Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 95.7%

Time: 10.8s

Alternatives: 13

Speedup: 0.7×

• 32.8% 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: 92.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 10^{+282}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 1e+282) t_1 (+ (fma y z x) (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 1e+282) {
		tmp = t_1;
	} else {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 1e+282)
		tmp = t_1;
	else
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+282], t$95$1, N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 1.00000000000000003e282

   1. Initial program 99.0%

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

   if 1.00000000000000003e282 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 74.1%

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

      1. associate-+l+ 74.1%

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

      2. +-commutative 74.1%

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

      3. fma-define 74.1%

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

      4. associate-*l* 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. distribute-rgt-out 91.8%

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

      8. remove-double-neg 91.8%

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

      9. *-commutative 91.8%

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

      10. distribute-lft-neg-out 91.8%

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

      11. sub-neg 91.8%

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

      12. sub-neg 91.8%

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

      13. distribute-lft-neg-out 91.8%

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

      14. *-commutative 91.8%

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

      15. remove-double-neg 91.8%

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

      16. *-commutative 91.8%

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

   3. Simplified 91.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq 10^{+282}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.7%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. fma-define 0.0%

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

      4. associate-*l* 22.2%

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

      5. *-commutative 22.2%

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

      6. *-commutative 22.2%

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

      7. distribute-rgt-out 66.7%

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

      8. remove-double-neg 66.7%

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

      9. *-commutative 66.7%

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

      10. distribute-lft-neg-out 66.7%

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

      11. sub-neg 66.7%

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

      12. sub-neg 66.7%

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

      13. distribute-lft-neg-out 66.7%

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

      14. *-commutative 66.7%

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

      15. remove-double-neg 66.7%

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

      16. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 78.5%

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

   6. Taylor expanded in x around 0 78.5%

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

4. Final simplification 97.0%

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

Alternative 3: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.65 \cdot 10^{+139}:\\ \;\;\;\;t\_1 + z \cdot \left(y + \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= x -1e+112)
     (+ x (* z (+ y (* a b))))
     (if (<= x 4.65e+139) (+ t_1 (* z (+ y (/ x z)))) (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (x <= -1e+112) {
		tmp = x + (z * (y + (a * b)));
	} else if (x <= 4.65e+139) {
		tmp = t_1 + (z * (y + (x / z)));
	} else {
		tmp = x + 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 = a * (t + (z * b))
    if (x <= (-1d+112)) then
        tmp = x + (z * (y + (a * b)))
    else if (x <= 4.65d+139) then
        tmp = t_1 + (z * (y + (x / z)))
    else
        tmp = x + 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 = a * (t + (z * b));
	double tmp;
	if (x <= -1e+112) {
		tmp = x + (z * (y + (a * b)));
	} else if (x <= 4.65e+139) {
		tmp = t_1 + (z * (y + (x / z)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if x <= -1e+112:
		tmp = x + (z * (y + (a * b)))
	elif x <= 4.65e+139:
		tmp = t_1 + (z * (y + (x / z)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (x <= -1e+112)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	elseif (x <= 4.65e+139)
		tmp = Float64(t_1 + Float64(z * Float64(y + Float64(x / z))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (x <= -1e+112)
		tmp = x + (z * (y + (a * b)));
	elseif (x <= 4.65e+139)
		tmp = t_1 + (z * (y + (x / z)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+112], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.65e+139], N[(t$95$1 + N[(z * N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999993e111

