Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 97.1%

Time: 10.1s

Alternatives: 13

Speedup: 0.3×

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.5% 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: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + t_2\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b)))
        (t_2 (* a (+ t (* z b)))))
   (if (<= t_1 (- INFINITY))
     (+ (fma y z x) t_2)
     (if (<= t_1 INFINITY) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(y, z, x) + t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(fma(y, z, x) + t_2);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   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-def 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. *-commutative 84.9%

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

      5. *-commutative 84.9%

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

      6. associate-*l* 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%

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

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*l* 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in a around inf 82.4%

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

4. Final simplification 98.8%

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

Alternative 2: 97.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := \left(t_1 + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1 + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (+ (+ t_1 (* t a)) (* (* z a) b))))
   (if (<= t_2 (- INFINITY))
     (+ t_1 (+ (* z (* a b)) (* t a)))
     (if (<= t_2 INFINITY) t_2 (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = (t_1 + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 + ((z * (a * b)) + (t * a));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = (t_1 + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 + ((z * (a * b)) + (t * a));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	t_2 = (t_1 + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 + ((z * (a * b)) + (t * a))
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	t_2 = Float64(Float64(t_1 + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 + Float64(Float64(z * Float64(a * b)) + Float64(t * a)));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	t_2 = (t_1 + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 + ((z * (a * b)) + (t * a));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = a * (t + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   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%

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

      3. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*l* 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in a around inf 82.4%

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

4. Final simplification 98.8%

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

Alternative 3: 39.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-263}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-236}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-174}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= x -1.02e+53)
     x
     (if (<= x -1.08e-7)
       (* y z)
       (if (<= x -1.25e-54)
         (* t a)
         (if (<= x -3.1e-263)
           (* y z)
           (if (<= x 9e-267)
             t_1
             (if (<= x 2.15e-236)
               (* y z)
               (if (<= x 1.32e-174)
                 (* t a)
                 (if (<= x 1.05e-96) (* y z) (if (<= x 4.7e-6) t_1 x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (x <= -1.02e+53) {
		tmp = x;
	} else if (x <= -1.08e-7) {
		tmp = y * z;
	} else if (x <= -1.25e-54) {
		tmp = t * a;
	} else if (x <= -3.1e-263) {
		tmp = y * z;
	} else if (x <= 9e-267) {
		tmp = t_1;
	} else if (x <= 2.15e-236) {
		tmp = y * z;
	} else if (x <= 1.32e-174) {
		tmp = t * a;
	} else if (x <= 1.05e-96) {
		tmp = y * z;
	} else if (x <= 4.7e-6) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (x <= (-1.02d+53)) then
        tmp = x
    else if (x <= (-1.08d-7)) then
        tmp = y * z
    else if (x <= (-1.25d-54)) then
        tmp = t * a
    else if (x <= (-3.1d-263)) then
        tmp = y * z
    else if (x <= 9d-267) then
        tmp = t_1
    else if (x <= 2.15d-236) then
        tmp = y * z
    else if (x <= 1.32d-174) then
        tmp = t * a
    else if (x <= 1.05d-96) then
        tmp = y * z
    else if (x <= 4.7d-6) then
        tmp = t_1
    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 t_1 = a * (z * b);
	double tmp;
	if (x <= -1.02e+53) {
		tmp = x;
	} else if (x <= -1.08e-7) {
		tmp = y * z;
	} else if (x <= -1.25e-54) {
		tmp = t * a;
	} else if (x <= -3.1e-263) {
		tmp = y * z;
	} else if (x <= 9e-267) {
		tmp = t_1;
	} else if (x <= 2.15e-236) {
		tmp = y * z;
	} else if (x <= 1.32e-174) {
		tmp = t * a;
	} else if (x <= 1.05e-96) {
		tmp = y * z;
	} else if (x <= 4.7e-6) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if x <= -1.02e+53:
		tmp = x
	elif x <= -1.08e-7:
		tmp = y * z
	elif x <= -1.25e-54:
		tmp = t * a
	elif x <= -3.1e-263:
		tmp = y * z
	elif x <= 9e-267:
		tmp = t_1
	elif x <= 2.15e-236:
		tmp = y * z
	elif x <= 1.32e-174:
		tmp = t * a
	elif x <= 1.05e-96:
		tmp = y * z
	elif x <= 4.7e-6:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (x <= -1.02e+53)
		tmp = x;
	elseif (x <= -1.08e-7)
		tmp = Float64(y * z);
	elseif (x <= -1.25e-54)
		tmp = Float64(t * a);
	elseif (x <= -3.1e-263)
		tmp = Float64(y * z);
	elseif (x <= 9e-267)
		tmp = t_1;
	elseif (x <= 2.15e-236)
		tmp = Float64(y * z);
	elseif (x <= 1.32e-174)
		tmp = Float64(t * a);
	elseif (x <= 1.05e-96)
		tmp = Float64(y * z);
	elseif (x <= 4.7e-6)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (x <= -1.02e+53)
		tmp = x;
	elseif (x <= -1.08e-7)
		tmp = y * z;
	elseif (x <= -1.25e-54)
		tmp = t * a;
	elseif (x <= -3.1e-263)
		tmp = y * z;
	elseif (x <= 9e-267)
		tmp = t_1;
	elseif (x <= 2.15e-236)
		tmp = y * z;
	elseif (x <= 1.32e-174)
		tmp = t * a;
	elseif (x <= 1.05e-96)
		tmp = y * z;
	elseif (x <= 4.7e-6)
		tmp = t_1;
	else
		tmp = x;
	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[x, -1.02e+53], x, If[LessEqual[x, -1.08e-7], N[(y * z), $MachinePrecision], If[LessEqual[x, -1.25e-54], N[(t * a), $MachinePrecision], If[LessEqual[x, -3.1e-263], N[(y * z), $MachinePrecision], If[LessEqual[x, 9e-267], t$95$1, If[LessEqual[x, 2.15e-236], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.32e-174], N[(t * a), $MachinePrecision], If[LessEqual[x, 1.05e-96], N[(y * z), $MachinePrecision], If[LessEqual[x, 4.7e-6], t$95$1, x]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.01999999999999999e53 or 4.69999999999999989e-6 < x

