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

Percentage Accurate: 99.9% → 99.9%

Time: 8.3s

Alternatives: 8

Speedup: 1.0×

• 29.1% 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: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+138} \lor \neg \left(z \leq 220000\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.26e+138) (not (<= z 220000.0)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.26e+138) || !(z <= 220000.0)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (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 <= (-1.26d+138)) .or. (.not. (z <= 220000.0d0))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (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 <= -1.26e+138) || !(z <= 220000.0)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.26e+138) or not (z <= 220000.0):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.26e+138) || !(z <= 220000.0))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.26e+138) || ~((z <= 220000.0)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.26e+138], N[Not[LessEqual[z, 220000.0]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25999999999999994e138 or 2.2e5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.4%

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

   if -1.25999999999999994e138 < z < 2.2e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 91.5%

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

      1. *-commutative 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+138} \lor \neg \left(z \leq 220000\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-26} \lor \neg \left(y \leq 9.5 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-26) (not (<= y 9.5e+52)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-26) || !(y <= 9.5e+52)) {
		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 <= (-2.6d-26)) .or. (.not. (y <= 9.5d+52))) 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 <= -2.6e-26) || !(y <= 9.5e+52)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e-26) or not (y <= 9.5e+52):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e-26) || !(y <= 9.5e+52))
		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 <= -2.6e-26) || ~((y <= 9.5e+52)))
		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, -2.6e-26], N[Not[LessEqual[y, 9.5e+52]], $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 < -2.6000000000000001e-26 or 9.49999999999999994e52 < 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 95.3%

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

      1. mul-1-neg 95.3%

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

      2. distribute-rgt-neg-in 95.3%

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

      3. fmm-def 95.3%

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

      4. *-commutative 95.3%

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

      5. associate-/l* 95.3%

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

      6. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r/ 83.7%

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

      3. associate-*r* 83.7%

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

      4. neg-mul-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in y around 0 88.4%

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

   if -2.6000000000000001e-26 < y < 9.49999999999999994e52

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-26} \lor \neg \left(y \leq 9.5 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{+109} \lor \neg \left(y \leq 3 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.46e+109) (not (<= y 3e+53))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.46e+109) || !(y <= 3e+53)) {
		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 <= (-1.46d+109)) .or. (.not. (y <= 3d+53))) 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 <= -1.46e+109) || !(y <= 3e+53)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.46e+109) or not (y <= 3e+53):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.46e+109) || !(y <= 3e+53))
		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 <= -1.46e+109) || ~((y <= 3e+53)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.46e+109], N[Not[LessEqual[y, 3e+53]], $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 < -1.46e109 or 2.99999999999999998e53 < 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 96.5%

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

      1. mul-1-neg 96.5%

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

      2. distribute-rgt-neg-in 96.5%

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

      3. fmm-def 96.5%

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

      4. *-commutative 96.5%

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

      5. associate-/l* 96.5%

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

      6. metadata-eval 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in t around 0 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*r/ 90.4%

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

      3. associate-*r* 90.4%

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

      4. neg-mul-1 90.4%

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

   8. Simplified 90.4%

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

   9. Taylor expanded in z around 0 79.6%

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

   if -1.46e109 < y < 2.99999999999999998e53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.1%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{+109} \lor \neg \left(y \leq 3 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-25} \lor \neg \left(y \leq 2.7 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e-25) (not (<= y 2.7e+53))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-25) || !(y <= 2.7e+53)) {
		tmp = y * (x * y);
	} 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 ((y <= (-3.9d-25)) .or. (.not. (y <= 2.7d+53))) then
        tmp = y * (x * y)
    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 ((y <= -3.9e-25) || !(y <= 2.7e+53)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.9e-25) or not (y <= 2.7e+53):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e-25) || !(y <= 2.7e+53))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.9e-25) || ~((y <= 2.7e+53)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e-25], N[Not[LessEqual[y, 2.7e+53]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e-25 or 2.70000000000000019e53 < 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 95.3%

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

      1. mul-1-neg 95.3%

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

      2. distribute-rgt-neg-in 95.3%

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

      3. fmm-def 95.3%

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

      4. *-commutative 95.3%

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

      5. associate-/l* 95.3%

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

      6. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r/ 83.7%

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

      3. associate-*r* 83.7%

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

      4. neg-mul-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in z around 0 72.0%

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

   if -3.9e-25 < y < 2.70000000000000019e53

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-25} \lor \neg \left(y \leq 2.7 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-141}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.05e-141) t (if (<= t 1.5e-83) (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-141) {
		tmp = t;
	} else if (t <= 1.5e-83) {
		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 (t <= (-1.05d-141)) then
        tmp = t
    else if (t <= 1.5d-83) 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 (t <= -1.05e-141) {
		tmp = t;
	} else if (t <= 1.5e-83) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e-141:
		tmp = t
	elif t <= 1.5e-83:
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e-141)
		tmp = t;
	elseif (t <= 1.5e-83)
		tmp = Float64(y * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e-141)
		tmp = t;
	elseif (t <= 1.5e-83)
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e-141], t, If[LessEqual[t, 1.5e-83], N[(y * z), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e-141 or 1.50000000000000005e-83 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 60.0%

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

   if -1.05e-141 < t < 1.50000000000000005e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 66.6%

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

   4. Taylor expanded in y around inf 66.6%

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

   5. Taylor expanded in z around inf 55.0%

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

Alternative 7: 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 8: 38.8% 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 44.8%

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

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))