1
	elif (t <= 3e+37) or (not (t <= 1.65e+55) and (t <= 5e+93)):
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (t <= -1.02e+39)
		tmp = Float64(t * a);
	elseif (t <= -1.55e-204)
		tmp = t_1;
	elseif (t <= 5.1e-248)
		tmp = x;
	elseif (t <= 1.9e-212)
		tmp = Float64(y * z);
	elseif (t <= 1.3e-141)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 1.15e-76)
		tmp = Float64(y * z);
	elseif (t <= 2100.0)
		tmp = t_1;
	elseif ((t <= 3e+37) || (!(t <= 1.65e+55) && (t <= 5e+93)))
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (t <= -1.02e+39)
		tmp = t * a;
	elseif (t <= -1.55e-204)
		tmp = t_1;
	elseif (t <= 5.1e-248)
		tmp = x;
	elseif (t <= 1.9e-212)
		tmp = y * z;
	elseif (t <= 1.3e-141)
		tmp = a * (z * b);
	elseif (t <= 1.15e-76)
		tmp = y * z;
	elseif (t <= 2100.0)
		tmp = t_1;
	elseif ((t <= 3e+37) || (~((t <= 1.65e+55)) && (t <= 5e+93)))
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t, -1.02e+39], N[(t * a), $MachinePrecision], If[LessEqual[t, -1.55e-204], t$95$1, If[LessEqual[t, 5.1e-248], x, If[LessEqual[t, 1.9e-212], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.3e-141], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-76], N[(y * z), $MachinePrecision], If[LessEqual[t, 2100.0], t$95$1, If[Or[LessEqual[t, 3e+37], And[N[Not[LessEqual[t, 1.65e+55]], $MachinePrecision], LessEqual[t, 5e+93]]], x, N[(t * a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.02e39 or 3.00000000000000022e37 < t < 1.65e55 or 5.0000000000000001e93 < t

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. *-un-lft-identity 93.0%

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

      3. fma-define 93.0%

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

      4. *-commutative 93.0%

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

      5. fma-define 93.1%

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

      6. *-commutative 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around inf 60.9%

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

   if -1.02e39 < t < -1.55e-204 or 1.15000000000000003e-76 < t < 2100

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. fma-undefine 68.4%

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

   5. Applied egg-rr 68.4%

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

   6. Taylor expanded in b around inf 46.0%

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

      1. associate-*r* 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*r* 48.0%

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

   8. Simplified 48.0%

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

   if -1.55e-204 < t < 5.09999999999999972e-248 or 2100 < t < 3.00000000000000022e37 or 1.65e55 < t < 5.0000000000000001e93

   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* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 54.0%

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

   if 5.09999999999999972e-248 < t < 1.90000000000000011e-212 or 1.30000000000000005e-141 < t < 1.15000000000000003e-76

   1. Initial program 89.2%

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

      1. associate-+l+ 89.2%

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

      2. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in y around inf 78.1%

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

      1. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if 1.90000000000000011e-212 < t < 1.30000000000000005e-141

   1. Initial program 87.9%

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

      1. associate-+l+ 87.9%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. +-commutative 93.7%

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

      3. associate-*r* 87.6%

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

      4. distribute-rgt-in 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in y around 0 87.9%

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

   9. Taylor expanded in x around 0 63.9%

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

       1. *-commutative 63.9%

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

   11. Simplified 63.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+39}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-204}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-212}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 2100:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+37} \lor \neg \left(t \leq 1.65 \cdot 10^{+55}\right) \land t \leq 5 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 INFINITY) t_1 (* 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)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} 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)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(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)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (t + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.0%

