Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 96.6%

Time: 13.0s

Alternatives: 18

Speedup: 0.6×

• 31.6% 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: 92.5% 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: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;b \leq -2 \cdot 10^{+47} \lor \neg \left(b \leq 6 \cdot 10^{-36}\right):\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (or (<= b -2e+47) (not (<= b 6e-36)))
     (+ t_1 (* b (* a (+ z (/ t b)))))
     (+ t_1 (+ (* t a) (* a (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if ((b <= -2e+47) || !(b <= 6e-36)) {
		tmp = t_1 + (b * (a * (z + (t / b))));
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if ((b <= (-2d+47)) .or. (.not. (b <= 6d-36))) then
        tmp = t_1 + (b * (a * (z + (t / b))))
    else
        tmp = t_1 + ((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 t_1 = x + (y * z);
	double tmp;
	if ((b <= -2e+47) || !(b <= 6e-36)) {
		tmp = t_1 + (b * (a * (z + (t / b))));
	} else {
		tmp = t_1 + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if (b <= -2e+47) or not (b <= 6e-36):
		tmp = t_1 + (b * (a * (z + (t / b))))
	else:
		tmp = t_1 + ((t * a) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if ((b <= -2e+47) || !(b <= 6e-36))
		tmp = Float64(t_1 + Float64(b * Float64(a * Float64(z + Float64(t / b)))));
	else
		tmp = Float64(t_1 + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if ((b <= -2e+47) || ~((b <= 6e-36)))
		tmp = t_1 + (b * (a * (z + (t / b))));
	else
		tmp = t_1 + ((t * a) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2e+47], N[Not[LessEqual[b, 6e-36]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(a * N[(z + N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0000000000000001e47 or 6.0000000000000003e-36 < b

   1. Initial program 92.1%

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

      1. associate-+l+ 92.1%

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

      2. associate-*l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf 94.6%

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

      1. associate-/l* 96.2%

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

      2. distribute-lft-out 97.0%

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

   7. Simplified 97.0%

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

   if -2.0000000000000001e47 < b < 6.0000000000000003e-36

   1. Initial program 92.8%

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

      1. associate-+l+ 92.8%

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

      2. associate-*l* 99.2%

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

   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
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+47} \lor \neg \left(b \leq 6 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x + y \cdot z\right) + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(z + N[(N[(x / y), $MachinePrecision] + N[(N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $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 98.2%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. fma-define 0.0%

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

      4. associate-*l* 33.3%

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

      5. *-commutative 33.3%

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

      6. *-commutative 33.3%

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

      7. distribute-rgt-out 80.0%

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

      8. *-commutative 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in y around inf 93.3%

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

4. Final simplification 97.9%

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

Alternative 3: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b + \left(\left(x + y \cdot z\right) + t \cdot a\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (* z a) b) (+ (+ x (* y z)) (* t a)))))
   (if (<= t_1 5e+295) t_1 (+ (* y z) (* 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) + ((x + (y * z)) + (t * a));
	double tmp;
	if (t_1 <= 5e+295) {
		tmp = t_1;
	} else {
		tmp = (y * z) + (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) :: t_1
    real(8) :: tmp
    t_1 = ((z * a) * b) + ((x + (y * z)) + (t * a))
    if (t_1 <= 5d+295) then
        tmp = t_1
    else
        tmp = (y * z) + (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 t_1 = ((z * a) * b) + ((x + (y * z)) + (t * a));
	double tmp;
	if (t_1 <= 5e+295) {
		tmp = t_1;
	} else {
		tmp = (y * z) + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * a) * b) + ((x + (y * z)) + (t * a))
	tmp = 0
	if t_1 <= 5e+295:
		tmp = t_1
	else:
		tmp = (y * z) + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * a) * b) + Float64(Float64(x + Float64(y * z)) + Float64(t * a)))
	tmp = 0.0
	if (t_1 <= 5e+295)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * z) + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * a) * b) + ((x + (y * z)) + (t * a));
	tmp = 0.0;
	if (t_1 <= 5e+295)
		tmp = t_1;
	else
		tmp = (y * z) + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+295], t$95$1, N[(N[(y * z), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $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)) < 4.99999999999999991e295

   1. Initial program 99.2%

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

   if 4.99999999999999991e295 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 73.4%

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

      1. associate-+l+ 73.4%

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

      2. +-commutative 73.4%

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

      3. fma-define 73.4%

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

      4. associate-*l* 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. distribute-rgt-out 94.0%

