Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 9

Speedup: 1.0×

• 29.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (fma x y z) y t))

C

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

Julia

function code(x, y, z, t)
	return fma(fma(x, y, z), y, t)
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-define 99.9%

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

   2. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-105}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+37}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -1.25e+61)
     t_1
     (if (<= y -1.05e-105)
       (* y z)
       (if (<= y 4.5) t (if (<= y 4.6e+37) (* y z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.25e+61) {
		tmp = t_1;
	} else if (y <= -1.05e-105) {
		tmp = y * z;
	} else if (y <= 4.5) {
		tmp = t;
	} else if (y <= 4.6e+37) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * y)
    if (y <= (-1.25d+61)) then
        tmp = t_1
    else if (y <= (-1.05d-105)) then
        tmp = y * z
    else if (y <= 4.5d0) then
        tmp = t
    else if (y <= 4.6d+37) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.25e+61) {
		tmp = t_1;
	} else if (y <= -1.05e-105) {
		tmp = y * z;
	} else if (y <= 4.5) {
		tmp = t;
	} else if (y <= 4.6e+37) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -1.25e+61:
		tmp = t_1
	elif y <= -1.05e-105:
		tmp = y * z
	elif y <= 4.5:
		tmp = t
	elif y <= 4.6e+37:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -1.25e+61)
		tmp = t_1;
	elseif (y <= -1.05e-105)
		tmp = Float64(y * z);
	elseif (y <= 4.5)
		tmp = t;
	elseif (y <= 4.6e+37)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -1.25e+61)
		tmp = t_1;
	elseif (y <= -1.05e-105)
		tmp = y * z;
	elseif (y <= 4.5)
		tmp = t;
	elseif (y <= 4.6e+37)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+61], t$95$1, If[LessEqual[y, -1.05e-105], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.5], t, If[LessEqual[y, 4.6e+37], N[(y * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000004e61 or 4.60000000000000005e37 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 97.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 97.4%

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

      2. *-commutative 97.4%

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

      3. distribute-rgt-neg-in 97.4%

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

      4. fma-neg 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-/l* 97.4%

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

      7. metadata-eval 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in t around 0 87.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 87.6%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 87.6%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 87.6%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 87.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 87.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 87.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 84.2%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 84.2%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 84.2%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 84.2%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 84.2%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 84.2%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 84.2%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 84.2%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 84.2%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 84.2%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 89.3%

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

   10. Taylor expanded in z around 0 73.0%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot y\right)} \]
   11. Step-by-step derivation

       1. *-commutative 73.0%

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

   12. Simplified 73.0%

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

   if -1.25000000000000004e61 < y < -1.05e-105 or 4.5 < y < 4.60000000000000005e37

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 97.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 97.6%

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

      2. *-commutative 97.6%

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

      3. distribute-rgt-neg-in 97.6%

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

      4. fma-neg 97.6%

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

      5. *-commutative 97.6%

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

      6. associate-/l* 95.3%

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

      7. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around 0 77.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 77.3%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 77.3%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 77.3%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 77.3%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 75.0%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 75.0%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 75.0%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 75.0%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 75.0%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 75.0%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 75.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 75.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 75.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 75.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 75.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 75.0%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 58.0%

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

   if -1.05e-105 < y < 4.5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-105}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+37}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+62}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 9.5:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -1.3e+114)
     t_1
     (if (<= y -5.3e+62)
       (+ t (* x (* y y)))
       (if (<= y 9.5) (+ t (* y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.3e+114) {
		tmp = t_1;
	} else if (y <= -5.3e+62) {
		tmp = t + (x * (y * y));
	} else if (y <= 9.5) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z + (x * y))
    if (y <= (-1.3d+114)) then
        tmp = t_1
    else if (y <= (-5.3d+62)) then
        tmp = t + (x * (y * y))
    else if (y <= 9.5d0) then
        tmp = t + (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.3e+114) {
		tmp = t_1;
	} else if (y <= -5.3e+62) {
		tmp = t + (x * (y * y));
	} else if (y <= 9.5) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -1.3e+114:
		tmp = t_1
	elif y <= -5.3e+62:
		tmp = t + (x * (y * y))
	elif y <= 9.5:
		tmp = t + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -1.3e+114)
		tmp = t_1;
	elseif (y <= -5.3e+62)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	elseif (y <= 9.5)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -1.3e+114)
		tmp = t_1;
	elseif (y <= -5.3e+62)
		tmp = t + (x * (y * y));
	elseif (y <= 9.5)
		tmp = t + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+114], t$95$1, If[LessEqual[y, -5.3e+62], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e114 or 9.5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 98.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 98.1%

