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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

• 29.3% 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 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. Add Preprocessing

Alternative 2: 78.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+167} \lor \neg \left(y \leq -5.2 \cdot 10^{+138}\right) \land \left(y \leq -3.4 \cdot 10^{+93} \lor \neg \left(y \leq 2.4 \cdot 10^{+20}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e+167)
         (and (not (<= y -5.2e+138))
              (or (<= y -3.4e+93) (not (<= y 2.4e+20)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e+167) || (!(y <= -5.2e+138) && ((y <= -3.4e+93) || !(y <= 2.4e+20)))) {
		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 <= (-5d+167)) .or. (.not. (y <= (-5.2d+138))) .and. (y <= (-3.4d+93)) .or. (.not. (y <= 2.4d+20))) 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 <= -5e+167) || (!(y <= -5.2e+138) && ((y <= -3.4e+93) || !(y <= 2.4e+20)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e+167) or (not (y <= -5.2e+138) and ((y <= -3.4e+93) or not (y <= 2.4e+20))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e+167) || (!(y <= -5.2e+138) && ((y <= -3.4e+93) || !(y <= 2.4e+20))))
		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 <= -5e+167) || (~((y <= -5.2e+138)) && ((y <= -3.4e+93) || ~((y <= 2.4e+20)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e+167], And[N[Not[LessEqual[y, -5.2e+138]], $MachinePrecision], Or[LessEqual[y, -3.4e+93], N[Not[LessEqual[y, 2.4e+20]], $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 < -4.9999999999999997e167 or -5.2000000000000002e138 < y < -3.4e93 or 2.4e20 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around -inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. distribute-rgt-neg-in 90.5%

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

      3. fma-neg 90.5%

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

      4. +-commutative 90.5%

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

      5. fma-undefine 90.5%

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

      6. *-commutative 90.5%

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

      7. associate-/l* 90.5%

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

      8. fma-undefine 90.5%

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

      9. *-commutative 90.5%

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

      10. fma-undefine 90.5%

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

      11. metadata-eval 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in t around 0 96.0%

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

   7. Taylor expanded in z around 0 76.5%

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

      1. *-commutative 76.5%

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

   9. Simplified 76.5%

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

   if -4.9999999999999997e167 < y < -5.2000000000000002e138 or -3.4e93 < y < 2.4e20

   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 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+167} \lor \neg \left(y \leq -5.2 \cdot 10^{+138}\right) \land \left(y \leq -3.4 \cdot 10^{+93} \lor \neg \left(y \leq 2.4 \cdot 10^{+20}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+38} \lor \neg \left(y \leq 1.8 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+38) (not (<= y 1.8e-19)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+38) || !(y <= 1.8e-19)) {
		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 <= (-1.9d+38)) .or. (.not. (y <= 1.8d-19))) 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 <= -1.9e+38) || !(y <= 1.8e-19)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+38) or not (y <= 1.8e-19):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+38) || !(y <= 1.8e-19))
		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 <= -1.9e+38) || ~((y <= 1.8e-19)))
		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, -1.9e+38], N[Not[LessEqual[y, 1.8e-19]], $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 < -1.8999999999999999e38 or 1.8000000000000001e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around -inf 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-rgt-neg-in 90.3%

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

      3. fma-neg 90.3%

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

      4. +-commutative 90.3%

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

      5. fma-undefine 90.3%

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

      6. *-commutative 90.3%

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

      7. associate-/l* 88.8%

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

      8. fma-undefine 88.8%

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

      9. *-commutative 88.8%

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

      10. fma-undefine 88.8%

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

      11. metadata-eval 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in t around 0 92.0%

