Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.8% → 96.7%

Time: 10.3s

Alternatives: 13

Speedup: 0.5×

• 32.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% 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: 96.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.4%

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

   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%

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

      3. fma-def 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. *-commutative 0.0%

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

      5. associate-*l* 23.1%

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

      6. *-commutative 23.1%

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

      7. distribute-lft-out 69.2%

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

      8. remove-double-neg 69.2%

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

      9. *-commutative 69.2%

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

      10. distribute-lft-neg-out 69.2%

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

      11. sub-neg 69.2%

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

      12. sub-neg 69.2%

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

      13. distribute-lft-neg-in 69.2%

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

      14. remove-double-neg 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in y around 0 92.3%

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

   5. Taylor expanded in x around 0 92.3%

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

4. Final simplification 98.1%

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

Alternative 2: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-112}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-130}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 1450000000000:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -2.5e-73)
     t_1
     (if (<= z -5.3e-112)
       (+ x (* a (* z b)))
       (if (<= z -2.35e-130)
         (+ (* t a) (* y z))
         (if (<= z -8.5e-156)
           (* a (+ t (* z b)))
           (if (<= z 1450000000000.0) (+ 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 <= -2.5e-73) {
		tmp = t_1;
	} else if (z <= -5.3e-112) {
		tmp = x + (a * (z * b));
	} else if (z <= -2.35e-130) {
		tmp = (t * a) + (y * z);
	} else if (z <= -8.5e-156) {
		tmp = a * (t + (z * b));
	} else if (z <= 1450000000000.0) {
		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 <= (-2.5d-73)) then
        tmp = t_1
    else if (z <= (-5.3d-112)) then
        tmp = x + (a * (z * b))
    else if (z <= (-2.35d-130)) then
        tmp = (t * a) + (y * z)
    else if (z <= (-8.5d-156)) then
        tmp = a * (t + (z * b))
    else if (z <= 1450000000000.0d0) 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 <= -2.5e-73) {
		tmp = t_1;
	} else if (z <= -5.3e-112) {
		tmp = x + (a * (z * b));
	} else if (z <= -2.35e-130) {
		tmp = (t * a) + (y * z);
	} else if (z <= -8.5e-156) {
		tmp = a * (t + (z * b));
	} else if (z <= 1450000000000.0) {
		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 <= -2.5e-73:
		tmp = t_1
	elif z <= -5.3e-112:
		tmp = x + (a * (z * b))
	elif z <= -2.35e-130:
		tmp = (t * a) + (y * z)
	elif z <= -8.5e-156:
		tmp = a * (t + (z * b))
	elif z <= 1450000000000.0:
		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 <= -2.5e-73)
		tmp = t_1;
	elseif (z <= -5.3e-112)
		tmp = Float64(x + Float64(a * Float64(z * b)));
	elseif (z <= -2.35e-130)
		tmp = Float64(Float64(t * a) + Float64(y * z));
	elseif (z <= -8.5e-156)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (z <= 1450000000000.0)
		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 <= -2.5e-73)
		tmp = t_1;
	elseif (z <= -5.3e-112)
		tmp = x + (a * (z * b));
	elseif (z <= -2.35e-130)
		tmp = (t * a) + (y * z);
	elseif (z <= -8.5e-156)
		tmp = a * (t + (z * b));
	elseif (z <= 1450000000000.0)
		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, -2.5e-73], t$95$1, If[LessEqual[z, -5.3e-112], N[(x + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-130], N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e-156], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1450000000000.0], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.4999999999999999e-73 or 1.45e12 < z

   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* 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 80.2%

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

   if -2.4999999999999999e-73 < z < -5.3000000000000004e-112

   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-def 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. *-commutative 100.0%

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

      5. associate-*l* 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-lft-out 100.0%

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

      8. remove-double-neg 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-lft-neg-out 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-lft-neg-in 100.0%

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

      14. remove-double-neg 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. Taylor expanded in y around 0 91.0%

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

   5. Taylor expanded in t around 0 82.3%

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

   if -5.3000000000000004e-112 < z < -2.34999999999999984e-130

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   if -2.34999999999999984e-130 < z < -8.5e-156

   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. +-commutative 99.6%

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

      3. fma-def 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-*l* 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-lft-out 99.6%