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. associate-*l* 95.0%

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

   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. Add Preprocessing

   5. Taylor expanded in t around 0 86.1%

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

      1. associate-*r* 88.6%

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

      2. distribute-rgt-in 91.1%

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

      3. +-commutative 91.1%

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

   7. Simplified 91.1%

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

   if -9.9999999999999993e111 < x < 4.6500000000000001e139

   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. +-commutative 95.0%

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

      3. fma-define 95.0%

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

      4. associate-*l* 94.4%

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

      5. *-commutative 94.4%

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

      6. *-commutative 94.4%

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

      7. distribute-rgt-out 95.6%

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

      8. remove-double-neg 95.6%

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

      9. *-commutative 95.6%

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

      10. distribute-lft-neg-out 95.6%

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

      11. sub-neg 95.6%

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

      12. sub-neg 95.6%

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

      13. distribute-lft-neg-out 95.6%

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

      14. *-commutative 95.6%

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

      15. remove-double-neg 95.6%

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

      16. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around inf 93.8%

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

   if 4.6500000000000001e139 < x

   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. +-commutative 95.0%

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

      3. fma-define 95.0%

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

      4. associate-*l* 92.5%

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

      5. *-commutative 92.5%

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

      6. *-commutative 92.5%

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

      7. distribute-rgt-out 95.0%

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

      8. remove-double-neg 95.0%

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

      9. *-commutative 95.0%

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

      10. distribute-lft-neg-out 95.0%

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

      11. sub-neg 95.0%

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

      12. sub-neg 95.0%

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

      13. distribute-lft-neg-out 95.0%

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

      14. *-commutative 95.0%

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

      15. remove-double-neg 95.0%

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

      16. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0 90.4%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.65 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + z \cdot \left(y + \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+106}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.2e-80)
   (* y z)
   (if (<= z 1.9e-85) x (if (<= z 1.75e+106) (* t a) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e-80) {
		tmp = y * z;
	} else if (z <= 1.9e-85) {
		tmp = x;
	} else if (z <= 1.75e+106) {
		tmp = t * a;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.2d-80)) then
        tmp = y * z
    else if (z <= 1.9d-85) then
        tmp = x
    else if (z <= 1.75d+106) then
        tmp = t * a
    else
        tmp = z * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e-80) {
		tmp = y * z;
	} else if (z <= 1.9e-85) {
		tmp = x;
	} else if (z <= 1.75e+106) {
		tmp = t * a;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.2e-80:
		tmp = y * z
	elif z <= 1.9e-85:
		tmp = x
	elif z <= 1.75e+106:
		tmp = t * a
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.2e-80)
		tmp = Float64(y * z);
	elseif (z <= 1.9e-85)
		tmp = x;
	elseif (z <= 1.75e+106)
		tmp = Float64(t * a);
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.2e-80)
		tmp = y * z;
	elseif (z <= 1.9e-85)
		tmp = x;
	elseif (z <= 1.75e+106)
		tmp = t * a;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.2e-80], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.9e-85], x, If[LessEqual[z, 1.75e+106], N[(t * a), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999999e-80

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in z around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. flip3-+ 22.3%

         \[\leadsto \color{blue}{\frac{{y}^{3} + {\left(a \cdot b\right)}^{3}}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \cdot z \]

      3. associate-*l/ 18.3%

         \[\leadsto \color{blue}{\frac{\left({y}^{3} + {\left(a \cdot b\right)}^{3}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \]

      4. pow3 18.3%

         \[\leadsto \frac{\left({y}^{3} + \color{blue}{\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) \cdot \left(a \cdot b\right)}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      5. +-commutative 18.3%

         \[\leadsto \frac{\color{blue}{\left(\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) \cdot \left(a \cdot b\right) + {y}^{3}\right)} \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      6. pow3 18.3%

         \[\leadsto \frac{\left(\color{blue}{{\left(a \cdot b\right)}^{3}} + {y}^{3}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      7. fma-define 18.3%

         \[\leadsto \frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\color{blue}{\mathsf{fma}\left(y, y, \left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \]

      8. distribute-rgt-out-- 18.3%

         \[\leadsto \frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\mathsf{fma}\left(y, y, \color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b - y\right)}\right)} \]

   7. Applied egg-rr 18.3%

      \[\leadsto \color{blue}{\frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\mathsf{fma}\left(y, y, \left(a \cdot b\right) \cdot \left(a \cdot b - y\right)\right)}} \]

   8. Taylor expanded in a around 0 44.8%

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

      1. *-commutative 44.8%

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

   10. Simplified 44.8%

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

   if -3.1999999999999999e-80 < z < 1.8999999999999999e-85

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 70.1%

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

      1. associate-*r* 74.9%

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

      2. distribute-rgt-in 74.9%

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

      3. +-commutative 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in y around 0 60.1%