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

      2. *-commutative 98.1%

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

      3. distribute-rgt-neg-in 98.1%

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

      4. fma-neg 98.1%

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

      5. *-commutative 98.1%

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

      6. associate-/l* 98.1%

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

      7. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in t around 0 95.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 95.1%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 95.1%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 95.1%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 95.1%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 95.1%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 95.1%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 91.4%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 91.4%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 91.4%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 91.4%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 91.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 91.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 91.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 91.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 91.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 91.4%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 96.1%

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

   if -1.3e114 < y < -5.3000000000000003e62

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y \cdot z}{x} + {y}^{2}\right)} + t \]
   4. Step-by-step derivation

      1. +-commutative 87.9%

         \[\leadsto x \cdot \color{blue}{\left({y}^{2} + \frac{y \cdot z}{x}\right)} + t \]

      2. unpow2 87.9%

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

      3. associate-/l* 94.1%

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

      4. distribute-lft-out 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in y around inf 88.7%

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

   if -5.3000000000000003e62 < y < 9.5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+62}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 9.5:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+65} \lor \neg \left(y \leq 220\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+65) (not (<= y 220.0)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+65) || !(y <= 220.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.8d+65)) .or. (.not. (y <= 220.0d0))) then
        tmp = y * (z + (x * y))
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+65) || !(y <= 220.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+65) or not (y <= 220.0):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+65) || !(y <= 220.0))
		tmp = Float64(y * Float64(z + Float64(x * y)));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.8e+65) || ~((y <= 220.0)))
		tmp = y * (z + (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+65], N[Not[LessEqual[y, 220.0]], $MachinePrecision]], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999989e65 or 220 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 98.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 98.3%

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

      2. *-commutative 98.3%

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

      3. distribute-rgt-neg-in 98.3%

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

      4. fma-neg 98.3%

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

      5. *-commutative 98.3%

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

      6. associate-/l* 98.3%

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

      7. metadata-eval 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in t around 0 90.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 90.6%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 90.6%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 90.6%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 90.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 90.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 90.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 87.4%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 87.4%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 87.4%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 87.4%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 87.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 87.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 87.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 87.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 87.4%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 87.4%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 91.5%

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

   if -1.79999999999999989e65 < y < 220

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+65} \lor \neg \left(y \leq 220\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+115}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+107}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+115)
   (+ t (* y z))
   (if (<= z 7.4e+107) (+ t (* y (* x y))) (* y (+ z (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+115) {
		tmp = t + (y * z);
	} else if (z <= 7.4e+107) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d+115)) then
        tmp = t + (y * z)
    else if (z <= 7.4d+107) then
        tmp = t + (y * (x * y))
    else
        tmp = y * (z + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+115) {
		tmp = t + (y * z);
	} else if (z <= 7.4e+107) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+115:
		tmp = t + (y * z)
	elif z <= 7.4e+107:
		tmp = t + (y * (x * y))
	else:
		tmp = y * (z + (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+115)
		tmp = Float64(t + Float64(y * z));
	elseif (z <= 7.4e+107)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = Float64(y * Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e+115)
		tmp = t + (y * z);
	elseif (z <= 7.4e+107)
		tmp = t + (y * (x * y));
	else
		tmp = y * (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+115], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+107], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000002e115

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.6%

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

   if -1.45000000000000002e115 < z < 7.4e107

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 91.9%

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

      1. *-commutative 91.9%

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

   5. Simplified 91.9%

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

   if 7.4e107 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. fma-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-/l* 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 84.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 84.3%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 84.3%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 84.3%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 84.3%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 84.3%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 84.3%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 84.3%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 84.3%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 84.3%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 84.3%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 84.3%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 84.3%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 84.3%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 84.3%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 84.3%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 84.3%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 84.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+115}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+107}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+75} \lor \neg \left(y \leq 9 \cdot 10^{+37}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.3e+75) (not (<= y 9e+37))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.3e+75) || !(y <= 9e+37)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.3d+75)) .or. (.not. (y <= 9d+37))) then
        tmp = y * (x * y)
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.3e+75) || !(y <= 9e+37)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.3e+75) or not (y <= 9e+37):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.3e+75) || !(y <= 9e+37))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.3e+75) || ~((y <= 9e+37)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.3e+75], N[Not[LessEqual[y, 9e+37]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2999999999999998e75 or 8.99999999999999923e37 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 98.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 98.1%

