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

Percentage Accurate: 99.9% → 99.9%

Time: 4.8s

Alternatives: 6

Speedup: 1.0×

• 28.9% 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

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

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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+67} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+137}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (or (<= t_1 -1e+67) (not (<= t_1 5e+137)))
     (* (fma y x z) y)
     (fma z y t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if ((t_1 <= -1e+67) || !(t_1 <= 5e+137)) {
		tmp = fma(y, x, z) * y;
	} else {
		tmp = fma(z, y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if ((t_1 <= -1e+67) || !(t_1 <= 5e+137))
		tmp = Float64(fma(y, x, z) * y);
	else
		tmp = fma(z, y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+67], N[Not[LessEqual[t$95$1, 5e+137]], $MachinePrecision]], N[(N[(y * x + z), $MachinePrecision] * y), $MachinePrecision], N[(z * y + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -9.99999999999999983e66 or 5.0000000000000002e137 < (*.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. remove-double-neg N/A

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

      2. mul-1-neg N/A

         \[\leadsto {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{-1 \cdot \left(x + \frac{z}{y}\right)}\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)}\right)\right) \]

      4. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)} \]

      5. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - {y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)} \]

      6. unsub-neg N/A

         \[\leadsto \color{blue}{0 + \left(\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right)} \]

      7. mul0-rgt N/A

         \[\leadsto \color{blue}{y \cdot 0} + \left(\mathsf{neg}\left({y}^{2} \cdot \left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right) \]

      8. distribute-rgt-neg-out N/A

         \[\leadsto y \cdot 0 + \color{blue}{{y}^{2} \cdot \left(\mathsf{neg}\left(\left(-1 \cdot x + -1 \cdot \frac{z}{y}\right)\right)\right)} \]

      9. distribute-lft-out N/A

         \[\leadsto y \cdot 0 + {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{-1 \cdot \left(x + \frac{z}{y}\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto y \cdot 0 + {y}^{2} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\left(x + \frac{z}{y}\right)\right)\right)}\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto y \cdot 0 + {y}^{2} \cdot \color{blue}{\left(x + \frac{z}{y}\right)} \]

      12. unpow2 N/A

          \[\leadsto y \cdot 0 + \color{blue}{\left(y \cdot y\right)} \cdot \left(x + \frac{z}{y}\right) \]

      13. associate-*l* N/A

          \[\leadsto y \cdot 0 + \color{blue}{y \cdot \left(y \cdot \left(x + \frac{z}{y}\right)\right)} \]

      14. distribute-lft-in N/A

          \[\leadsto \color{blue}{y \cdot \left(0 + y \cdot \left(x + \frac{z}{y}\right)\right)} \]

      15. +-lft-identity N/A

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

      16. distribute-rgt-in N/A

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

      17. cancel-sign-sub N/A

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

      18. mul-1-neg N/A

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

   5. Applied rewrites 93.7%

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

   if -9.99999999999999983e66 < (*.f64 (+.f64 (*.f64 x y) z) y) < 5.0000000000000002e137

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 92.4

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

   5. Applied rewrites 92.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z\right) \cdot y \leq -1 \cdot 10^{+67} \lor \neg \left(\left(x \cdot y + z\right) \cdot y \leq 5 \cdot 10^{+137}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+259} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+178}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (or (<= t_1 -2e+259) (not (<= t_1 5e+178))) (* (* x y) y) (fma z y t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if ((t_1 <= -2e+259) || !(t_1 <= 5e+178)) {
		tmp = (x * y) * y;
	} else {
		tmp = fma(z, y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if ((t_1 <= -2e+259) || !(t_1 <= 5e+178))
		tmp = Float64(Float64(x * y) * y);
	else
		tmp = fma(z, y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+259], N[Not[LessEqual[t$95$1, 5e+178]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision], N[(z * y + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -2e259 or 4.9999999999999999e178 < (*.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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 77.0

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

   5. Applied rewrites 77.0%

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

   7. Applied rewrites 77.7%

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

   if -2e259 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.9999999999999999e178

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 85.6

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

   5. Applied rewrites 85.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z\right) \cdot y \leq -2 \cdot 10^{+259} \lor \neg \left(\left(x \cdot y + z\right) \cdot y \leq 5 \cdot 10^{+178}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+259}:\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (<= t_1 -2e+259)
     (* (* x y) y)
     (if (<= t_1 5e+178) (fma z y t) (* (* y y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if (t_1 <= -2e+259) {
		tmp = (x * y) * y;
	} else if (t_1 <= 5e+178) {
		tmp = fma(z, y, t);
	} else {
		tmp = (y * y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if (t_1 <= -2e+259)
		tmp = Float64(Float64(x * y) * y);
	elseif (t_1 <= 5e+178)
		tmp = fma(z, y, t);
	else
		tmp = Float64(Float64(y * y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+259], N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 5e+178], N[(z * y + t), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -2e259

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 80.6%

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

   if -2e259 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.9999999999999999e178

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 85.6

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

   5. Applied rewrites 85.6%

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

   if 4.9999999999999999e178 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 74.6

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

   5. Applied rewrites 74.6%

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

Alternative 5: 65.8% 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 66.3

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

5. Applied rewrites 66.3%

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

Alternative 6: 29.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ z \cdot y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. unpow2 N/A

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

   4. lower-*.f64 40.6

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

5. Applied rewrites 40.6%

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

7. Applied rewrites 41.7%

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

8. Taylor expanded in t around -inf

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

   1. associate-*r* N/A

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

   2. lower-*.f64 N/A

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

   3. mul-1-neg N/A

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

   4. lower-neg.f64 N/A

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

   5. sub-neg N/A

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

   6. associate-/l* N/A

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

   7. associate-*r* N/A

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

   8. metadata-eval N/A

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

   9. lower-fma.f64 N/A

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

   10. mul-1-neg N/A

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

   11. lower-neg.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. +-commutative N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 84.5

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

10. Applied rewrites 84.5%

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

11. Taylor expanded in z around inf

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

13. Applied rewrites 30.7%

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

14. Final simplification 30.7%

    \[\leadsto z \cdot y \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))