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

      1. associate-*r* 14.5%

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

      2. *-commutative 14.5%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in x around inf 53.3%

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

   if 1.8999999999999999e-85 < z < 1.7499999999999999e106

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 70.8%

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

   6. Taylor expanded in x around 0 42.3%

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

   if 1.7499999999999999e106 < z

   1. Initial program 82.6%

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

      1. associate-+l+ 82.6%

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

      2. associate-*l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 83.9%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. associate-*r* 49.1%

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

      2. *-commutative 49.1%

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

   8. Simplified 49.1%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-80}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+106}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{+81}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.1e+81)
   (+ (+ (* a (* z b)) (* t a)) (+ x (* 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 (z <= 1.1e+81) {
		tmp = ((a * (z * b)) + (t * a)) + (x + (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 (z <= 1.1d+81) then
        tmp = ((a * (z * b)) + (t * a)) + (x + (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 (z <= 1.1e+81) {
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.1e+81:
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.1e+81)
		tmp = Float64(Float64(Float64(a * Float64(z * b)) + Float64(t * a)) + Float64(x + 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 (z <= 1.1e+81)
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.1e+81], N[(N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(x + 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 z < 1.09999999999999993e81

   1. Initial program 96.7%

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

      1. associate-+l+ 96.7%

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

      2. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   if 1.09999999999999993e81 < z

   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. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in t around 0 83.0%

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

      1. associate-*r* 88.7%

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

      2. distribute-rgt-in 94.9%

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

      3. +-commutative 94.9%

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

   7. Simplified 94.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{+81}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-83} \lor \neg \left(z \leq 5.8 \cdot 10^{+16}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.8e-83) (not (<= z 5.8e+16)))
   (+ x (* z (+ y (* a b))))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-83) || !(z <= 5.8e+16)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.8d-83)) .or. (.not. (z <= 5.8d+16))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-83) || !(z <= 5.8e+16)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.8e-83) or not (z <= 5.8e+16):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.8e-83) || !(z <= 5.8e+16))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.8e-83) || ~((z <= 5.8e+16)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.8e-83], N[Not[LessEqual[z, 5.8e+16]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999998e-83 or 5.8e16 < z

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. associate-*l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. associate-*r* 86.3%

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

      2. distribute-rgt-in 88.6%

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

      3. +-commutative 88.6%

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

   7. Simplified 88.6%

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

   if -5.7999999999999998e-83 < z < 5.8e16

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. +-commutative 98.5%

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

      3. fma-define 98.5%

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

      4. associate-*l* 99.2%

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

      5. *-commutative 99.2%

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

      6. *-commutative 99.2%

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

      7. distribute-rgt-out 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-out 100.0%

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

      14. *-commutative 100.0%

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

      15. remove-double-neg 100.0%

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

      16. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 91.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-83} \lor \neg \left(z \leq 5.8 \cdot 10^{+16}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+151} \lor \neg \left(y \leq 5.2 \cdot 10^{+142}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e+151) (not (<= y 5.2e+142)))
   (+ x (* y z))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e+151) || !(y <= 5.2e+142)) {
		tmp = x + (y * z);
	} 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 ((y <= (-2.6d+151)) .or. (.not. (y <= 5.2d+142))) then
        tmp = x + (y * z)
    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 ((y <= -2.6e+151) || !(y <= 5.2e+142)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e+151) or not (y <= 5.2e+142):
		tmp = x + (y * z)
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e+151) || !(y <= 5.2e+142))
		tmp = Float64(x + Float64(y * z));
	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 ((y <= -2.6e+151) || ~((y <= 5.2e+142)))
		tmp = x + (y * z);
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e+151], N[Not[LessEqual[y, 5.2e+142]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000013e151 or 5.20000000000000043e142 < y