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

      8. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around 0 94.0%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot a\right) \cdot b + \left(\left(x + y \cdot z\right) + t \cdot a\right) \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(\left(x + y \cdot z\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+32}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= t -1.95e+32)
     (* t a)
     (if (<= t 3.8e-166)
       (* y z)
       (if (<= t 1.15e-106)
         t_1
         (if (<= t 1.15e-47)
           x
           (if (<= t 2.65e+26) t_1 (if (<= t 6e+51) 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 <= -1.95e+32) {
		tmp = t * a;
	} else if (t <= 3.8e-166) {
		tmp = y * z;
	} else if (t <= 1.15e-106) {
		tmp = t_1;
	} else if (t <= 1.15e-47) {
		tmp = x;
	} else if (t <= 2.65e+26) {
		tmp = t_1;
	} else if (t <= 6e+51) {
		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 <= (-1.95d+32)) then
        tmp = t * a
    else if (t <= 3.8d-166) then
        tmp = y * z
    else if (t <= 1.15d-106) then
        tmp = t_1
    else if (t <= 1.15d-47) then
        tmp = x
    else if (t <= 2.65d+26) then
        tmp = t_1
    else if (t <= 6d+51) 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 <= -1.95e+32) {
		tmp = t * a;
	} else if (t <= 3.8e-166) {
		tmp = y * z;
	} else if (t <= 1.15e-106) {
		tmp = t_1;
	} else if (t <= 1.15e-47) {
		tmp = x;
	} else if (t <= 2.65e+26) {
		tmp = t_1;
	} else if (t <= 6e+51) {
		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 <= -1.95e+32:
		tmp = t * a
	elif t <= 3.8e-166:
		tmp = y * z
	elif t <= 1.15e-106:
		tmp = t_1
	elif t <= 1.15e-47:
		tmp = x
	elif t <= 2.65e+26:
		tmp = t_1
	elif t <= 6e+51:
		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 <= -1.95e+32)
		tmp = Float64(t * a);
	elseif (t <= 3.8e-166)
		tmp = Float64(y * z);
	elseif (t <= 1.15e-106)
		tmp = t_1;
	elseif (t <= 1.15e-47)
		tmp = x;
	elseif (t <= 2.65e+26)
		tmp = t_1;
	elseif (t <= 6e+51)
		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 <= -1.95e+32)
		tmp = t * a;
	elseif (t <= 3.8e-166)
		tmp = y * z;
	elseif (t <= 1.15e-106)
		tmp = t_1;
	elseif (t <= 1.15e-47)
		tmp = x;
	elseif (t <= 2.65e+26)
		tmp = t_1;
	elseif (t <= 6e+51)
		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, -1.95e+32], N[(t * a), $MachinePrecision], If[LessEqual[t, 3.8e-166], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.15e-106], t$95$1, If[LessEqual[t, 1.15e-47], x, If[LessEqual[t, 2.65e+26], t$95$1, If[LessEqual[t, 6e+51], x, N[(t * a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.95e32 or 6e51 < t

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. +-commutative 92.3%

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

      3. fma-define 92.3%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 85.6%

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

   6. Taylor expanded in b around inf 72.5%

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

      1. associate-/l* 69.3%

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

      2. distribute-lft-out 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in t around inf 58.1%

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

       1. *-commutative 58.1%

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

   11. Simplified 58.1%

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

   if -1.95e32 < t < 3.79999999999999982e-166

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if 3.79999999999999982e-166 < t < 1.15e-106 or 1.14999999999999991e-47 < t < 2.64999999999999984e26