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

      8. remove-double-neg 99.6%

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

      9. *-commutative 99.6%

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

      10. distribute-lft-neg-out 99.6%

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

      11. sub-neg 99.6%

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

      12. sub-neg 99.6%

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

      13. distribute-lft-neg-in 99.6%

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

      14. remove-double-neg 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

   if -8.5e-156 < z < 1.45e12

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 80.2%

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

      1. +-commutative 80.2%

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

   6. Simplified 80.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-112}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-130}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 1450000000000:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 3: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-211}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (+ t (* z b))))))
   (if (<= a -7.8e-17)
     t_1
     (if (<= a -3.1e-211)
       (+ (* (* z a) b) (+ (* t a) (* y z)))
       (if (<= a 5.2e-5) (+ (+ x (* y z)) (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (t + (z * b)));
	double tmp;
	if (a <= -7.8e-17) {
		tmp = t_1;
	} else if (a <= -3.1e-211) {
		tmp = ((z * a) * b) + ((t * a) + (y * z));
	} else if (a <= 5.2e-5) {
		tmp = (x + (y * z)) + (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 = x + (a * (t + (z * b)))
    if (a <= (-7.8d-17)) then
        tmp = t_1
    else if (a <= (-3.1d-211)) then
        tmp = ((z * a) * b) + ((t * a) + (y * z))
    else if (a <= 5.2d-5) then
        tmp = (x + (y * z)) + (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 = x + (a * (t + (z * b)));
	double tmp;
	if (a <= -7.8e-17) {
		tmp = t_1;
	} else if (a <= -3.1e-211) {
		tmp = ((z * a) * b) + ((t * a) + (y * z));
	} else if (a <= 5.2e-5) {
		tmp = (x + (y * z)) + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (t + (z * b)))
	tmp = 0
	if a <= -7.8e-17:
		tmp = t_1
	elif a <= -3.1e-211:
		tmp = ((z * a) * b) + ((t * a) + (y * z))
	elif a <= 5.2e-5:
		tmp = (x + (y * z)) + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(t + Float64(z * b))))
	tmp = 0.0
	if (a <= -7.8e-17)
		tmp = t_1;
	elseif (a <= -3.1e-211)
		tmp = Float64(Float64(Float64(z * a) * b) + Float64(Float64(t * a) + Float64(y * z)));
	elseif (a <= 5.2e-5)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (t + (z * b)));
	tmp = 0.0;
	if (a <= -7.8e-17)
		tmp = t_1;
	elseif (a <= -3.1e-211)
		tmp = ((z * a) * b) + ((t * a) + (y * z));
	elseif (a <= 5.2e-5)
		tmp = (x + (y * z)) + (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e-17], t$95$1, If[LessEqual[a, -3.1e-211], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-5], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.79999999999999979e-17 or 5.19999999999999968e-5 < a

   1. Initial program 88.1%

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

      1. associate-+l+ 88.1%

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

      2. +-commutative 88.1%

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

      3. fma-def 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-*l* 92.4%

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

      6. *-commutative 92.4%

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

      7. distribute-lft-out 96.9%

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

      8. remove-double-neg 96.9%

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

      9. *-commutative 96.9%

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

      10. distribute-lft-neg-out 96.9%

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

      11. sub-neg 96.9%

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

      12. sub-neg 96.9%

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

      13. distribute-lft-neg-in 96.9%

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

      14. remove-double-neg 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 94.6%