   1. Initial program 94.0%

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

      1. associate-+l+ 94.0%

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

      2. +-commutative 94.0%

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

      3. fma-define 94.0%

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

      4. associate-*l* 92.5%

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

      5. *-commutative 92.5%

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

      6. *-commutative 92.5%

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

      7. distribute-rgt-out 95.5%

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

      8. remove-double-neg 95.5%

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

      9. *-commutative 95.5%

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

      10. distribute-lft-neg-out 95.5%

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

      11. sub-neg 95.5%

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

      12. sub-neg 95.5%

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

      13. distribute-lft-neg-out 95.5%

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

      14. *-commutative 95.5%

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

      15. remove-double-neg 95.5%

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

      16. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around inf 82.7%

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

   6. Taylor expanded in a around 0 76.9%

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

   7. Taylor expanded in z around 0 86.8%

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

      1. *-commutative 86.8%

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

   9. Simplified 86.8%

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

   if -2.60000000000000013e151 < y < 5.20000000000000043e142

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. +-commutative 94.3%

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

      3. fma-define 94.3%

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

      4. associate-*l* 94.8%

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

      5. *-commutative 94.8%

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

      6. *-commutative 94.8%

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

      7. distribute-rgt-out 95.9%

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

      8. remove-double-neg 95.9%

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

      9. *-commutative 95.9%

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

      10. distribute-lft-neg-out 95.9%

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

      11. sub-neg 95.9%

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

      12. sub-neg 95.9%

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

      13. distribute-lft-neg-out 95.9%

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

      14. *-commutative 95.9%

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

      15. remove-double-neg 95.9%

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

      16. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 86.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+151} \lor \neg \left(y \leq 5.2 \cdot 10^{+142}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.4e+124)
   (* t a)
   (if (<= t 3.9e-156) x (if (<= t 4.5e+27) (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.4e+124) {
		tmp = t * a;
	} else if (t <= 3.9e-156) {
		tmp = x;
	} else if (t <= 4.5e+27) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.4d+124)) then
        tmp = t * a
    else if (t <= 3.9d-156) then
        tmp = x
    else if (t <= 4.5d+27) then
        tmp = y * z
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.4e+124) {
		tmp = t * a;
	} else if (t <= 3.9e-156) {
		tmp = x;
	} else if (t <= 4.5e+27) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.4e+124:
		tmp = t * a
	elif t <= 3.9e-156:
		tmp = x
	elif t <= 4.5e+27:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.4e+124)
		tmp = Float64(t * a);
	elseif (t <= 3.9e-156)
		tmp = x;
	elseif (t <= 4.5e+27)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.4e+124)
		tmp = t * a;
	elseif (t <= 3.9e-156)
		tmp = x;
	elseif (t <= 4.5e+27)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.4e+124], N[(t * a), $MachinePrecision], If[LessEqual[t, 3.9e-156], x, If[LessEqual[t, 4.5e+27], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.40000000000000016e124 or 4.4999999999999999e27 < t

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in z around 0 74.4%

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

   6. Taylor expanded in x around 0 52.4%

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

   if -7.40000000000000016e124 < t < 3.9000000000000001e-156

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 88.3%

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

      1. associate-*r* 92.4%

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

      2. distribute-rgt-in 93.3%

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

      3. +-commutative 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. associate-*r* 26.5%

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

      2. *-commutative 26.5%

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

   10. Simplified 69.3%

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

   11. Taylor expanded in x around inf 45.6%

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

   if 3.9000000000000001e-156 < t < 4.4999999999999999e27

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. flip3-+ 27.0%

         \[\leadsto \color{blue}{\frac{{y}^{3} + {\left(a \cdot b\right)}^{3}}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \cdot z \]

      3. associate-*l/ 21.5%

         \[\leadsto \color{blue}{\frac{\left({y}^{3} + {\left(a \cdot b\right)}^{3}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \]

      4. pow3 21.5%

         \[\leadsto \frac{\left({y}^{3} + \color{blue}{\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) \cdot \left(a \cdot b\right)}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      5. +-commutative 21.5%

         \[\leadsto \frac{\color{blue}{\left(\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) \cdot \left(a \cdot b\right) + {y}^{3}\right)} \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      6. pow3 21.5%

         \[\leadsto \frac{\left(\color{blue}{{\left(a \cdot b\right)}^{3}} + {y}^{3}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      7. fma-define 21.5%

         \[\leadsto \frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\color{blue}{\mathsf{fma}\left(y, y, \left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \]

      8. distribute-rgt-out-- 21.5%

         \[\leadsto \frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\mathsf{fma}\left(y, y, \color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b - y\right)}\right)} \]