   1. Initial program 90.5%

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

      1. associate-+l+ 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 54.7%

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

   if -1.01999999999999999e53 < x < -1.08000000000000001e-7 or -1.25000000000000004e-54 < x < -3.10000000000000004e-263 or 8.9999999999999999e-267 < x < 2.14999999999999986e-236 or 1.31999999999999999e-174 < x < 1.05000000000000001e-96

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 54.7%

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

      1. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   if -1.08000000000000001e-7 < x < -1.25000000000000004e-54 or 2.14999999999999986e-236 < x < 1.31999999999999999e-174

   1. Initial program 95.6%

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

      1. associate-+l+ 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 56.8%

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

   if -3.10000000000000004e-263 < x < 8.9999999999999999e-267 or 1.05000000000000001e-96 < x < 4.69999999999999989e-6

   1. Initial program 95.2%

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

      1. associate-+l+ 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 78.9%

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

   5. Taylor expanded in t around 0 49.3%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-263}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-267}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-236}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-174}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-96}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 39.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-263}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-267}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-237}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-172}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.86 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3e+53)
   x
   (if (<= x -2.5e-5)
     (* y z)
     (if (<= x -1.25e-54)
       (* t a)
       (if (<= x -2e-263)
         (* y z)
         (if (<= x 8.5e-267)
           (* a (* z b))
           (if (<= x 5.5e-237)
             (* y z)
             (if (<= x 1.75e-172)
               (* t a)
               (if (<= x 3.8e-95)
                 (* y z)
                 (if (<= x 1.86e-6) (* z (* a b)) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+53) {
		tmp = x;
	} else if (x <= -2.5e-5) {
		tmp = y * z;
	} else if (x <= -1.25e-54) {
		tmp = t * a;
	} else if (x <= -2e-263) {
		tmp = y * z;
	} else if (x <= 8.5e-267) {
		tmp = a * (z * b);
	} else if (x <= 5.5e-237) {
		tmp = y * z;
	} else if (x <= 1.75e-172) {
		tmp = t * a;
	} else if (x <= 3.8e-95) {
		tmp = y * z;
	} else if (x <= 1.86e-6) {
		tmp = z * (a * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3d+53)) then
        tmp = x
    else if (x <= (-2.5d-5)) then
        tmp = y * z
    else if (x <= (-1.25d-54)) then
        tmp = t * a
    else if (x <= (-2d-263)) then
        tmp = y * z
    else if (x <= 8.5d-267) then
        tmp = a * (z * b)
    else if (x <= 5.5d-237) then
        tmp = y * z
    else if (x <= 1.75d-172) then
        tmp = t * a
    else if (x <= 3.8d-95) then
        tmp = y * z
    else if (x <= 1.86d-6) then
        tmp = z * (a * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+53) {
		tmp = x;
	} else if (x <= -2.5e-5) {
		tmp = y * z;
	} else if (x <= -1.25e-54) {
		tmp = t * a;
	} else if (x <= -2e-263) {
		tmp = y * z;