   1. Initial program 93.8%

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

      1. associate-+l+ 93.8%

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

      2. +-commutative 93.8%

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

      3. fma-define 93.8%

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

      4. associate-*l* 95.9%

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

      5. *-commutative 95.9%

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

      6. *-commutative 95.9%

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

      7. distribute-rgt-out 95.9%

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

      8. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 76.5%

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

   6. Taylor expanded in b around inf 74.1%

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

      1. associate-/l* 74.1%

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

      2. distribute-lft-out 74.4%

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

   8. Simplified 74.4%

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

   9. Taylor expanded in b around inf 59.7%

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

   if 1.15e-106 < t < 1.14999999999999991e-47 or 2.64999999999999984e26 < t < 6e51

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in x around inf 50.8%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+32}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-168}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-106}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.5e+33)
   (* t a)
   (if (<= t 6.7e-168)
     (* y z)
     (if (<= t 1.15e-106)
       (* (* z a) b)
       (if (<= t 7e-49)
         x
         (if (<= t 6.2e+25) (* a (* z b)) (if (<= t 7.8e+51) x (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.5e+33) {
		tmp = t * a;
	} else if (t <= 6.7e-168) {
		tmp = y * z;
	} else if (t <= 1.15e-106) {
		tmp = (z * a) * b;
	} else if (t <= 7e-49) {
		tmp = x;
	} else if (t <= 6.2e+25) {
		tmp = a * (z * b);
	} else if (t <= 7.8e+51) {
		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 <= (-4.5d+33)) then
        tmp = t * a
    else if (t <= 6.7d-168) then
        tmp = y * z
    else if (t <= 1.15d-106) then
        tmp = (z * a) * b
    else if (t <= 7d-49) then
        tmp = x
    else if (t <= 6.2d+25) then
        tmp = a * (z * b)
    else if (t <= 7.8d+51) 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 <= -4.5e+33) {
		tmp = t * a;
	} else if (t <= 6.7e-168) {
		tmp = y * z;
	} else if (t <= 1.15e-106) {
		tmp = (z * a) * b;
	} else if (t <= 7e-49) {
		tmp = x;
	} else if (t <= 6.2e+25) {
		tmp = a * (z * b);
	} else if (t <= 7.8e+51) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.5e+33:
		tmp = t * a
	elif t <= 6.7e-168:
		tmp = y * z
	elif t <= 1.15e-106:
		tmp = (z * a) * b
	elif t <= 7e-49:
		tmp = x
	elif t <= 6.2e+25:
		tmp = a * (z * b)
	elif t <= 7.8e+51:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.5e+33)
		tmp = Float64(t * a);
	elseif (t <= 6.7e-168)
		tmp = Float64(y * z);
	elseif (t <= 1.15e-106)
		tmp = Float64(Float64(z * a) * b);
	elseif (t <= 7e-49)
		tmp = x;
	elseif (t <= 6.2e+25)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 7.8e+51)
		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 <= -4.5e+33)
		tmp = t * a;
	elseif (t <= 6.7e-168)
		tmp = y * z;
	elseif (t <= 1.15e-106)
		tmp = (z * a) * b;
	elseif (t <= 7e-49)
		tmp = x;
	elseif (t <= 6.2e+25)
		tmp = a * (z * b);
	elseif (t <= 7.8e+51)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.5e+33], N[(t * a), $MachinePrecision], If[LessEqual[t, 6.7e-168], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.15e-106], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 7e-49], x, If[LessEqual[t, 6.2e+25], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+51], x, N[(t * a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.5e33 or 7.79999999999999968e51 < t

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. +-commutative 92.3%

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

      3. fma-define 92.3%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 85.6%

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

   6. Taylor expanded in b around inf 72.5%

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

      1. associate-/l* 69.3%

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

      2. distribute-lft-out 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in t around inf 58.1%

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

       1. *-commutative 58.1%

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

   11. Simplified 58.1%

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

   if -4.5e33 < t < 6.69999999999999988e-168

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if 6.69999999999999988e-168 < t < 1.15e-106

   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. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 92.1%

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

   6. Taylor expanded in b around inf 92.1%

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

      1. associate-/l* 92.1%

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

      2. distribute-lft-out 92.1%

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

   8. Simplified 92.1%

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

   9. Taylor expanded in b around inf 67.3%

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

       1. *-commutative 67.3%

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

       2. associate-*r* 67.4%

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

   11. Simplified 67.4%

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

   if 1.15e-106 < t < 7.00000000000000012e-49 or 6.1999999999999996e25 < t < 7.79999999999999968e51