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

   if -7.79999999999999979e-17 < a < -3.09999999999999995e-211

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.0%

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

   if -3.09999999999999995e-211 < a < 5.19999999999999968e-5

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 90.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-17}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-211}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 4: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ t_2 := x + y \cdot z\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))) (t_2 (+ x (* y z))))
   (if (<= z -1.25e+165)
     t_2
     (if (<= z -4.8e+94)
       t_1
       (if (<= z -4.8e-20)
         t_2
         (if (<= z 3.6e+81) (+ x (* t a)) (if (<= z 1.8e+189) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double t_2 = x + (y * z);
	double tmp;
	if (z <= -1.25e+165) {
		tmp = t_2;
	} else if (z <= -4.8e+94) {
		tmp = t_1;
	} else if (z <= -4.8e-20) {
		tmp = t_2;
	} else if (z <= 3.6e+81) {
		tmp = x + (t * a);
	} else if (z <= 1.8e+189) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (a * b)
    t_2 = x + (y * z)
    if (z <= (-1.25d+165)) then
        tmp = t_2
    else if (z <= (-4.8d+94)) then
        tmp = t_1
    else if (z <= (-4.8d-20)) then
        tmp = t_2
    else if (z <= 3.6d+81) then
        tmp = x + (t * a)
    else if (z <= 1.8d+189) then
        tmp = t_2
    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 * (a * b);
	double t_2 = x + (y * z);
	double tmp;
	if (z <= -1.25e+165) {
		tmp = t_2;
	} else if (z <= -4.8e+94) {
		tmp = t_1;
	} else if (z <= -4.8e-20) {
		tmp = t_2;
	} else if (z <= 3.6e+81) {
		tmp = x + (t * a);
	} else if (z <= 1.8e+189) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	t_2 = x + (y * z)
	tmp = 0
	if z <= -1.25e+165:
		tmp = t_2
	elif z <= -4.8e+94:
		tmp = t_1
	elif z <= -4.8e-20:
		tmp = t_2
	elif z <= 3.6e+81:
		tmp = x + (t * a)
	elif z <= 1.8e+189:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	t_2 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -1.25e+165)
		tmp = t_2;
	elseif (z <= -4.8e+94)
		tmp = t_1;
	elseif (z <= -4.8e-20)
		tmp = t_2;
	elseif (z <= 3.6e+81)
		tmp = Float64(x + Float64(t * a));
	elseif (z <= 1.8e+189)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	t_2 = x + (y * z);
	tmp = 0.0;
	if (z <= -1.25e+165)
		tmp = t_2;
	elseif (z <= -4.8e+94)
		tmp = t_1;
	elseif (z <= -4.8e-20)
		tmp = t_2;
	elseif (z <= 3.6e+81)
		tmp = x + (t * a);
	elseif (z <= 1.8e+189)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+165], t$95$2, If[LessEqual[z, -4.8e+94], t$95$1, If[LessEqual[z, -4.8e-20], t$95$2, If[LessEqual[z, 3.6e+81], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+189], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999993e165 or -4.79999999999999965e94 < z < -4.79999999999999986e-20 or 3.60000000000000005e81 < z < 1.80000000000000004e189

   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* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around 0 63.6%

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

   if -1.24999999999999993e165 < z < -4.79999999999999965e94 or 1.80000000000000004e189 < z

   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. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in z around inf 87.1%

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

   5. Taylor expanded in y around 0 64.1%

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

   if -4.79999999999999986e-20 < z < 3.60000000000000005e81

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 69.7%

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

      1. +-commutative 69.7%

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

   6. Simplified 69.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+165}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+94}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+189}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 5: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-13} \lor \neg \left(a \leq 4.7 \cdot 10^{-120} \lor \neg \left(a \leq 4 \cdot 10^{-94}\right) \land a \leq 4.8 \cdot 10^{-5}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -9e-13)
         (not (or (<= a 4.7e-120) (and (not (<= a 4e-94)) (<= a 4.8e-5)))))
   (* 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 <= -9e-13) || !((a <= 4.7e-120) || (!(a <= 4e-94) && (a <= 4.8e-5)))) {
		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 <= (-9d-13)) .or. (.not. (a <= 4.7d-120) .or. (.not. (a <= 4d-94)) .and. (a <= 4.8d-5))) 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 <= -9e-13) || !((a <= 4.7e-120) || (!(a <= 4e-94) && (a <= 4.8e-5)))) {
		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 <= -9e-13) or not ((a <= 4.7e-120) or (not (a <= 4e-94) and (a <= 4.8e-5))):
		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 <= -9e-13) || !((a <= 4.7e-120) || (!(a <= 4e-94) && (a <= 4.8e-5))))
		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 <= -9e-13) || ~(((a <= 4.7e-120) || (~((a <= 4e-94)) && (a <= 4.8e-5)))))
		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, -9e-13], N[Not[Or[LessEqual[a, 4.7e-120], And[N[Not[LessEqual[a, 4e-94]], $MachinePrecision], LessEqual[a, 4.8e-5]]]], $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 < -9e-13 or 4.70000000000000016e-120 < a < 3.9999999999999998e-94 or 4.8000000000000001e-5 < a

   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. +-commutative 88.5%

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

      3. fma-def 88.5%

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

      4. *-commutative 88.5%

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

      5. associate-*l* 92.7%

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

      6. *-commutative 92.7%

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

      7. distribute-lft-out 97.1%

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

      8. remove-double-neg 97.1%

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

      9. *-commutative 97.1%

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

      10. distribute-lft-neg-out 97.1%

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

      11. sub-neg 97.1%

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

      12. sub-neg 97.1%

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

      13. distribute-lft-neg-in 97.1%

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

      14. remove-double-neg 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around 0 94.8%

