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

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 6

Speedup: 1.1×

• 29.8% 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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x \cdot y + z\right) \cdot y + t \]
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. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ t_2 := \mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+69}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)) (t_2 (* (fma y x z) y)))
   (if (<= t_1 -5e+267) t_2 (if (<= t_1 1e+69) (fma z y t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double t_2 = fma(y, x, z) * y;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = t_2;
	} else if (t_1 <= 1e+69) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	t_2 = Float64(fma(y, x, z) * y)
	tmp = 0.0
	if (t_1 <= -5e+267)
		tmp = t_2;
	elseif (t_1 <= 1e+69)
		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[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+267], t$95$2, If[LessEqual[t$95$1, 1e+69], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -4.9999999999999999e267 or 1.0000000000000001e69 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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. associate-*l* N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

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

      9. *-rgt-identity N/A

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

      10. *-commutative N/A

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

      11. distribute-rgt-in N/A

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

      12. +-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if -4.9999999999999999e267 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1.0000000000000001e69

   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 92.0

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

   5. Applied rewrites 92.0%

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

Alternative 3: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(y \cdot y\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (<= t_1 (- INFINITY))
     (* (* y y) x)
     (if (<= t_1 5e+212) (fma z y t) (* (* x y) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y * y) * x;
	} else if (t_1 <= 5e+212) {
		tmp = fma(z, y, t);
	} else {
		tmp = (x * y) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * y) * x);
	elseif (t_1 <= 5e+212)
		tmp = fma(z, y, t);
	else
		tmp = Float64(Float64(x * y) * y);
	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, (-Infinity)], N[(N[(y * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+212], N[(z * y + t), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -inf.0

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 83.8

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

   5. Applied rewrites 83.8%

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

   if -inf.0 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.99999999999999992e212

   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 87.1

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

   5. Applied rewrites 87.1%

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

   if 4.99999999999999992e212 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 83.0

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

   5. Applied rewrites 83.0%

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

   7. Applied rewrites 84.7%

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

Alternative 4: 80.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ t_2 := \left(x \cdot y\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)) (t_2 (* (* x y) y)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 5e+212) (fma z y t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double t_2 = (x * y) * y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 5e+212) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	t_2 = Float64(Float64(x * y) * y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 5e+212)
		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[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 5e+212], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -inf.0 or 4.99999999999999992e212 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 83.3

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

   5. Applied rewrites 83.3%

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

   7. Applied rewrites 83.3%

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

   if -inf.0 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.99999999999999992e212

   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 87.1

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

   5. Applied rewrites 87.1%

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

Alternative 5: 65.6% 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 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 67.9

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

5. Applied rewrites 67.9%

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

Alternative 6: 29.2% 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 100.0%

   \[\left(x \cdot y + z\right) \cdot y + t \]
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. associate-*l* N/A

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

   3. distribute-rgt-in N/A

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

   4. distribute-rgt-in N/A

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

   5. *-commutative N/A

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

   6. associate-*l/ N/A

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

   7. associate-/l* N/A

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

   8. *-inverses N/A

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

   9. *-rgt-identity N/A

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

   10. *-commutative N/A

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

   11. distribute-rgt-in N/A

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

   12. +-commutative N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 N/A

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

   15. +-commutative N/A

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

   16. *-commutative N/A

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

   17. lower-fma.f64 58.5

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

5. Applied rewrites 58.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 27.4%

   \[\leadsto z \cdot \color{blue}{y} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024296 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))