	} else if (x <= 8.5e-267) {
		tmp = a * (z * b);
	} else if (x <= 5.5e-237) {
		tmp = y * z;
	} else if (x <= 1.75e-172) {
		tmp = t * a;
	} else if (x <= 3.8e-95) {
		tmp = y * z;
	} else if (x <= 1.86e-6) {
		tmp = z * (a * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3e+53:
		tmp = x
	elif x <= -2.5e-5:
		tmp = y * z
	elif x <= -1.25e-54:
		tmp = t * a
	elif x <= -2e-263:
		tmp = y * z
	elif x <= 8.5e-267:
		tmp = a * (z * b)
	elif x <= 5.5e-237:
		tmp = y * z
	elif x <= 1.75e-172:
		tmp = t * a
	elif x <= 3.8e-95:
		tmp = y * z
	elif x <= 1.86e-6:
		tmp = z * (a * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3e+53)
		tmp = x;
	elseif (x <= -2.5e-5)
		tmp = Float64(y * z);
	elseif (x <= -1.25e-54)
		tmp = Float64(t * a);
	elseif (x <= -2e-263)
		tmp = Float64(y * z);
	elseif (x <= 8.5e-267)
		tmp = Float64(a * Float64(z * b));
	elseif (x <= 5.5e-237)
		tmp = Float64(y * z);
	elseif (x <= 1.75e-172)
		tmp = Float64(t * a);
	elseif (x <= 3.8e-95)
		tmp = Float64(y * z);
	elseif (x <= 1.86e-6)
		tmp = Float64(z * Float64(a * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3e+53)
		tmp = x;
	elseif (x <= -2.5e-5)
		tmp = y * z;
	elseif (x <= -1.25e-54)
		tmp = t * a;
	elseif (x <= -2e-263)
		tmp = y * z;
	elseif (x <= 8.5e-267)
		tmp = a * (z * b);
	elseif (x <= 5.5e-237)
		tmp = y * z;
	elseif (x <= 1.75e-172)
		tmp = t * a;
	elseif (x <= 3.8e-95)
		tmp = y * z;
	elseif (x <= 1.86e-6)
		tmp = z * (a * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3e+53], x, If[LessEqual[x, -2.5e-5], N[(y * z), $MachinePrecision], If[LessEqual[x, -1.25e-54], N[(t * a), $MachinePrecision], If[LessEqual[x, -2e-263], N[(y * z), $MachinePrecision], If[LessEqual[x, 8.5e-267], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-237], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.75e-172], N[(t * a), $MachinePrecision], If[LessEqual[x, 3.8e-95], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.86e-6], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.99999999999999998e53 or 1.86e-6 < x

   1. Initial program 90.5%

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

      1. associate-+l+ 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 54.7%

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

   if -2.99999999999999998e53 < x < -2.50000000000000012e-5 or -1.25000000000000004e-54 < x < -2e-263 or 8.49999999999999987e-267 < x < 5.49999999999999981e-237 or 1.75000000000000014e-172 < x < 3.7999999999999997e-95

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 54.7%

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

      1. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   if -2.50000000000000012e-5 < x < -1.25000000000000004e-54 or 5.49999999999999981e-237 < x < 1.75000000000000014e-172

   1. Initial program 95.6%

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

      1. associate-+l+ 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 56.8%

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

   if -2e-263 < x < 8.49999999999999987e-267

   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%

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

      3. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around inf 85.9%

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

   5. Taylor expanded in t around 0 47.0%

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

   if 3.7999999999999997e-95 < x < 1.86e-6

   1. Initial program 89.9%

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

      1. associate-+l+ 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in a around inf 71.1%