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in x around inf 50.8%

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

   if 7.00000000000000012e-49 < t < 6.1999999999999996e25

   1. Initial program 87.6%

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

      1. associate-+l+ 87.6%

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

      2. +-commutative 87.6%

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

      3. fma-define 87.6%

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

      4. associate-*l* 91.8%

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

      5. *-commutative 91.8%

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

      6. *-commutative 91.8%

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

      7. distribute-rgt-out 91.8%

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

      8. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in y around 0 61.0%

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

   6. Taylor expanded in b around inf 56.1%

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

      1. associate-/l* 56.1%

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

      2. distribute-lft-out 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in b around inf 52.0%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-168}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-106}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-166}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.55e+31)
   (* t a)
   (if (<= t 2.5e-166)
     (* y z)
     (if (<= t 1.1e-106)
       (* (* z a) b)
       (if (<= t 2e-46)
         x
         (if (<= t 2.1e+26) (* z (* a b)) (if (<= t 6.2e+51) x (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.55e+31) {
		tmp = t * a;
	} else if (t <= 2.5e-166) {
		tmp = y * z;
	} else if (t <= 1.1e-106) {
		tmp = (z * a) * b;
	} else if (t <= 2e-46) {
		tmp = x;
	} else if (t <= 2.1e+26) {
		tmp = z * (a * b);
	} else if (t <= 6.2e+51) {
		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 <= (-1.55d+31)) then
        tmp = t * a
    else if (t <= 2.5d-166) then
        tmp = y * z
    else if (t <= 1.1d-106) then
        tmp = (z * a) * b
    else if (t <= 2d-46) then
        tmp = x
    else if (t <= 2.1d+26) then
        tmp = z * (a * b)
    else if (t <= 6.2d+51) 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 <= -1.55e+31) {
		tmp = t * a;
	} else if (t <= 2.5e-166) {
		tmp = y * z;
	} else if (t <= 1.1e-106) {
		tmp = (z * a) * b;
	} else if (t <= 2e-46) {
		tmp = x;
	} else if (t <= 2.1e+26) {
		tmp = z * (a * b);
	} else if (t <= 6.2e+51) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.55e+31:
		tmp = t * a
	elif t <= 2.5e-166:
		tmp = y * z
	elif t <= 1.1e-106:
		tmp = (z * a) * b
	elif t <= 2e-46:
		tmp = x
	elif t <= 2.1e+26:
		tmp = z * (a * b)
	elif t <= 6.2e+51:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.55e+31)
		tmp = Float64(t * a);
	elseif (t <= 2.5e-166)
		tmp = Float64(y * z);
	elseif (t <= 1.1e-106)
		tmp = Float64(Float64(z * a) * b);
	elseif (t <= 2e-46)
		tmp = x;
	elseif (t <= 2.1e+26)
		tmp = Float64(z * Float64(a * b));
	elseif (t <= 6.2e+51)
		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 <= -1.55e+31)
		tmp = t * a;
	elseif (t <= 2.5e-166)
		tmp = y * z;
	elseif (t <= 1.1e-106)
		tmp = (z * a) * b;
	elseif (t <= 2e-46)
		tmp = x;
	elseif (t <= 2.1e+26)
		tmp = z * (a * b);
	elseif (t <= 6.2e+51)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.55e+31], N[(t * a), $MachinePrecision], If[LessEqual[t, 2.5e-166], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.1e-106], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 2e-46], x, If[LessEqual[t, 2.1e+26], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+51], x, N[(t * a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.5500000000000001e31 or 6.20000000000000022e51 < t

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. +-commutative 92.3%

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

      3. fma-define 92.3%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 85.6%

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

   6. Taylor expanded in b around inf 72.5%

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

      1. associate-/l* 69.3%

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

      2. distribute-lft-out 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in t around inf 58.1%

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

       1. *-commutative 58.1%

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

   11. Simplified 58.1%

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

   if -1.5500000000000001e31 < t < 2.5e-166

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if 2.5e-166 < t < 1.09999999999999997e-106

   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. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 92.1%

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

   6. Taylor expanded in b around inf 92.1%

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

      1. associate-/l* 92.1%

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

      2. distribute-lft-out 92.1%

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

   8. Simplified 92.1%

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

   9. Taylor expanded in b around inf 67.3%

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

       1. *-commutative 67.3%

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

       2. associate-*r* 67.4%

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

   11. Simplified 67.4%

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

   if 1.09999999999999997e-106 < t < 2.00000000000000005e-46 or 2.1000000000000001e26 < t < 6.20000000000000022e51

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in x around inf 50.8%

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

   if 2.00000000000000005e-46 < t < 2.1000000000000001e26

   1. Initial program 87.6%

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

      1. associate-+l+ 87.6%

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

      2. +-commutative 87.6%

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

      3. fma-define 87.6%

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

      4. associate-*l* 91.8%

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

      5. *-commutative 91.8%

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

      6. *-commutative 91.8%

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

      7. distribute-rgt-out 91.8%

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

      8. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in y around 0 61.0%

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

   6. Taylor expanded in b around inf 56.1%

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

      1. associate-/l* 56.1%

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

      2. distribute-lft-out 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in b around inf 52.0%