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

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

   1. Initial program 0.0%

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

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in a around inf 91.7%

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

4. Final simplification 97.7%

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

Alternative 5: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+223} \lor \neg \left(z \leq 3.8 \cdot 10^{+288}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= z -3.5e-51)
     t_1
     (if (<= z 5.5e+31)
       (+ x (* t a))
       (if (or (<= z 4.4e+223) (not (<= z 3.8e+288))) t_1 (* (* z a) 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 (z <= -3.5e-51) {
		tmp = t_1;
	} else if (z <= 5.5e+31) {
		tmp = x + (t * a);
	} else if ((z <= 4.4e+223) || !(z <= 3.8e+288)) {
		tmp = t_1;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (z <= (-3.5d-51)) then
        tmp = t_1
    else if (z <= 5.5d+31) then
        tmp = x + (t * a)
    else if ((z <= 4.4d+223) .or. (.not. (z <= 3.8d+288))) then
        tmp = t_1
    else
        tmp = (z * a) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -3.5e-51) {
		tmp = t_1;
	} else if (z <= 5.5e+31) {
		tmp = x + (t * a);
	} else if ((z <= 4.4e+223) || !(z <= 3.8e+288)) {
		tmp = t_1;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if z <= -3.5e-51:
		tmp = t_1
	elif z <= 5.5e+31:
		tmp = x + (t * a)
	elif (z <= 4.4e+223) or not (z <= 3.8e+288):
		tmp = t_1
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -3.5e-51)
		tmp = t_1;
	elseif (z <= 5.5e+31)
		tmp = Float64(x + Float64(t * a));
	elseif ((z <= 4.4e+223) || !(z <= 3.8e+288))
		tmp = t_1;
	else
		tmp = Float64(Float64(z * a) * 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 (z <= -3.5e-51)
		tmp = t_1;
	elseif (z <= 5.5e+31)
		tmp = x + (t * a);
	elseif ((z <= 4.4e+223) || ~((z <= 3.8e+288)))
		tmp = t_1;
	else
		tmp = (z * a) * 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[z, -3.5e-51], t$95$1, If[LessEqual[z, 5.5e+31], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.4e+223], N[Not[LessEqual[z, 3.8e+288]], $MachinePrecision]], t$95$1, N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999997e-51 or 5.50000000000000002e31 < z < 4.3999999999999999e223 or 3.80000000000000008e288 < z

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around 0 65.0%

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

   if -3.4999999999999997e-51 < z < 5.50000000000000002e31

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 83.1%

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

      1. +-commutative 83.1%

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

   7. Simplified 83.1%

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

   if 4.3999999999999999e223 < z < 3.80000000000000008e288

   1. Initial program 72.7%

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

   3. Taylor expanded in x around 0 70.8%

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

      1. +-commutative 70.8%

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

      2. *-commutative 70.8%

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

      3. fma-undefine 70.8%

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

   5. Applied egg-rr 70.8%

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

   6. Taylor expanded in b around inf 81.0%

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

      1. associate-*r* 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r* 89.0%

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

   8. Simplified 89.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-51}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+223} \lor \neg \left(z \leq 3.8 \cdot 10^{+288}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= t -1.15e+96)
     (* t a)
     (if (<= t 7.6e-211)
       t_1
       (if (<= t 2.9e-173) (* a (* z b)) (if (<= t 4.5e+100) t_1 (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (t <= -1.15e+96) {
		tmp = t * a;
	} else if (t <= 7.6e-211) {
		tmp = t_1;
	} else if (t <= 2.9e-173) {
		tmp = a * (z * b);
	} else if (t <= 4.5e+100) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (t <= (-1.15d+96)) then
        tmp = t * a
    else if (t <= 7.6d-211) then
        tmp = t_1
    else if (t <= 2.9d-173) then
        tmp = a * (z * b)
    else if (t <= 4.5d+100) then
        tmp = t_1
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (t <= -1.15e+96) {
		tmp = t * a;
	} else if (t <= 7.6e-211) {
		tmp = t_1;
	} else if (t <= 2.9e-173) {
		tmp = a * (z * b);
	} else if (t <= 4.5e+100) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if t <= -1.15e+96:
		tmp = t * a
	elif t <= 7.6e-211:
		tmp = t_1
	elif t <= 2.9e-173:
		tmp = a * (z * b)
	elif t <= 4.5e+100:
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (t <= -1.15e+96)
		tmp = Float64(t * a);
	elseif (t <= 7.6e-211)
		tmp = t_1;
	elseif (t <= 2.9e-173)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 4.5e+100)
		tmp = t_1;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (t <= -1.15e+96)
		tmp = t * a;
	elseif (t <= 7.6e-211)
		tmp = t_1;
	elseif (t <= 2.9e-173)
		tmp = a * (z * b);
	elseif (t <= 4.5e+100)
		tmp = t_1;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+96], N[(t * a), $MachinePrecision], If[LessEqual[t, 7.6e-211], t$95$1, If[LessEqual[t, 2.9e-173], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+100], t$95$1, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000008e96 or 4.50000000000000036e100 < t

