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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 7

Speedup: 1.0×

• 29.5% 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: 77.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+97} \lor \neg \left(y \leq -4.9 \cdot 10^{+61} \lor \neg \left(y \leq -4.05 \cdot 10^{+27}\right) \land y \leq 245000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.6e+97)
         (not
          (or (<= y -4.9e+61)
              (and (not (<= y -4.05e+27)) (<= y 245000000000.0)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.6e+97) || !((y <= -4.9e+61) || (!(y <= -4.05e+27) && (y <= 245000000000.0)))) {
		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 <= (-7.6d+97)) .or. (.not. (y <= (-4.9d+61)) .or. (.not. (y <= (-4.05d+27))) .and. (y <= 245000000000.0d0))) 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 <= -7.6e+97) || !((y <= -4.9e+61) || (!(y <= -4.05e+27) && (y <= 245000000000.0)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.6e+97) or not ((y <= -4.9e+61) or (not (y <= -4.05e+27) and (y <= 245000000000.0))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.6e+97) || !((y <= -4.9e+61) || (!(y <= -4.05e+27) && (y <= 245000000000.0))))
		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 <= -7.6e+97) || ~(((y <= -4.9e+61) || (~((y <= -4.05e+27)) && (y <= 245000000000.0)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.6e+97], N[Not[Or[LessEqual[y, -4.9e+61], And[N[Not[LessEqual[y, -4.05e+27]], $MachinePrecision], LessEqual[y, 245000000000.0]]]], $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 < -7.60000000000000071e97 or -4.90000000000000025e61 < y < -4.05000000000000015e27 or 2.45e11 < y

   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. Taylor expanded in t around inf 88.8%

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

      1. +-commutative 88.8%

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

      2. +-commutative 88.8%

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

      3. fma-undefine 88.8%

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

      4. *-commutative 88.8%

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

      5. associate-/l* 88.9%

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

      6. fma-define 88.9%

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

      7. fma-undefine 88.9%

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

      8. *-commutative 88.9%

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

      9. fma-undefine 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in t around 0 94.7%

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

   9. Taylor expanded in z around 0 78.8%

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

       1. *-commutative 78.8%

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

   11. Simplified 78.8%

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

   if -7.60000000000000071e97 < y < -4.90000000000000025e61 or -4.05000000000000015e27 < y < 2.45e11

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+97} \lor \neg \left(y \leq -4.9 \cdot 10^{+61} \lor \neg \left(y \leq -4.05 \cdot 10^{+27}\right) \land y \leq 245000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-13} \lor \neg \left(y \leq 1.14 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.75e-13) (not (<= y 1.14e-69)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.75e-13) || !(y <= 1.14e-69)) {
		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 <= (-1.75d-13)) .or. (.not. (y <= 1.14d-69))) 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 <= -1.75e-13) || !(y <= 1.14e-69)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.75e-13) or not (y <= 1.14e-69):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.75e-13) || !(y <= 1.14e-69))
		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 <= -1.75e-13) || ~((y <= 1.14e-69)))
		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, -1.75e-13], N[Not[LessEqual[y, 1.14e-69]], $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 < -1.7500000000000001e-13 or 1.14000000000000006e-69 < y

   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. Taylor expanded in t around inf 89.6%

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

      1. +-commutative 89.6%

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

      2. +-commutative 89.6%

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

      3. fma-undefine 89.6%

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

      4. *-commutative 89.6%

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

      5. associate-/l* 88.9%

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

      6. fma-define 88.9%

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

      7. fma-undefine 88.9%

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

      8. *-commutative 88.9%

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

      9. fma-undefine 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in t around 0 89.5%

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

   if -1.7500000000000001e-13 < y < 1.14000000000000006e-69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-13} \lor \neg \left(y \leq 1.14 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-12} \lor \neg \left(y \leq 1.14 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.4e-12) (not (<= y 1.14e-69))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.4e-12) || !(y <= 1.14e-69)) {
		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 <= (-5.4d-12)) .or. (.not. (y <= 1.14d-69))) 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 <= -5.4e-12) || !(y <= 1.14e-69)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.4e-12) or not (y <= 1.14e-69):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.4e-12) || !(y <= 1.14e-69))
		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 <= -5.4e-12) || ~((y <= 1.14e-69)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.4e-12], N[Not[LessEqual[y, 1.14e-69]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -5.39999999999999961e-12 or 1.14000000000000006e-69 < y

   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. Taylor expanded in t around inf 89.6%

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

      1. +-commutative 89.6%

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

      2. +-commutative 89.6%

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

      3. fma-undefine 89.6%

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

      4. *-commutative 89.6%

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

      5. associate-/l* 88.9%

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

      6. fma-define 88.9%

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

      7. fma-undefine 88.9%

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

      8. *-commutative 88.9%

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

      9. fma-undefine 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in t around 0 89.5%

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

   9. Taylor expanded in z around 0 70.4%

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

       1. *-commutative 70.4%

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

   11. Simplified 70.4%

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

   if -5.39999999999999961e-12 < y < 1.14000000000000006e-69

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 68.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-12} \lor \neg \left(y \leq 1.14 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+102} \lor \neg \left(z \leq 7 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.7e+102) (not (<= z 7e+84))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e+102) || !(z <= 7e+84)) {
		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 <= (-3.7d+102)) .or. (.not. (z <= 7d+84))) 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 <= -3.7e+102) || !(z <= 7e+84)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.7e+102) or not (z <= 7e+84):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.7e+102) || !(z <= 7e+84))
		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 <= -3.7e+102) || ~((z <= 7e+84)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.7e+102], N[Not[LessEqual[z, 7e+84]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000023e102 or 6.9999999999999998e84 < z

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 84.8%

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

      1. +-commutative 84.8%

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

      2. +-commutative 84.8%

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

      3. fma-undefine 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-/l* 84.6%

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

      6. fma-define 84.6%

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

      7. fma-undefine 84.6%

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

      8. *-commutative 84.6%

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

      9. fma-undefine 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in z around inf 67.8%

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

   if -3.70000000000000023e102 < z < 6.9999999999999998e84

   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. Taylor expanded in y around 0 45.0%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+102} \lor \neg \left(z \leq 7 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 7: 38.6% 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. 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. Taylor expanded in y around 0 36.2%

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))