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

       1. associate-*r* 60.0%

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

       2. *-commutative 60.0%

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

       3. *-commutative 60.0%

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

   11. Simplified 60.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-166}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+54} \lor \neg \left(a \leq -6.2 \cdot 10^{+19} \lor \neg \left(a \leq -4.6 \cdot 10^{-27}\right) \land a \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.95e+54)
         (not (or (<= a -6.2e+19) (and (not (<= a -4.6e-27)) (<= a 1.1e+57)))))
   (* 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 <= -1.95e+54) || !((a <= -6.2e+19) || (!(a <= -4.6e-27) && (a <= 1.1e+57)))) {
		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 <= (-1.95d+54)) .or. (.not. (a <= (-6.2d+19)) .or. (.not. (a <= (-4.6d-27))) .and. (a <= 1.1d+57))) 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 <= -1.95e+54) || !((a <= -6.2e+19) || (!(a <= -4.6e-27) && (a <= 1.1e+57)))) {
		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 <= -1.95e+54) or not ((a <= -6.2e+19) or (not (a <= -4.6e-27) and (a <= 1.1e+57))):
		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 <= -1.95e+54) || !((a <= -6.2e+19) || (!(a <= -4.6e-27) && (a <= 1.1e+57))))
		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 <= -1.95e+54) || ~(((a <= -6.2e+19) || (~((a <= -4.6e-27)) && (a <= 1.1e+57)))))
		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, -1.95e+54], N[Not[Or[LessEqual[a, -6.2e+19], And[N[Not[LessEqual[a, -4.6e-27]], $MachinePrecision], LessEqual[a, 1.1e+57]]]], $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 < -1.9500000000000001e54 or -6.2e19 < a < -4.5999999999999999e-27 or 1.1e57 < a

   1. Initial program 84.0%

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

      1. associate-+l+ 84.0%

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

      2. +-commutative 84.0%

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

      3. fma-define 84.0%

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

      4. associate-*l* 91.4%

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

      5. *-commutative 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-rgt-out 97.4%

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

      8. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 89.3%

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

   6. Taylor expanded in x around 0 82.7%

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

   if -1.9500000000000001e54 < a < -6.2e19 or -4.5999999999999999e-27 < a < 1.1e57

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in a around 0 79.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+54} \lor \neg \left(a \leq -6.2 \cdot 10^{+19} \lor \neg \left(a \leq -4.6 \cdot 10^{-27}\right) \land a \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{+93} \lor \neg \left(y \leq -3.55 \cdot 10^{+50} \lor \neg \left(y \leq -0.45\right) \land y \leq 8.5 \cdot 10^{+65}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.76e+93)
         (not (or (<= y -3.55e+50) (and (not (<= y -0.45)) (<= y 8.5e+65)))))
   (+ x (* y z))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.76e+93) || !((y <= -3.55e+50) || (!(y <= -0.45) && (y <= 8.5e+65)))) {
		tmp = x + (y * z);
	} 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 ((y <= (-1.76d+93)) .or. (.not. (y <= (-3.55d+50)) .or. (.not. (y <= (-0.45d0))) .and. (y <= 8.5d+65))) then
        tmp = x + (y * z)
    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 ((y <= -1.76e+93) || !((y <= -3.55e+50) || (!(y <= -0.45) && (y <= 8.5e+65)))) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.76e+93) or not ((y <= -3.55e+50) or (not (y <= -0.45) and (y <= 8.5e+65))):
		tmp = x + (y * z)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.76e+93) || !((y <= -3.55e+50) || (!(y <= -0.45) && (y <= 8.5e+65))))
		tmp = Float64(x + Float64(y * z));
	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 ((y <= -1.76e+93) || ~(((y <= -3.55e+50) || (~((y <= -0.45)) && (y <= 8.5e+65)))))
		tmp = x + (y * z);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.76e+93], N[Not[Or[LessEqual[y, -3.55e+50], And[N[Not[LessEqual[y, -0.45]], $MachinePrecision], LessEqual[y, 8.5e+65]]]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75999999999999994e93 or -3.54999999999999996e50 < y < -0.450000000000000011 or 8.50000000000000075e65 < y

   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* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in a around 0 78.4%

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

   if -1.75999999999999994e93 < y < -3.54999999999999996e50 or -0.450000000000000011 < y < 8.50000000000000075e65

   1. Initial program 94.9%

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

      1. associate-+l+ 94.9%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around 0 70.9%

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

      1. +-commutative 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{+93} \lor \neg \left(y \leq -3.55 \cdot 10^{+50} \lor \neg \left(y \leq -0.45\right) \land y \leq 8.5 \cdot 10^{+65}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= t -4.9e+33)
     (* t a)
     (if (<= t 1.62e-34)
       t_1
       (if (<= t 2.55e+20) (* z (* a b)) (if (<= t 7.8e+51) 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 <= -4.9e+33) {
		tmp = t * a;
	} else if (t <= 1.62e-34) {
		tmp = t_1;
	} else if (t <= 2.55e+20) {
		tmp = z * (a * b);
	} else if (t <= 7.8e+51) {
		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 <= (-4.9d+33)) then
        tmp = t * a
    else if (t <= 1.62d-34) then
        tmp = t_1
    else if (t <= 2.55d+20) then
        tmp = z * (a * b)
    else if (t <= 7.8d+51) 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 <= -4.9e+33) {
		tmp = t * a;
	} else if (t <= 1.62e-34) {
		tmp = t_1;
	} else if (t <= 2.55e+20) {
		tmp = z * (a * b);
	} else if (t <= 7.8e+51) {
		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 <= -4.9e+33:
		tmp = t * a
	elif t <= 1.62e-34:
		tmp = t_1
	elif t <= 2.55e+20:
		tmp = z * (a * b)
	elif t <= 7.8e+51:
		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 <= -4.9e+33)
		tmp = Float64(t * a);
	elseif (t <= 1.62e-34)
		tmp = t_1;
	elseif (t <= 2.55e+20)
		tmp = Float64(z * Float64(a * b));
	elseif (t <= 7.8e+51)
		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 <= -4.9e+33)
		tmp = t * a;
	elseif (t <= 1.62e-34)
		tmp = t_1;
	elseif (t <= 2.55e+20)
		tmp = z * (a * b);
	elseif (t <= 7.8e+51)
		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, -4.9e+33], N[(t * a), $MachinePrecision], If[LessEqual[t, 1.62e-34], t$95$1, If[LessEqual[t, 2.55e+20], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+51], t$95$1, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.90000000000000014e33 or 7.79999999999999968e51 < t