   1. Initial program 93.1%

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

      1. associate-+l+ 93.1%

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

      2. *-un-lft-identity 93.1%

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

      3. fma-define 93.1%

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

      4. *-commutative 93.1%

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

      5. fma-define 93.1%

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

      6. *-commutative 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around inf 64.3%

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

   if -1.15000000000000008e96 < t < 7.60000000000000023e-211 or 2.8999999999999998e-173 < t < 4.50000000000000036e100

   1. Initial program 93.9%

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

      1. associate-+l+ 93.9%

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

      2. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in a around 0 69.6%

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

   if 7.60000000000000023e-211 < t < 2.8999999999999998e-173

   1. Initial program 85.5%

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

      1. associate-+l+ 85.5%

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

      2. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. +-commutative 85.7%

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

      2. +-commutative 85.7%

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

      3. associate-*r* 71.8%

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

      4. distribute-rgt-in 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in y around 0 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-211}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+35}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8e+35)
   (* t a)
   (if (<= t 3.6e-250)
     x
     (if (<= t 4.5e-30) (* y z) (if (<= t 6.6e+93) x (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8e+35) {
		tmp = t * a;
	} else if (t <= 3.6e-250) {
		tmp = x;
	} else if (t <= 4.5e-30) {
		tmp = y * z;
	} else if (t <= 6.6e+93) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8d+35)) then
        tmp = t * a
    else if (t <= 3.6d-250) then
        tmp = x
    else if (t <= 4.5d-30) then
        tmp = y * z
    else if (t <= 6.6d+93) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8e+35) {
		tmp = t * a;
	} else if (t <= 3.6e-250) {
		tmp = x;
	} else if (t <= 4.5e-30) {
		tmp = y * z;
	} else if (t <= 6.6e+93) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8e+35:
		tmp = t * a
	elif t <= 3.6e-250:
		tmp = x
	elif t <= 4.5e-30:
		tmp = y * z
	elif t <= 6.6e+93:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8e+35)
		tmp = Float64(t * a);
	elseif (t <= 3.6e-250)
		tmp = x;
	elseif (t <= 4.5e-30)
		tmp = Float64(y * z);
	elseif (t <= 6.6e+93)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8e+35)
		tmp = t * a;
	elseif (t <= 3.6e-250)
		tmp = x;
	elseif (t <= 4.5e-30)
		tmp = y * z;
	elseif (t <= 6.6e+93)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8e+35], N[(t * a), $MachinePrecision], If[LessEqual[t, 3.6e-250], x, If[LessEqual[t, 4.5e-30], N[(y * z), $MachinePrecision], If[LessEqual[t, 6.6e+93], x, N[(t * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.9999999999999997e35 or 6.60000000000000017e93 < t

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. *-un-lft-identity 92.6%

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

      3. fma-define 92.6%

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

      4. *-commutative 92.6%

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

      5. fma-define 92.6%

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

      6. *-commutative 92.6%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in t around inf 61.3%

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

   if -7.9999999999999997e35 < t < 3.59999999999999982e-250 or 4.49999999999999967e-30 < t < 6.60000000000000017e93