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

   5. Taylor expanded in x around 0 83.3%

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

   if -9e-13 < a < 4.70000000000000016e-120 or 3.9999999999999998e-94 < a < 4.8000000000000001e-5

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around 0 70.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-13} \lor \neg \left(a \leq 4.7 \cdot 10^{-120} \lor \neg \left(a \leq 4 \cdot 10^{-94}\right) \land a \leq 4.8 \cdot 10^{-5}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 91.9% accurate, 1.0× speedup

Math

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

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(x + Float64(y * z)) + Float64(Float64(t * a) + Float64(a * Float64(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[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.4%

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

   1. associate-+l+ 93.4%

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

   2. associate-*l* 92.7%

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

3. Simplified 92.7%

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

4. Final simplification 92.7%

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

Alternative 7: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00116 \lor \neg \left(z \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.00116) (not (<= z 1.75e+86)))
   (* z (+ y (* a b)))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00116) || !(z <= 1.75e+86)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.00116d0)) .or. (.not. (z <= 1.75d+86))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00116) || !(z <= 1.75e+86)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.00116) or not (z <= 1.75e+86):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.00116) || !(z <= 1.75e+86))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.00116) || ~((z <= 1.75e+86)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.00116], N[Not[LessEqual[z, 1.75e+86]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00116 or 1.75000000000000009e86 < z

   1. Initial program 86.8%

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

      1. associate-+l+ 86.8%

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

      2. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 84.6%

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

   if -0.00116 < z < 1.75000000000000009e86

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. +-commutative 99.2%

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

      3. fma-def 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*l* 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-out 99.9%

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

      8. remove-double-neg 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-lft-neg-out 99.9%

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

      11. sub-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. distribute-lft-neg-in 99.9%

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

      14. remove-double-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 88.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00116 \lor \neg \left(z \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8: 87.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-12} \lor \neg \left(a \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.2e-12) (not (<= a 1.65e-9)))
   (+ 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 <= -4.2e-12) || !(a <= 1.65e-9)) {
		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 <= (-4.2d-12)) .or. (.not. (a <= 1.65d-9))) 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 <= -4.2e-12) || !(a <= 1.65e-9)) {
		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 <= -4.2e-12) or not (a <= 1.65e-9):
		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 <= -4.2e-12) || !(a <= 1.65e-9))
		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 <= -4.2e-12) || ~((a <= 1.65e-9)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (y * z)) + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.2e-12], N[Not[LessEqual[a, 1.65e-9]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.19999999999999988e-12 or 1.65000000000000009e-9 < a

   1. Initial program 87.9%

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

      1. associate-+l+ 87.9%

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

      2. +-commutative 87.9%

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

      3. fma-def 87.9%

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

      4. *-commutative 87.9%

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

      5. associate-*l* 92.3%

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

      6. *-commutative 92.3%

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

      7. distribute-lft-out 96.9%

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

      8. remove-double-neg 96.9%

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

      9. *-commutative 96.9%

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

      10. distribute-lft-neg-out 96.9%

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

      11. sub-neg 96.9%

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

      12. sub-neg 96.9%

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

      13. distribute-lft-neg-in 96.9%

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

      14. remove-double-neg 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 94.6%

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

   if -4.19999999999999988e-12 < a < 1.65000000000000009e-9

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 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. Taylor expanded in t around inf 85.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-12} \lor \neg \left(a \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]

Alternative 9: 73.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-62} \lor \neg \left(z \leq 59000000000000\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.35e-62) (not (<= z 59000000000000.0)))
   (* 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 <= -1.35e-62) || !(z <= 59000000000000.0)) {
		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 <= (-1.35d-62)) .or. (.not. (z <= 59000000000000.0d0))) 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 <= -1.35e-62) || !(z <= 59000000000000.0)) {
		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 <= -1.35e-62) or not (z <= 59000000000000.0):
		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 <= -1.35e-62) || !(z <= 59000000000000.0))
		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 <= -1.35e-62) || ~((z <= 59000000000000.0)))
		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, -1.35e-62], N[Not[LessEqual[z, 59000000000000.0]], $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 < -1.3500000000000001e-62 or 5.9e13 < z