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. +-commutative 92.3%

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

      3. fma-define 92.3%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 85.6%

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

   6. Taylor expanded in b around inf 72.5%

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

      1. associate-/l* 69.3%

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

      2. distribute-lft-out 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in t around inf 58.1%

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

       1. *-commutative 58.1%

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

   11. Simplified 58.1%

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

   if -4.90000000000000014e33 < t < 1.62000000000000006e-34 or 2.55e20 < t < 7.79999999999999968e51

   1. Initial program 93.3%

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

      1. associate-+l+ 93.3%

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

      2. associate-*l* 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

   5. Taylor expanded in a around 0 74.0%

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

   if 1.62000000000000006e-34 < t < 2.55e20

   1. Initial program 78.7%

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

      1. associate-+l+ 78.7%

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

      2. +-commutative 78.7%

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

      3. fma-define 78.7%

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

      4. associate-*l* 86.2%

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

      5. *-commutative 86.2%

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

      6. *-commutative 86.2%

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

      7. distribute-rgt-out 86.2%

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

      8. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around 0 73.5%

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

   6. Taylor expanded in b around inf 65.1%

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

      1. associate-/l* 65.1%

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

      2. distribute-lft-out 66.0%

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

   8. Simplified 66.0%

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

   9. Taylor expanded in b around inf 72.2%

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

       1. associate-*r* 85.9%

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

       2. *-commutative 85.9%

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

       3. *-commutative 85.9%

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

   11. Simplified 85.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-34}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{-21} \lor \neg \left(b \leq 1.75 \cdot 10^{-41}\right):\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (or (<= b -2.05e-21) (not (<= b 1.75e-41)))
     (+ t_1 (* b (* a (+ z (/ t b)))))
     (+ 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 ((b <= -2.05e-21) || !(b <= 1.75e-41)) {
		tmp = t_1 + (b * (a * (z + (t / b))));
	} else {
		tmp = t_1 + (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 ((b <= (-2.05d-21)) .or. (.not. (b <= 1.75d-41))) then
        tmp = t_1 + (b * (a * (z + (t / b))))
    else
        tmp = t_1 + (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 ((b <= -2.05e-21) || !(b <= 1.75e-41)) {
		tmp = t_1 + (b * (a * (z + (t / b))));
	} else {
		tmp = t_1 + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if (b <= -2.05e-21) or not (b <= 1.75e-41):
		tmp = t_1 + (b * (a * (z + (t / b))))
	else:
		tmp = t_1 + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if ((b <= -2.05e-21) || !(b <= 1.75e-41))
		tmp = Float64(t_1 + Float64(b * Float64(a * Float64(z + Float64(t / b)))));
	else
		tmp = Float64(t_1 + 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 ((b <= -2.05e-21) || ~((b <= 1.75e-41)))
		tmp = t_1 + (b * (a * (z + (t / b))));
	else
		tmp = t_1 + (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[Or[LessEqual[b, -2.05e-21], N[Not[LessEqual[b, 1.75e-41]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(a * N[(z + N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.04999999999999997e-21 or 1.75e-41 < b

   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* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in b around inf 95.1%