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

   5. Taylor expanded in t around 0 51.9%

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

      1. expm1-log1p-u 31.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)\right)} \]

      2. expm1-udef 31.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} - 1} \]

      3. sub-neg 31.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + \left(-1\right)} \]

      4. metadata-eval 31.2%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + \color{blue}{-1} \]

   7. Applied egg-rr 31.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + -1} \]
   8. Step-by-step derivation

      1. metadata-eval 31.2%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + \color{blue}{\left(-1\right)} \]

      2. sub-neg 31.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} - 1} \]

      3. expm1-def 31.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)\right)} \]

      4. expm1-log1p 51.9%

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

      5. associate-*r* 61.6%

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

      6. *-commutative 61.6%

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

   9. Simplified 61.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-263}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-267}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-237}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-172}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.86 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+163}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (* a (+ t (* z b)))))
   (if (<= a -3.8e-87)
     t_2
     (if (<= a 5500000000.0)
       t_1
       (if (<= a 3.15e+115)
         t_2
         (if (<= a 5.5e+126) t_1 (if (<= a 1.8e+163) (+ x (* t a)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -3.8e-87) {
		tmp = t_2;
	} else if (a <= 5500000000.0) {
		tmp = t_1;
	} else if (a <= 3.15e+115) {
		tmp = t_2;
	} else if (a <= 5.5e+126) {
		tmp = t_1;
	} else if (a <= 1.8e+163) {
		tmp = x + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * z)
    t_2 = a * (t + (z * b))
    if (a <= (-3.8d-87)) then
        tmp = t_2
    else if (a <= 5500000000.0d0) then
        tmp = t_1
    else if (a <= 3.15d+115) then
        tmp = t_2
    else if (a <= 5.5d+126) then
        tmp = t_1
    else if (a <= 1.8d+163) then
        tmp = x + (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -3.8e-87) {
		tmp = t_2;
	} else if (a <= 5500000000.0) {
		tmp = t_1;
	} else if (a <= 3.15e+115) {
		tmp = t_2;
	} else if (a <= 5.5e+126) {
		tmp = t_1;
	} else if (a <= 1.8e+163) {
		tmp = x + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	t_2 = a * (t + (z * b))
	tmp = 0
	if a <= -3.8e-87:
		tmp = t_2
	elif a <= 5500000000.0:
		tmp = t_1
	elif a <= 3.15e+115:
		tmp = t_2
	elif a <= 5.5e+126:
		tmp = t_1
	elif a <= 1.8e+163:
		tmp = x + (t * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -3.8e-87)
		tmp = t_2;
	elseif (a <= 5500000000.0)
		tmp = t_1;
	elseif (a <= 3.15e+115)
		tmp = t_2;
	elseif (a <= 5.5e+126)
		tmp = t_1;
	elseif (a <= 1.8e+163)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	t_2 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -3.8e-87)
		tmp = t_2;
	elseif (a <= 5500000000.0)
		tmp = t_1;
	elseif (a <= 3.15e+115)
		tmp = t_2;
	elseif (a <= 5.5e+126)
		tmp = t_1;
	elseif (a <= 1.8e+163)
		tmp = x + (t * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e-87], t$95$2, If[LessEqual[a, 5500000000.0], t$95$1, If[LessEqual[a, 3.15e+115], t$95$2, If[LessEqual[a, 5.5e+126], t$95$1, If[LessEqual[a, 1.8e+163], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8e-87 or 5.5e9 < a < 3.1499999999999998e115 or 1.79999999999999989e163 < a

   1. Initial program 84.5%

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

      1. associate-+l+ 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-*l* 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in a around inf 72.4%

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

   if -3.8e-87 < a < 5.5e9 or 3.1499999999999998e115 < a < 5.5000000000000004e126

   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%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 83.6%

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

   if 5.5000000000000004e126 < a < 1.79999999999999989e163

   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. *-commutative 88.9%

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

      3. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in z around 0 78.6%

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

      1. +-commutative 78.6%

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

   6. Simplified 78.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 5500000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+163}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 6: 91.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+191}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+191)
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* y z)) (+ (* z (* a b)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+191) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + ((z * (a * b)) + (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 <= (-9.2d+191)) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (y * z)) + ((z * (a * b)) + (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 <= -9.2e+191) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e+191:
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+191)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(z * Float64(a * b)) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.2e+191)
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+191], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999997e191