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

      2. *-commutative 98.1%

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

      3. distribute-rgt-neg-in 98.1%

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

      4. fma-neg 98.1%

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

      5. *-commutative 98.1%

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

      6. associate-/l* 98.1%

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

      7. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in t around 0 90.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 90.6%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 90.6%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 90.6%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 90.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 90.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 90.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 87.0%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 87.0%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 87.0%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 87.0%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 87.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 87.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 87.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 87.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 87.0%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 87.0%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 91.5%

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

   10. Taylor expanded in z around 0 75.2%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot y\right)} \]
   11. Step-by-step derivation

       1. *-commutative 75.2%

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

   12. Simplified 75.2%

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

   if -5.2999999999999998e75 < y < 8.99999999999999923e37

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+75} \lor \neg \left(y \leq 9 \cdot 10^{+37}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+90} \lor \neg \left(z \leq 6.5 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e+90) (not (<= z 6.5e+58))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+90) || !(z <= 6.5e+58)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.4d+90)) .or. (.not. (z <= 6.5d+58))) then
        tmp = y * z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+90) || !(z <= 6.5e+58)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e+90) or not (z <= 6.5e+58):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e+90) || !(z <= 6.5e+58))
		tmp = Float64(y * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e+90) || ~((z <= 6.5e+58)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e+90], N[Not[LessEqual[z, 6.5e+58]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000018e90 or 6.49999999999999998e58 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. fma-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-/l* 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 81.6%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right)} \]

      2. *-commutative 81.6%

         \[\leadsto -\color{blue}{\left(z \cdot \left(-1 \cdot \frac{x \cdot y}{z} - 1\right)\right) \cdot y} \]

      3. fma-neg 81.6%

         \[\leadsto -\left(z \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)}\right) \cdot y \]

      4. *-commutative 81.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right)\right) \cdot y \]

      5. associate-*r/ 81.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right)\right) \cdot y \]

      6. metadata-eval 81.6%

         \[\leadsto -\left(z \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right)\right) \cdot y \]

      7. associate-*r* 81.6%

         \[\leadsto -\color{blue}{z \cdot \left(\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      8. distribute-rgt-neg-in 81.6%

         \[\leadsto \color{blue}{z \cdot \left(-\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot y\right)} \]

      9. *-commutative 81.6%

         \[\leadsto z \cdot \left(-\color{blue}{y \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)}\right) \]

      10. distribute-lft-neg-in 81.6%

          \[\leadsto z \cdot \color{blue}{\left(\left(-y\right) \cdot \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right)\right)} \]

      11. fma-undefine 81.6%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \frac{x}{z}\right) + -1\right)}\right) \]

      12. neg-mul-1 81.6%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{\left(-y \cdot \frac{x}{z}\right)} + -1\right)\right) \]

      13. distribute-rgt-neg-in 81.6%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \left(\color{blue}{y \cdot \left(-\frac{x}{z}\right)} + -1\right)\right) \]

      14. fma-define 81.6%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \color{blue}{\mathsf{fma}\left(y, -\frac{x}{z}, -1\right)}\right) \]

      15. distribute-neg-frac2 81.6%

          \[\leadsto z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \color{blue}{\frac{x}{-z}}, -1\right)\right) \]

   8. Simplified 81.6%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) \cdot \mathsf{fma}\left(y, \frac{x}{-z}, -1\right)\right)} \]

   9. Taylor expanded in y around 0 65.3%

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

   if -3.40000000000000018e90 < z < 6.49999999999999998e58

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 49.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+90} \lor \neg \left(z \leq 6.5 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(z + x \cdot y\right) \]
4. Add Preprocessing

Alternative 9: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 38.2%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024106 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))