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

   if -1.8999999999999999e38 < y < 1.8000000000000001e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+38} \lor \neg \left(y \leq 1.8 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+23}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e+63)
   (* y (+ z (* x y)))
   (if (<= z 6e+23) (+ t (* y (* x y))) (+ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e+63) {
		tmp = y * (z + (x * y));
	} else if (z <= 6e+23) {
		tmp = t + (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 (z <= (-1.75d+63)) then
        tmp = y * (z + (x * y))
    else if (z <= 6d+23) then
        tmp = t + (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 (z <= -1.75e+63) {
		tmp = y * (z + (x * y));
	} else if (z <= 6e+23) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e+63:
		tmp = y * (z + (x * y))
	elif z <= 6e+23:
		tmp = t + (y * (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e+63)
		tmp = Float64(y * Float64(z + Float64(x * y)));
	elseif (z <= 6e+23)
		tmp = Float64(t + 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 (z <= -1.75e+63)
		tmp = y * (z + (x * y));
	elseif (z <= 6e+23)
		tmp = t + (y * (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e+63], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+23], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000015e63

   1. Initial program 100.0%

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

   3. Taylor expanded in t around -inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. distribute-rgt-neg-in 91.3%

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

      3. fma-neg 91.3%

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

      4. +-commutative 91.3%

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

      5. fma-undefine 91.3%

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

      6. *-commutative 91.3%

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

      7. associate-/l* 91.1%

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

      8. fma-undefine 91.1%

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

      9. *-commutative 91.1%

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

      10. fma-undefine 91.1%

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

      11. metadata-eval 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in t around 0 86.7%

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

   if -1.75000000000000015e63 < z < 6.0000000000000002e23

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

   if 6.0000000000000002e23 < 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 84.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+23}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+39} \lor \neg \left(y \leq 1.8 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.7e+39) (not (<= y 1.8e-19))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.7e+39) || !(y <= 1.8e-19)) {
		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 <= (-2.7d+39)) .or. (.not. (y <= 1.8d-19))) 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 <= -2.7e+39) || !(y <= 1.8e-19)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.7e+39) or not (y <= 1.8e-19):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.7e+39) || !(y <= 1.8e-19))
		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 <= -2.7e+39) || ~((y <= 1.8e-19)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.7e+39], N[Not[LessEqual[y, 1.8e-19]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000003e39 or 1.8000000000000001e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around -inf 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-rgt-neg-in 90.3%

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

      3. fma-neg 90.3%

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

      4. +-commutative 90.3%

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

      5. fma-undefine 90.3%

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

      6. *-commutative 90.3%

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

      7. associate-/l* 88.8%

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

      8. fma-undefine 88.8%

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

      9. *-commutative 88.8%

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

      10. fma-undefine 88.8%

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

      11. metadata-eval 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in t around 0 92.0%

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

   7. Taylor expanded in z around 0 66.4%

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

      1. *-commutative 66.4%

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

   9. Simplified 66.4%

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

   if -2.70000000000000003e39 < y < 1.8000000000000001e-19

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+39} \lor \neg \left(y \leq 1.8 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15000000 \lor \neg \left(z \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -15000000.0) (not (<= z 4e+18))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -15000000.0) || !(z <= 4e+18)) {
		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 <= (-15000000.0d0)) .or. (.not. (z <= 4d+18))) 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 <= -15000000.0) || !(z <= 4e+18)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -15000000.0) or not (z <= 4e+18):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -15000000.0) || !(z <= 4e+18))
		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 <= -15000000.0) || ~((z <= 4e+18)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -15000000.0], N[Not[LessEqual[z, 4e+18]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e7 or 4e18 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around -inf 94.0%

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

      1. mul-1-neg 94.0%

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

      2. distribute-rgt-neg-in 94.0%

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

      3. fma-neg 94.0%

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

      4. +-commutative 94.0%

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

      5. fma-undefine 94.0%

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

      6. *-commutative 94.0%

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

      7. associate-/l* 93.8%

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

      8. fma-undefine 93.8%

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

      9. *-commutative 93.8%

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

      10. fma-undefine 93.8%

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

      11. metadata-eval 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in z around inf 62.5%

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

   if -1.5e7 < z < 4e18

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 52.1%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15000000 \lor \neg \left(z \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. 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: 38.3% 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 37.9%

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

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))