   1. Initial program 71.4%

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

      1. associate-+l+ 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-*l* 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in t around 0 71.4%

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

      1. associate-*r* 71.7%

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

      2. distribute-rgt-in 95.5%

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

      3. +-commutative 95.5%

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

   6. Simplified 95.5%

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

   if -9.1999999999999997e191 < y

   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. *-commutative 93.3%

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

      3. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+191}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \end{array} \]

Alternative 7: 39.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-269}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-174}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 0.00062:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.32e+54)
   x
   (if (<= x -2.2e-7)
     (* y z)
     (if (<= x -1.25e-54)
       (* t a)
       (if (<= x -1.85e-269)
         (* y z)
         (if (<= x 4.5e-174) (* t a) (if (<= x 0.00062) (* y z) x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.32e+54) {
		tmp = x;
	} else if (x <= -2.2e-7) {
		tmp = y * z;
	} else if (x <= -1.25e-54) {
		tmp = t * a;
	} else if (x <= -1.85e-269) {
		tmp = y * z;
	} else if (x <= 4.5e-174) {
		tmp = t * a;
	} else if (x <= 0.00062) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.32d+54)) then
        tmp = x
    else if (x <= (-2.2d-7)) then
        tmp = y * z
    else if (x <= (-1.25d-54)) then
        tmp = t * a
    else if (x <= (-1.85d-269)) then
        tmp = y * z
    else if (x <= 4.5d-174) then
        tmp = t * a
    else if (x <= 0.00062d0) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.32e+54) {
		tmp = x;
	} else if (x <= -2.2e-7) {
		tmp = y * z;
	} else if (x <= -1.25e-54) {
		tmp = t * a;
	} else if (x <= -1.85e-269) {
		tmp = y * z;
	} else if (x <= 4.5e-174) {
		tmp = t * a;
	} else if (x <= 0.00062) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.32e+54:
		tmp = x
	elif x <= -2.2e-7:
		tmp = y * z
	elif x <= -1.25e-54:
		tmp = t * a
	elif x <= -1.85e-269:
		tmp = y * z
	elif x <= 4.5e-174:
		tmp = t * a
	elif x <= 0.00062:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.32e+54)
		tmp = x;
	elseif (x <= -2.2e-7)
		tmp = Float64(y * z);
	elseif (x <= -1.25e-54)
		tmp = Float64(t * a);
	elseif (x <= -1.85e-269)
		tmp = Float64(y * z);
	elseif (x <= 4.5e-174)
		tmp = Float64(t * a);
	elseif (x <= 0.00062)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.32e+54)
		tmp = x;
	elseif (x <= -2.2e-7)
		tmp = y * z;
	elseif (x <= -1.25e-54)
		tmp = t * a;
	elseif (x <= -1.85e-269)
		tmp = y * z;
	elseif (x <= 4.5e-174)
		tmp = t * a;
	elseif (x <= 0.00062)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.32e+54], x, If[LessEqual[x, -2.2e-7], N[(y * z), $MachinePrecision], If[LessEqual[x, -1.25e-54], N[(t * a), $MachinePrecision], If[LessEqual[x, -1.85e-269], N[(y * z), $MachinePrecision], If[LessEqual[x, 4.5e-174], N[(t * a), $MachinePrecision], If[LessEqual[x, 0.00062], N[(y * z), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3200000000000001e54 or 6.2e-4 < x

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. *-commutative 90.4%

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

      3. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around inf 55.2%

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

   if -1.3200000000000001e54 < x < -2.2000000000000001e-7 or -1.25000000000000004e-54 < x < -1.84999999999999989e-269 or 4.49999999999999964e-174 < x < 6.2e-4

   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. *-commutative 89.2%

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

      3. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

   6. Simplified 45.3%

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

   if -2.2000000000000001e-7 < x < -1.25000000000000004e-54 or -1.84999999999999989e-269 < x < 4.49999999999999964e-174