   7. Applied egg-rr 21.5%

      \[\leadsto \color{blue}{\frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\mathsf{fma}\left(y, y, \left(a \cdot b\right) \cdot \left(a \cdot b - y\right)\right)}} \]

   8. Taylor expanded in a around 0 44.3%

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

      1. *-commutative 44.3%

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

   10. Simplified 44.3%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35000000000 \lor \neg \left(z \leq 1.7 \cdot 10^{+106}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -35000000000.0) (not (<= z 1.7e+106)))
   (* 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 <= -35000000000.0) || !(z <= 1.7e+106)) {
		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 <= (-35000000000.0d0)) .or. (.not. (z <= 1.7d+106))) 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 <= -35000000000.0) || !(z <= 1.7e+106)) {
		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 <= -35000000000.0) or not (z <= 1.7e+106):
		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 <= -35000000000.0) || !(z <= 1.7e+106))
		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 <= -35000000000.0) || ~((z <= 1.7e+106)))
		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, -35000000000.0], N[Not[LessEqual[z, 1.7e+106]], $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 < -3.5e10 or 1.69999999999999997e106 < z

   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. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 82.3%

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

   if -3.5e10 < z < 1.69999999999999997e106

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 76.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35000000000 \lor \neg \left(z \leq 1.7 \cdot 10^{+106}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-7} \lor \neg \left(y \leq 8.6 \cdot 10^{+104}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.95e-7) (not (<= y 8.6e+104))) (+ x (* y z)) (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.95e-7) || !(y <= 8.6e+104)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.95d-7)) .or. (.not. (y <= 8.6d+104))) then
        tmp = x + (y * z)
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.95e-7) || !(y <= 8.6e+104)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.95e-7) or not (y <= 8.6e+104):
		tmp = x + (y * z)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.95e-7) || !(y <= 8.6e+104))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.95e-7) || ~((y <= 8.6e+104)))
		tmp = x + (y * z);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.95e-7], N[Not[LessEqual[y, 8.6e+104]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000012e-7 or 8.6000000000000003e104 < y

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. +-commutative 94.3%

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

      3. fma-define 94.3%

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

      4. associate-*l* 92.4%

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

      5. *-commutative 92.4%

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

      6. *-commutative 92.4%

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

      7. distribute-rgt-out 95.2%

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

      8. remove-double-neg 95.2%

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

      9. *-commutative 95.2%

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

      10. distribute-lft-neg-out 95.2%

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

      11. sub-neg 95.2%

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

      12. sub-neg 95.2%

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

      13. distribute-lft-neg-out 95.2%

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

      14. *-commutative 95.2%

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

      15. remove-double-neg 95.2%

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

      16. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 81.8%

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

   6. Taylor expanded in a around 0 66.9%

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

   7. Taylor expanded in z around 0 77.6%

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

      1. *-commutative 77.6%

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

   9. Simplified 77.6%

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

   if -1.95000000000000012e-7 < y < 8.6000000000000003e104

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 68.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-7} \lor \neg \left(y \leq 8.6 \cdot 10^{+104}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5500000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5500000000000.0)
   (* y z)
   (if (<= z 4.2e+106) (+ x (* t a)) (* z (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5500000000000.0) {
		tmp = y * z;
	} else if (z <= 4.2e+106) {
		tmp = x + (t * a);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5500000000000.0d0)) then
        tmp = y * z
    else if (z <= 4.2d+106) then
        tmp = x + (t * a)
    else
        tmp = z * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5500000000000.0) {
		tmp = y * z;
	} else if (z <= 4.2e+106) {
		tmp = x + (t * a);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5500000000000.0:
		tmp = y * z
	elif z <= 4.2e+106:
		tmp = x + (t * a)
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5500000000000.0)
		tmp = Float64(y * z);
	elseif (z <= 4.2e+106)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5500000000000.0)
		tmp = y * z;
	elseif (z <= 4.2e+106)
		tmp = x + (t * a);
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5500000000000.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 4.2e+106], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5e12

   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* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. flip3-+ 33.6%

         \[\leadsto \color{blue}{\frac{{y}^{3} + {\left(a \cdot b\right)}^{3}}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \cdot z \]