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

      1. associate-/l* 96.5%

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

      2. distribute-lft-out 97.3%

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

   7. Simplified 97.3%

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

   if -2.04999999999999997e-21 < b < 1.75e-41

   1. Initial program 92.0%

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

      1. associate-+l+ 92.0%

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

      2. associate-*l* 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 t around inf 96.1%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-21} \lor \neg \left(b \leq 1.75 \cdot 10^{-41}\right):\\ \;\;\;\;\left(x + y \cdot z\right) + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;y \cdot z + t \cdot a\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -9e+166)
     t_1
     (if (<= z -6.5e-27)
       (+ (* y z) (* t a))
       (if (<= z 1.6e-41) (+ x (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -9e+166) {
		tmp = t_1;
	} else if (z <= -6.5e-27) {
		tmp = (y * z) + (t * a);
	} else if (z <= 1.6e-41) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y + (a * b))
    if (z <= (-9d+166)) then
        tmp = t_1
    else if (z <= (-6.5d-27)) then
        tmp = (y * z) + (t * a)
    else if (z <= 1.6d-41) then
        tmp = x + (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -9e+166) {
		tmp = t_1;
	} else if (z <= -6.5e-27) {
		tmp = (y * z) + (t * a);
	} else if (z <= 1.6e-41) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -9e+166:
		tmp = t_1
	elif z <= -6.5e-27:
		tmp = (y * z) + (t * a)
	elif z <= 1.6e-41:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -9e+166)
		tmp = t_1;
	elseif (z <= -6.5e-27)
		tmp = Float64(Float64(y * z) + Float64(t * a));
	elseif (z <= 1.6e-41)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -9e+166)
		tmp = t_1;
	elseif (z <= -6.5e-27)
		tmp = (y * z) + (t * a);
	elseif (z <= 1.6e-41)
		tmp = x + (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+166], t$95$1, If[LessEqual[z, -6.5e-27], N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-41], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000061e166 or 1.60000000000000006e-41 < 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* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

   if -9.00000000000000061e166 < z < -6.50000000000000025e-27

   1. Initial program 88.9%

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

      1. associate-+l+ 88.9%

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

      2. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 86.8%

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

   6. Taylor expanded in x around 0 71.8%

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

   if -6.50000000000000025e-27 < z < 1.60000000000000006e-41

   1. Initial program 97.7%

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

      1. associate-+l+ 97.7%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;y \cdot z + t \cdot a\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-20} \lor \neg \left(a \leq 2.6 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot z + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1e-20) (not (<= a 2.6e+38)))
   (+ (* y z) (* 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 <= -1e-20) || !(a <= 2.6e+38)) {
		tmp = (y * z) + (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 <= (-1d-20)) .or. (.not. (a <= 2.6d+38))) then
        tmp = (y * z) + (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 <= -1e-20) || !(a <= 2.6e+38)) {
		tmp = (y * z) + (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 <= -1e-20) or not (a <= 2.6e+38):
		tmp = (y * z) + (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 <= -1e-20) || !(a <= 2.6e+38))
		tmp = Float64(Float64(y * z) + 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 <= -1e-20) || ~((a <= 2.6e+38)))
		tmp = (y * z) + (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, -1e-20], N[Not[LessEqual[a, 2.6e+38]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] + 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 < -9.99999999999999945e-21 or 2.5999999999999999e38 < a

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. +-commutative 85.7%

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

      3. fma-define 85.7%

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

      4. associate-*l* 92.7%

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

      5. *-commutative 92.7%

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

      6. *-commutative 92.7%

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

      7. distribute-rgt-out 98.3%

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

      8. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around 0 90.5%

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

   if -9.99999999999999945e-21 < a < 2.5999999999999999e38

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around inf 91.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-20} \lor \neg \left(a \leq 2.6 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot z + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-27} \lor \neg \left(a \leq 3.2 \cdot 10^{+45}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.4e-27) (not (<= a 3.2e+45)))
   (+ 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 <= -6.4e-27) || !(a <= 3.2e+45)) {
		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 <= (-6.4d-27)) .or. (.not. (a <= 3.2d+45))) 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 <= -6.4e-27) || !(a <= 3.2e+45)) {
		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 <= -6.4e-27) or not (a <= 3.2e+45):
		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 <= -6.4e-27) || !(a <= 3.2e+45))
		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 <= -6.4e-27) || ~((a <= 3.2e+45)))
		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, -6.4e-27], N[Not[LessEqual[a, 3.2e+45]], $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 < -6.39999999999999982e-27 or 3.2000000000000003e45 < a

   1. Initial program 84.9%

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

      1. associate-+l+ 84.9%

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

      2. +-commutative 84.9%

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

      3. fma-define 84.9%

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

      4. associate-*l* 91.9%

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

      5. *-commutative 91.9%

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

      6. *-commutative 91.9%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 86.8%