   1. Initial program 95.4%

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

      1. associate-+l+ 95.4%

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

      2. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 39.0%

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

   if 3.59999999999999982e-250 < t < 4.49999999999999967e-30

   1. Initial program 90.7%

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

      1. associate-+l+ 90.7%

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

      2. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+35}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e+112)
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* y z)) (+ (* t a) (* a (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+112) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6d+112)) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (y * z)) + ((t * a) + (a * (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+112) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6e+112:
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e+112)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6e+112)
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e+112], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999958e112

   1. Initial program 92.9%

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

      1. associate-+l+ 92.9%

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

      2. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. +-commutative 79.4%

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

      3. associate-*r* 93.0%

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

      4. distribute-rgt-in 95.4%

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

   7. Simplified 95.4%

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

   if -5.99999999999999958e112 < z

   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* 94.8%

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

   3. Simplified 94.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-111} \lor \neg \left(a \leq 2.8 \cdot 10^{-72}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.2e-111) (not (<= a 2.8e-72)))
   (+ 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 <= -3.2e-111) || !(a <= 2.8e-72)) {
		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 <= (-3.2d-111)) .or. (.not. (a <= 2.8d-72))) 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 <= -3.2e-111) || !(a <= 2.8e-72)) {
		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 <= -3.2e-111) or not (a <= 2.8e-72):
		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 <= -3.2e-111) || !(a <= 2.8e-72))
		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 <= -3.2e-111) || ~((a <= 2.8e-72)))
		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, -3.2e-111], N[Not[LessEqual[a, 2.8e-72]], $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 < -3.1999999999999998e-111 or 2.7999999999999998e-72 < a

   1. Initial program 90.1%

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

      1. associate-+l+ 90.1%

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

      2. +-commutative 90.1%

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

      3. fma-define 90.1%

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

      4. associate-*l* 93.1%

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

      5. *-commutative 93.1%

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

      6. *-commutative 93.1%

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

      7. distribute-rgt-out 96.2%

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

      8. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 87.8%

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

   if -3.1999999999999998e-111 < a < 2.7999999999999998e-72

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around 0 86.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-111} \lor \neg \left(a \leq 2.8 \cdot 10^{-72}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-50} \lor \neg \left(z \leq 1.26 \cdot 10^{+33}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e-50) (not (<= z 1.26e+33)))
   (+ x (* z (+ y (* a b))))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-50) || !(z <= 1.26e+33)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.2d-50)) .or. (.not. (z <= 1.26d+33))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-50) || !(z <= 1.26e+33)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e-50) or not (z <= 1.26e+33):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e-50) || !(z <= 1.26e+33))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e-50) || ~((z <= 1.26e+33)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e-50], N[Not[LessEqual[z, 1.26e+33]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000001e-50 or 1.26e33 < z

   1. Initial program 89.0%

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

      1. associate-+l+ 89.0%

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

      2. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. +-commutative 80.4%

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

      3. associate-*r* 87.6%

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

      4. distribute-rgt-in 90.5%

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

   7. Simplified 90.5%

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

   if -1.20000000000000001e-50 < z < 1.26e33

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. +-commutative 98.3%

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

      3. fma-define 98.3%

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

      4. associate-*l* 99.1%

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

      5. *-commutative 99.1%

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

      6. *-commutative 99.1%

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

      7. distribute-rgt-out 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 92.6%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-50} \lor \neg \left(z \leq 1.26 \cdot 10^{+33}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4000000000 \lor \neg \left(a \leq 4 \cdot 10^{-54}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4000000000.0) (not (<= a 4e-54)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* y z)) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4000000000.0) || !(a <= 4e-54)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4000000000.0d0)) .or. (.not. (a <= 4d-54))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (y * z)) + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4000000000.0) || !(a <= 4e-54)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4000000000.0) or not (a <= 4e-54):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (y * z)) + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4000000000.0) || !(a <= 4e-54))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4000000000.0) || ~((a <= 4e-54)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (y * z)) + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4000000000.0], N[Not[LessEqual[a, 4e-54]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4e9 or 4.0000000000000001e-54 < a

