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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

Alternatives: 5

Speedup: 1.0×

• 30.3% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + y \cdot x\right) \cdot y\\ t_2 := \mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ z (* y x)) y)) (t_2 (* (fma y x z) y)))
   (if (<= t_1 -4e+137) t_2 (if (<= t_1 4e+172) (fma z y t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z + (y * x)) * y;
	double t_2 = fma(y, x, z) * y;
	double tmp;
	if (t_1 <= -4e+137) {
		tmp = t_2;
	} else if (t_1 <= 4e+172) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z + Float64(y * x)) * y)
	t_2 = Float64(fma(y, x, z) * y)
	tmp = 0.0
	if (t_1 <= -4e+137)
		tmp = t_2;
	elseif (t_1 <= 4e+172)
		tmp = fma(z, y, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+137], t$95$2, If[LessEqual[t$95$1, 4e+172], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -4.0000000000000001e137 or 4.0000000000000003e172 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. unpow2 N/A

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

      2. sqr-neg-rev N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. distribute-lft-out N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. distribute-lft-out-- N/A

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

      13. *-commutative N/A

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

      14. *-commutative N/A

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

      15. associate-*r/ N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-inverses N/A

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

      19. *-rgt-identity N/A

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

   5. Applied rewrites 97.0%

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

   if -4.0000000000000001e137 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.0000000000000003e172

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 91.6

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

   5. Applied rewrites 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z + y \cdot x\right) \cdot y \leq -4 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{elif}\;\left(z + y \cdot x\right) \cdot y \leq 4 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -2650000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y x) y)))
   (if (<= y -2650000000.0) t_1 (if (<= y 1.85e+53) (fma z y t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * x) * y;
	double tmp;
	if (y <= -2650000000.0) {
		tmp = t_1;
	} else if (y <= 1.85e+53) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * x) * y)
	tmp = 0.0
	if (y <= -2650000000.0)
		tmp = t_1;
	elseif (y <= 1.85e+53)
		tmp = fma(z, y, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2650000000.0], t$95$1, If[LessEqual[y, 1.85e+53], N[(z * y + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e9 or 1.85e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. unpow2 N/A

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

      2. sqr-neg-rev N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. distribute-lft-out N/A

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

      9. +-commutative N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. distribute-lft-out-- N/A

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

      13. *-commutative N/A

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

      14. *-commutative N/A

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

      15. associate-*r/ N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-inverses N/A

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

      19. *-rgt-identity N/A

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

   5. Applied rewrites 92.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.0%

      \[\leadsto \left(x \cdot y\right) \cdot y \]

   if -2.65e9 < y < 1.85e53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 92.7

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

   5. Applied rewrites 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2650000000:\\ \;\;\;\;\left(y \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 63.5

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

5. Applied rewrites 63.5%

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

Alternative 5: 38.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 t))

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * t
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * t;
}

Python

def code(x, y, z, t):
	return 1.0 * t

Julia

function code(x, y, z, t)
	return Float64(1.0 * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * t;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * t), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. flip3-+ N/A

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

   5. clear-num N/A

      \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}{{\left(x \cdot y\right)}^{3} + {z}^{3}}}} + t \]

   6. un-div-inv N/A

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

   7. lower-/.f64 N/A

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

   8. clear-num N/A

      \[\leadsto \frac{y}{\color{blue}{\frac{1}{\frac{{\left(x \cdot y\right)}^{3} + {z}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(z \cdot z - \left(x \cdot y\right) \cdot z\right)}}}} + t \]

   9. flip3-+ N/A

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

   10. lift-+.f64 N/A

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

   11. inv-pow N/A

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

   12. lower-pow.f64 99.8

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

   13. lift-+.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. lower-fma.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Taylor expanded in z around 0

   \[\leadsto \color{blue}{t + x \cdot {y}^{2}} \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{x \cdot {y}^{2} + t} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{{y}^{2} \cdot x} + t \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left({y}^{2}, x, t\right)} \]

   4. unpow2 N/A

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

   5. lower-*.f64 69.4

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

7. Applied rewrites 69.4%

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

8. Taylor expanded in t around inf

   \[\leadsto t \cdot \color{blue}{\left(1 + \frac{x \cdot {y}^{2}}{t}\right)} \]
9. Step-by-step derivation

10. Applied rewrites 66.5%

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

11. Taylor expanded in x around 0

    \[\leadsto 1 \cdot t \]
12. Step-by-step derivation

13. Applied rewrites 31.9%

    \[\leadsto 1 \cdot t \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024298 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))