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 44.8%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-54}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-269}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-174}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 0.00062:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 53.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-218}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (* z (* a b))))
   (if (<= b -2.4e+209)
     t_2
     (if (<= b -3.4e-275)
       t_1
       (if (<= b 1.3e-218) (* t a) (if (<= b 1.9e+232) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = z * (a * b);
	double tmp;
	if (b <= -2.4e+209) {
		tmp = t_2;
	} else if (b <= -3.4e-275) {
		tmp = t_1;
	} else if (b <= 1.3e-218) {
		tmp = t * a;
	} else if (b <= 1.9e+232) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * z)
    t_2 = z * (a * b)
    if (b <= (-2.4d+209)) then
        tmp = t_2
    else if (b <= (-3.4d-275)) then
        tmp = t_1
    else if (b <= 1.3d-218) then
        tmp = t * a
    else if (b <= 1.9d+232) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = z * (a * b);
	double tmp;
	if (b <= -2.4e+209) {
		tmp = t_2;
	} else if (b <= -3.4e-275) {
		tmp = t_1;
	} else if (b <= 1.3e-218) {
		tmp = t * a;
	} else if (b <= 1.9e+232) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	t_2 = z * (a * b)
	tmp = 0
	if b <= -2.4e+209:
		tmp = t_2
	elif b <= -3.4e-275:
		tmp = t_1
	elif b <= 1.3e-218:
		tmp = t * a
	elif b <= 1.9e+232:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	t_2 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (b <= -2.4e+209)
		tmp = t_2;
	elseif (b <= -3.4e-275)
		tmp = t_1;
	elseif (b <= 1.3e-218)
		tmp = Float64(t * a);
	elseif (b <= 1.9e+232)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	t_2 = z * (a * b);
	tmp = 0.0;
	if (b <= -2.4e+209)
		tmp = t_2;
	elseif (b <= -3.4e-275)
		tmp = t_1;
	elseif (b <= 1.3e-218)
		tmp = t * a;
	elseif (b <= 1.9e+232)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+209], t$95$2, If[LessEqual[b, -3.4e-275], t$95$1, If[LessEqual[b, 1.3e-218], N[(t * a), $MachinePrecision], If[LessEqual[b, 1.9e+232], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.39999999999999996e209 or 1.9e232 < b

   1. Initial program 84.7%

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

      1. associate-+l+ 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*l* 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in a around inf 91.4%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. expm1-log1p-u 38.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)\right)} \]

      2. expm1-udef 38.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} - 1} \]

      3. sub-neg 38.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + \left(-1\right)} \]

      4. metadata-eval 38.3%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + \color{blue}{-1} \]

   7. Applied egg-rr 38.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + -1} \]
   8. Step-by-step derivation

      1. metadata-eval 38.3%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} + \color{blue}{\left(-1\right)} \]

      2. sub-neg 38.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)} - 1} \]

      3. expm1-def 38.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot z\right)\right)\right)} \]

      4. expm1-log1p 77.0%

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

      5. associate-*r* 80.0%

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

      6. *-commutative 80.0%

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

   9. Simplified 80.0%

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

   if -2.39999999999999996e209 < b < -3.39999999999999968e-275 or 1.29999999999999992e-218 < b < 1.9e232

   1. Initial program 93.6%

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

      1. associate-+l+ 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around 0 65.4%

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

   if -3.39999999999999968e-275 < b < 1.29999999999999992e-218

   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%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 64.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-275}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-218}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+232}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 9: 80.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-105} \lor \neg \left(z \leq 4.2 \cdot 10^{-246}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-105) (not (<= z 4.2e-246)))
   (+ x (* 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 <= -3e-105) || !(z <= 4.2e-246)) {
		tmp = x + (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 <= (-3d-105)) .or. (.not. (z <= 4.2d-246))) then
        tmp = x + (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 <= -3e-105) || !(z <= 4.2e-246)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e-105) or not (z <= 4.2e-246):
		tmp = x + (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 <= -3e-105) || !(z <= 4.2e-246))
		tmp = Float64(x + 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 <= -3e-105) || ~((z <= 4.2e-246)))
		tmp = x + (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, -3e-105], N[Not[LessEqual[z, 4.2e-246]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e-105 or 4.19999999999999989e-246 < z

   1. Initial program 89.5%

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

      1. associate-+l+ 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in t around 0 74.7%