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

   if -6.39999999999999982e-27 < a < 3.2000000000000003e45

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in a around 0 79.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-27} \lor \neg \left(a \leq 3.2 \cdot 10^{+45}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-26} \lor \neg \left(z \leq 1.4 \cdot 10^{-46}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e-26) (not (<= z 1.4e-46)))
   (* 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 <= -1.2e-26) || !(z <= 1.4e-46)) {
		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 <= (-1.2d-26)) .or. (.not. (z <= 1.4d-46))) 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 <= -1.2e-26) || !(z <= 1.4e-46)) {
		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 <= -1.2e-26) or not (z <= 1.4e-46):
		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 <= -1.2e-26) || !(z <= 1.4e-46))
		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 <= -1.2e-26) || ~((z <= 1.4e-46)))
		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, -1.2e-26], N[Not[LessEqual[z, 1.4e-46]], $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 < -1.2e-26 or 1.3999999999999999e-46 < z

   1. Initial program 88.5%

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

      1. associate-+l+ 88.5%

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

      2. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

   if -1.2e-26 < z < 1.3999999999999999e-46

   1. Initial program 97.7%

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

      1. associate-+l+ 97.7%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-26} \lor \neg \left(z \leq 1.4 \cdot 10^{-46}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-27}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e-27) (+ 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 <= -8e-27) {
		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 <= (-8d-27)) 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 <= -8e-27) {
		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 <= -8e-27:
		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 <= -8e-27)
		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 <= -8e-27)
		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[LessEqual[a, -8e-27], 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 < -8.0000000000000003e-27

   1. Initial program 84.4%

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

      1. associate-+l+ 84.4%

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

      2. +-commutative 84.4%

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

      3. fma-define 84.4%

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

      4. associate-*l* 93.3%

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

      5. *-commutative 93.3%

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

      6. *-commutative 93.3%

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

      7. distribute-rgt-out 97.3%

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

      8. *-commutative 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 88.7%

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

   if -8.0000000000000003e-27 < a

   1. Initial program 95.8%

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

      1. associate-+l+ 95.8%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 88.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-27}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+25} \lor \neg \left(t \leq 5.8 \cdot 10^{+51}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e+25) (not (<= t 5.8e+51))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e+25) || !(t <= 5.8e+51)) {
		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 <= (-1.4d+25)) .or. (.not. (t <= 5.8d+51))) 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 <= -1.4e+25) || !(t <= 5.8e+51)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e+25) or not (t <= 5.8e+51):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e+25) || !(t <= 5.8e+51))
		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 <= -1.4e+25) || ~((t <= 5.8e+51)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e+25], N[Not[LessEqual[t, 5.8e+51]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.4000000000000001e25 or 5.7999999999999997e51 < t

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. +-commutative 92.4%

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

      3. fma-define 92.4%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 84.9%

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

   6. Taylor expanded in b around inf 71.9%

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

      1. associate-/l* 68.8%

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

      2. distribute-lft-out 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in t around inf 57.6%

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

       1. *-commutative 57.6%

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

   11. Simplified 57.6%

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

   if -1.4000000000000001e25 < t < 5.7999999999999997e51

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf 31.3%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+25} \lor \neg \left(t \leq 5.8 \cdot 10^{+51}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+32} \lor \neg \left(t \leq 9.5 \cdot 10^{+46}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.6e+32) (not (<= t 9.5e+46))) (* t a) (* y z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.6e+32) || !(t <= 9.5e+46)) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.6d+32)) .or. (.not. (t <= 9.5d+46))) then
        tmp = t * a
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.6e+32) || !(t <= 9.5e+46)) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.6e+32) or not (t <= 9.5e+46):
		tmp = t * a
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.6e+32) || !(t <= 9.5e+46))
		tmp = Float64(t * a);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.6e+32) || ~((t <= 9.5e+46)))
		tmp = t * a;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.6e+32], N[Not[LessEqual[t, 9.5e+46]], $MachinePrecision]], N[(t * a), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.60000000000000039e32 or 9.5000000000000008e46 < t

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. +-commutative 92.4%

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

      3. fma-define 92.4%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-out 97.5%

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

      8. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 85.7%

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

   6. Taylor expanded in b around inf 72.8%

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

      1. associate-/l* 69.6%

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

      2. distribute-lft-out 71.3%

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

   8. Simplified 71.3%

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

   9. Taylor expanded in t around inf 57.6%

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

       1. *-commutative 57.6%

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

   11. Simplified 57.6%

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

   if -6.60000000000000039e32 < t < 9.5000000000000008e46

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around inf 42.7%

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

      1. *-commutative 42.7%

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

   7. Simplified 42.7%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+32} \lor \neg \left(t \leq 9.5 \cdot 10^{+46}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 26.6% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. associate-+l+ 92.5%

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

   2. associate-*l* 93.0%

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

3. Simplified 93.0%

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

5. Taylor expanded in x around inf 24.2%

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

6. Final simplification 24.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.5% 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 2024059 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (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)))