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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 7

Speedup: 1.0×

• 28.6% 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: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + y \cdot x\right) \cdot y\\ t_2 := \mathsf{fma}\left(x, y, z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ z (* y x)) y)) (t_2 (* (fma x y z) y)))
   (if (<= t_1 -1e+108) t_2 (if (<= t_1 2e+61) (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(x, y, z) * y;
	double tmp;
	if (t_1 <= -1e+108) {
		tmp = t_2;
	} else if (t_1 <= 2e+61) {
		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(x, y, z) * y)
	tmp = 0.0
	if (t_1 <= -1e+108)
		tmp = t_2;
	elseif (t_1 <= 2e+61)
		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[(x * y + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+108], t$95$2, If[LessEqual[t$95$1, 2e+61], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -1e108 or 1.9999999999999999e61 < (*.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 t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 95.3

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

   5. Applied rewrites 95.3%

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

   if -1e108 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1.9999999999999999e61

   1. Initial program 99.9%

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

   3. Taylor expanded in y 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 89.8

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

   5. Applied rewrites 89.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z + y \cdot x\right) \cdot y \leq -1 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right) \cdot y\\ \mathbf{elif}\;\left(z + y \cdot x\right) \cdot y \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + y \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+215}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+61}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ z (* y x)) y)))
   (if (<= t_1 -2e+215) (* z y) (if (<= t_1 2e+61) (* 1.0 t) (* z y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z + (y * x)) * y;
	double tmp;
	if (t_1 <= -2e+215) {
		tmp = z * y;
	} else if (t_1 <= 2e+61) {
		tmp = 1.0 * t;
	} else {
		tmp = z * y;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z + (y * x)) * y
    if (t_1 <= (-2d+215)) then
        tmp = z * y
    else if (t_1 <= 2d+61) then
        tmp = 1.0d0 * t
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z + (y * x)) * y;
	double tmp;
	if (t_1 <= -2e+215) {
		tmp = z * y;
	} else if (t_1 <= 2e+61) {
		tmp = 1.0 * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z + (y * x)) * y
	tmp = 0
	if t_1 <= -2e+215:
		tmp = z * y
	elif t_1 <= 2e+61:
		tmp = 1.0 * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z + Float64(y * x)) * y)
	tmp = 0.0
	if (t_1 <= -2e+215)
		tmp = Float64(z * y);
	elseif (t_1 <= 2e+61)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z + (y * x)) * y;
	tmp = 0.0;
	if (t_1 <= -2e+215)
		tmp = z * y;
	elseif (t_1 <= 2e+61)
		tmp = 1.0 * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+215], N[(z * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+61], N[(1.0 * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -1.99999999999999981e215 or 1.9999999999999999e61 < (*.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 z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 40.5

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

   5. Applied rewrites 40.5%

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

   if -1.99999999999999981e215 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1.9999999999999999e61

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 21.4

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

   5. Applied rewrites 21.4%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 87.0

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

   8. Applied rewrites 87.0%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 64.4%

       \[\leadsto 1 \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z + y \cdot x\right) \cdot y \leq -2 \cdot 10^{+215}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;\left(z + y \cdot x\right) \cdot y \leq 2 \cdot 10^{+61}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\left(y \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+49)
   (* (* y x) y)
   (if (<= y 2.55e+32) (fma z y t) (* (* y y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+49) {
		tmp = (y * x) * y;
	} else if (y <= 2.55e+32) {
		tmp = fma(z, y, t);
	} else {
		tmp = (y * y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+49)
		tmp = Float64(Float64(y * x) * y);
	elseif (y <= 2.55e+32)
		tmp = fma(z, y, t);
	else
		tmp = Float64(Float64(y * y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e+49], N[(N[(y * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 2.55e+32], N[(z * y + t), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999946e48

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot {y}^{2}} \]
   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 69.4

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

   5. Applied rewrites 69.4%

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

   7. Applied rewrites 77.1%

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

   if -9.99999999999999946e48 < y < 2.55000000000000002e32

   1. Initial program 99.9%

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

   3. Taylor expanded in y 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 84.5

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

   5. Applied rewrites 84.5%

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

   if 2.55000000000000002e32 < 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

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

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\left(y \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot x\right) \cdot y\\ \mathbf{if}\;y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y x) y)))
   (if (<= y -1e+49) t_1 (if (<= y 2.55e+32) (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 <= -1e+49) {
		tmp = t_1;
	} else if (y <= 2.55e+32) {
		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 <= -1e+49)
		tmp = t_1;
	elseif (y <= 2.55e+32)
		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, -1e+49], t$95$1, If[LessEqual[y, 2.55e+32], N[(z * y + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999946e48 or 2.55000000000000002e32 < 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

      \[\leadsto \color{blue}{x \cdot {y}^{2}} \]
   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 73.2

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

   5. Applied rewrites 73.2%

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

   7. Applied rewrites 75.4%

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

   if -9.99999999999999946e48 < y < 2.55000000000000002e32

   1. Initial program 99.9%

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

   3. Taylor expanded in y 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 84.5

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

   5. Applied rewrites 84.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\left(y \cdot x\right) \cdot y\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.1% 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 y 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 64.0

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

5. Applied rewrites 64.0%

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

Alternative 7: 30.2% 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 99.9%

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

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 30.4

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

5. Applied rewrites 30.4%

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

Reproduce

herbie shell --seed 2024248 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))