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

      1. associate-*r* 77.9%

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

      2. distribute-rgt-in 82.8%

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

      3. +-commutative 82.8%

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

   6. Simplified 82.8%

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

   if -3.0000000000000001e-105 < z < 4.19999999999999989e-246

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around 0 84.5%

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

      1. +-commutative 84.5%

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

   6. Simplified 84.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-105} \lor \neg \left(z \leq 4.2 \cdot 10^{-246}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 10: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+72} \lor \neg \left(t \leq 8.2 \cdot 10^{+15}\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.9e+72) (not (<= t 8.2e+15)))
   (+ x (+ (* t a) (* y z)))
   (+ x (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.9e+72) || !(t <= 8.2e+15)) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.9d+72)) .or. (.not. (t <= 8.2d+15))) then
        tmp = x + ((t * a) + (y * z))
    else
        tmp = x + (z * (y + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.9e+72) || !(t <= 8.2e+15)) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.9e+72) or not (t <= 8.2e+15):
		tmp = x + ((t * a) + (y * z))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.9e+72) || !(t <= 8.2e+15))
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.9e+72) || ~((t <= 8.2e+15)))
		tmp = x + ((t * a) + (y * z));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.9e+72], N[Not[LessEqual[t, 8.2e+15]], $MachinePrecision]], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9000000000000002e72 or 8.2e15 < t

   1. Initial program 91.4%

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

      1. associate-+l+ 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in b around 0 91.3%

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

   if -5.9000000000000002e72 < t < 8.2e15

   1. Initial program 91.6%

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

      1. associate-+l+ 91.6%

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

      2. *-commutative 91.6%

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

      3. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around 0 86.2%

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

      1. associate-*r* 85.6%

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

      2. distribute-rgt-in 90.2%

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

      3. +-commutative 90.2%

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

   6. Simplified 90.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+72} \lor \neg \left(t \leq 8.2 \cdot 10^{+15}\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 11: 64.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-51} \lor \neg \left(t \leq 15500000000\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.3e-51) (not (<= t 15500000000.0)))
   (+ x (* t a))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.3e-51) || !(t <= 15500000000.0)) {
		tmp = x + (t * a);
	} 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 ((t <= (-3.3d-51)) .or. (.not. (t <= 15500000000.0d0))) then
        tmp = x + (t * a)
    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 ((t <= -3.3e-51) || !(t <= 15500000000.0)) {
		tmp = x + (t * a);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.3e-51) or not (t <= 15500000000.0):
		tmp = x + (t * a)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.3e-51) || !(t <= 15500000000.0))
		tmp = Float64(x + Float64(t * a));
	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 ((t <= -3.3e-51) || ~((t <= 15500000000.0)))
		tmp = x + (t * a);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.3e-51], N[Not[LessEqual[t, 15500000000.0]], $MachinePrecision]], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999973e-51 or 1.55e10 < t

   1. Initial program 91.1%

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

      1. associate-+l+ 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around 0 68.5%

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

      1. +-commutative 68.5%

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

   6. Simplified 68.5%

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

   if -3.29999999999999973e-51 < t < 1.55e10

   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. *-commutative 92.0%

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

      3. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around 0 64.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-51} \lor \neg \left(t \leq 15500000000\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 12: 39.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-39}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+32) x (if (<= x 6.6e-39) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+32) {
		tmp = x;
	} else if (x <= 6.6e-39) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.5d+32)) then
        tmp = x
    else if (x <= 6.6d-39) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+32) {
		tmp = x;
	} else if (x <= 6.6e-39) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+32:
		tmp = x
	elif x <= 6.6e-39:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+32)
		tmp = x;
	elseif (x <= 6.6e-39)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.5e+32)
		tmp = x;
	elseif (x <= 6.6e-39)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+32], x, If[LessEqual[x, 6.6e-39], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e32 or 6.5999999999999997e-39 < x

   1. Initial program 90.6%

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

      1. associate-+l+ 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 51.3%

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

   if -2.4999999999999999e32 < x < 6.5999999999999997e-39

   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%

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

      3. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around inf 34.9%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-39}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 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 91.5%

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

   1. associate-+l+ 91.5%

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

   2. *-commutative 91.5%

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

   3. associate-*l* 92.7%

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

3. Simplified 92.7%

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

4. Taylor expanded in x around inf 29.3%

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

5. Final simplification 29.3%

   \[\leadsto x \]

Developer target: 97.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))