   1. Initial program 88.0%

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

      1. associate-+l+ 88.0%

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

      2. +-commutative 88.0%

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

      3. fma-define 88.0%

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

      4. associate-*l* 93.1%

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

      5. *-commutative 93.1%

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

      6. *-commutative 93.1%

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

      7. distribute-rgt-out 96.9%

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

      8. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around 0 92.0%

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

   if -4e9 < a < 4.0000000000000001e-54

   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* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around inf 93.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4000000000 \lor \neg \left(a \leq 4 \cdot 10^{-54}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-7} \lor \neg \left(a \leq 8.5 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.75e-7) (not (<= a 8.5e-50)))
   (* 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 <= -1.75e-7) || !(a <= 8.5e-50)) {
		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 <= (-1.75d-7)) .or. (.not. (a <= 8.5d-50))) 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 <= -1.75e-7) || !(a <= 8.5e-50)) {
		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 <= -1.75e-7) or not (a <= 8.5e-50):
		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 <= -1.75e-7) || !(a <= 8.5e-50))
		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 <= -1.75e-7) || ~((a <= 8.5e-50)))
		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, -1.75e-7], N[Not[LessEqual[a, 8.5e-50]], $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 < -1.74999999999999992e-7 or 8.50000000000000012e-50 < a

   1. Initial program 88.1%

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

      1. associate-+l+ 88.1%

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

      2. *-un-lft-identity 88.1%

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

      3. fma-define 88.1%

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

      4. *-commutative 88.1%

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

      5. fma-define 88.2%

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

      6. *-commutative 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in a around inf 81.2%

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

   if -1.74999999999999992e-7 < a < 8.50000000000000012e-50

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in a around 0 81.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-7} \lor \neg \left(a \leq 8.5 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-51} \lor \neg \left(z \leq 8 \cdot 10^{+57}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.5e-51) (not (<= z 8e+57)))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e-51) || !(z <= 8e+57)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.5d-51)) .or. (.not. (z <= 8d+57))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e-51) || !(z <= 8e+57)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.5e-51) or not (z <= 8e+57):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.5e-51) || !(z <= 8e+57))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.5e-51) || ~((z <= 8e+57)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.5e-51], N[Not[LessEqual[z, 8e+57]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000001e-51 or 8.00000000000000039e57 < z

   1. Initial program 88.3%

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

      1. associate-+l+ 88.3%

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

      2. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 78.2%

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

   if -1.50000000000000001e-51 < z < 8.00000000000000039e57

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. +-commutative 81.7%

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

   7. Simplified 81.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-51} \lor \neg \left(z \leq 8 \cdot 10^{+57}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+36} \lor \neg \left(t \leq 1.4 \cdot 10^{+94}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.2e+36) (not (<= t 1.4e+94))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.2e+36) || !(t <= 1.4e+94)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.2d+36)) .or. (.not. (t <= 1.4d+94))) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.2e+36) || !(t <= 1.4e+94)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.2e+36) or not (t <= 1.4e+94):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.2e+36) || !(t <= 1.4e+94))
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.2e+36) || ~((t <= 1.4e+94)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.2e+36], N[Not[LessEqual[t, 1.4e+94]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.1999999999999999e36 or 1.39999999999999999e94 < t

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. *-un-lft-identity 92.6%

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

      3. fma-define 92.6%

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

      4. *-commutative 92.6%

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

      5. fma-define 92.6%

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

      6. *-commutative 92.6%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in t around inf 61.3%

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

   if -6.1999999999999999e36 < t < 1.39999999999999999e94

   1. Initial program 93.9%

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

      1. associate-+l+ 93.9%

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

      2. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 33.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+36} \lor \neg \left(t \leq 1.4 \cdot 10^{+94}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.9% 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 93.4%

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

   1. associate-+l+ 93.4%

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

   2. associate-*l* 92.7%

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

3. Simplified 92.7%

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

5. Taylor expanded in x around inf 27.1%

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

6. Final simplification 27.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024042 
(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)))