   1. Initial program 89.0%

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

      1. associate-+l+ 89.0%

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

      2. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 80.6%

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

   if -1.3500000000000001e-62 < z < 5.9e13

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

   6. Simplified 76.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-62} \lor \neg \left(z \leq 59000000000000\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 10: 38.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.05 \cdot 10^{+150} \lor \neg \left(b \leq 1.65 \cdot 10^{+34}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.05e+150) (not (<= b 1.65e+34))) (* z (* a b)) (* y z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.05e+150) || !(b <= 1.65e+34)) {
		tmp = z * (a * b);
	} 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 ((b <= (-3.05d+150)) .or. (.not. (b <= 1.65d+34))) then
        tmp = z * (a * b)
    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 ((b <= -3.05e+150) || !(b <= 1.65e+34)) {
		tmp = z * (a * b);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.05e+150) or not (b <= 1.65e+34):
		tmp = z * (a * b)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.05e+150) || !(b <= 1.65e+34))
		tmp = Float64(z * Float64(a * b));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.05e+150) || ~((b <= 1.65e+34)))
		tmp = z * (a * b);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.05e+150], N[Not[LessEqual[b, 1.65e+34]], $MachinePrecision]], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.05000000000000013e150 or 1.64999999999999994e34 < b

   1. Initial program 91.0%

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

      1. associate-+l+ 91.0%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in z around inf 71.2%

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

   5. Taylor expanded in y around 0 61.3%

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

   if -3.05000000000000013e150 < b < 1.64999999999999994e34

   1. Initial program 95.0%

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

      1. associate-+l+ 95.0%

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

      2. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

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

   6. Simplified 35.4%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.05 \cdot 10^{+150} \lor \neg \left(b \leq 1.65 \cdot 10^{+34}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 11: 55.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+234} \lor \neg \left(b \leq 1.7 \cdot 10^{+35}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5e+234) (not (<= b 1.7e+35))) (* z (* a b)) (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+234) || !(b <= 1.7e+35)) {
		tmp = z * (a * 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 ((b <= (-5d+234)) .or. (.not. (b <= 1.7d+35))) then
        tmp = z * (a * 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 ((b <= -5e+234) || !(b <= 1.7e+35)) {
		tmp = z * (a * b);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5e+234) or not (b <= 1.7e+35):
		tmp = z * (a * b)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5e+234) || !(b <= 1.7e+35))
		tmp = Float64(z * Float64(a * 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 ((b <= -5e+234) || ~((b <= 1.7e+35)))
		tmp = z * (a * b);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5e+234], N[Not[LessEqual[b, 1.7e+35]], $MachinePrecision]], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.0000000000000003e234 or 1.7000000000000001e35 < b

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 72.6%

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

   5. Taylor expanded in y around 0 67.2%

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

   if -5.0000000000000003e234 < b < 1.7000000000000001e35

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around 0 53.6%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+234} \lor \neg \left(b \leq 1.7 \cdot 10^{+35}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 12: 39.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-69} \lor \neg \left(z \leq 13200000\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-69) (not (<= z 13200000.0))) (* y z) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-69) || !(z <= 13200000.0)) {
		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 ((z <= (-2d-69)) .or. (.not. (z <= 13200000.0d0))) 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 ((z <= -2e-69) || !(z <= 13200000.0)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-69) or not (z <= 13200000.0):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-69) || !(z <= 13200000.0))
		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 ((z <= -2e-69) || ~((z <= 13200000.0)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-69], N[Not[LessEqual[z, 13200000.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e-69 or 1.32e7 < z

   1. Initial program 89.4%

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

      1. associate-+l+ 89.4%

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

      2. associate-*l* 87.5%

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

   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. Taylor expanded in y around inf 41.3%

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

      1. *-commutative 41.3%

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

   6. Simplified 41.3%

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

   if -1.9999999999999999e-69 < z < 1.32e7

   1. Initial program 99.0%

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

      1. associate-+l+ 99.0%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 33.6%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-69} \lor \neg \left(z \leq 13200000\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 93.4%

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

   1. associate-+l+ 93.4%

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

   2. associate-*l* 92.7%

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

3. Simplified 92.7%

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

4. Taylor expanded in x around inf 20.1%

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

5. Final simplification 20.1%

   \[\leadsto x \]

Developer target: 97.6% 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 2023331 
(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)))