      3. associate-*l/ 27.5%

         \[\leadsto \color{blue}{\frac{\left({y}^{3} + {\left(a \cdot b\right)}^{3}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \]

      4. pow3 27.5%

         \[\leadsto \frac{\left({y}^{3} + \color{blue}{\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) \cdot \left(a \cdot b\right)}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      5. +-commutative 27.5%

         \[\leadsto \frac{\color{blue}{\left(\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) \cdot \left(a \cdot b\right) + {y}^{3}\right)} \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      6. pow3 27.5%

         \[\leadsto \frac{\left(\color{blue}{{\left(a \cdot b\right)}^{3}} + {y}^{3}\right) \cdot z}{y \cdot y + \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)} \]

      7. fma-define 27.5%

         \[\leadsto \frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\color{blue}{\mathsf{fma}\left(y, y, \left(a \cdot b\right) \cdot \left(a \cdot b\right) - y \cdot \left(a \cdot b\right)\right)}} \]

      8. distribute-rgt-out-- 27.5%

         \[\leadsto \frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\mathsf{fma}\left(y, y, \color{blue}{\left(a \cdot b\right) \cdot \left(a \cdot b - y\right)}\right)} \]

   7. Applied egg-rr 27.5%

      \[\leadsto \color{blue}{\frac{\left({\left(a \cdot b\right)}^{3} + {y}^{3}\right) \cdot z}{\mathsf{fma}\left(y, y, \left(a \cdot b\right) \cdot \left(a \cdot b - y\right)\right)}} \]

   8. Taylor expanded in a around 0 50.1%

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

      1. *-commutative 50.1%

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

   10. Simplified 50.1%

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

   if -5.5e12 < z < 4.2000000000000001e106

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 75.9%

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

   if 4.2000000000000001e106 < z

   1. Initial program 82.6%

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

      1. associate-+l+ 82.6%

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

      2. associate-*l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 83.9%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. associate-*r* 49.1%

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

      2. *-commutative 49.1%

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

   8. Simplified 49.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5500000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+121} \lor \neg \left(t \leq 5.8 \cdot 10^{+114}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.2e+121) (not (<= t 5.8e+114))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.2e+121) || !(t <= 5.8e+114)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.2d+121)) .or. (.not. (t <= 5.8d+114))) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.2e+121) || !(t <= 5.8e+114)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.2e+121) or not (t <= 5.8e+114):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.2e+121) || !(t <= 5.8e+114))
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.2e+121) || ~((t <= 5.8e+114)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.2e+121], N[Not[LessEqual[t, 5.8e+114]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999999e121 or 5.8000000000000001e114 < t

   1. Initial program 92.8%

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

      1. associate-+l+ 92.8%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in z around 0 72.7%

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

   6. Taylor expanded in x around 0 56.7%

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

   if -3.1999999999999999e121 < t < 5.8000000000000001e114

   1. Initial program 94.9%

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

      1. associate-+l+ 94.9%

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

      2. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around 0 86.0%

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

      1. associate-*r* 89.5%

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

      2. distribute-rgt-in 90.0%

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

      3. +-commutative 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in y around 0 62.7%

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

      1. associate-*r* 27.0%

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

      2. *-commutative 27.0%

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

   10. Simplified 65.0%

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

   11. Taylor expanded in x around inf 40.7%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+121} \lor \neg \left(t \leq 5.8 \cdot 10^{+114}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.5% 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 94.3%

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

   1. associate-+l+ 94.3%

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

   2. associate-*l* 94.2%

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

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. Add Preprocessing

5. Taylor expanded in t around 0 73.3%

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

   1. associate-*r* 78.2%

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

   2. distribute-rgt-in 79.3%

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

   3. +-commutative 79.3%

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

7. Simplified 79.3%

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

8. Taylor expanded in y around 0 52.7%

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

   1. associate-*r* 25.8%

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

   2. *-commutative 25.8%

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

10. Simplified 56.5%

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

11. Taylor expanded in x around inf 33.1%

    \[\leadsto \color{blue}{x} \]
12. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024176 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

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