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

Percentage Accurate: 99.9% → 99.9%

Time: 2.4s

Alternatives: 8

Speedup: 1.3×

• 28.8% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * x + z), $MachinePrecision] * y + 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. lift-*.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lower-fma.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ t_2 := \mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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+227) t_2 (if (<= t_1 5e+158) (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+227) {
		tmp = t_2;
	} else if (t_1 <= 5e+158) {
		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+227)
		tmp = t_2;
	elseif (t_1 <= 5e+158)
		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+227], t$95$2, If[LessEqual[t$95$1, 5e+158], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -4.9999999999999996e227 or 4.9999999999999996e158 < (*.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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 96.5

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

   5. Applied rewrites 96.5%

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

   if -4.9999999999999996e227 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.9999999999999996e158

   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

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

      2. *-commutative N/A

         \[\leadsto z \cdot y + t \]

      3. lower-fma.f64 84.6

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

   5. Applied rewrites 84.6%

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

Alternative 3: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{if}\;y \leq -4.85 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-52}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot y, x, t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma y x z) y)))
   (if (<= y -4.85e+58)
     t_1
     (if (<= y -1.4e-52)
       (fma (* y y) x t)
       (if (<= y 8.5e-43) (fma z y t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, x, z) * y;
	double tmp;
	if (y <= -4.85e+58) {
		tmp = t_1;
	} else if (y <= -1.4e-52) {
		tmp = fma((y * y), x, t);
	} else if (y <= 8.5e-43) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(y, x, z) * y)
	tmp = 0.0
	if (y <= -4.85e+58)
		tmp = t_1;
	elseif (y <= -1.4e-52)
		tmp = fma(Float64(y * y), x, t);
	elseif (y <= 8.5e-43)
		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 + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.85e+58], t$95$1, If[LessEqual[y, -1.4e-52], N[(N[(y * y), $MachinePrecision] * x + t), $MachinePrecision], If[LessEqual[y, 8.5e-43], N[(z * y + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8499999999999998e58 or 8.50000000000000056e-43 < y

   1. Initial program 99.9%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 88.7

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

   5. Applied rewrites 88.7%

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

   if -4.8499999999999998e58 < y < -1.39999999999999997e-52

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 66.9

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

   5. Applied rewrites 66.9%

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

   if -1.39999999999999997e-52 < y < 8.50000000000000056e-43

   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

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

      2. *-commutative N/A

         \[\leadsto z \cdot y + t \]

      3. lower-fma.f64 92.7

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

   5. Applied rewrites 92.7%

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

Alternative 4: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e+25)
   (* (* x y) y)
   (if (<= y 3.8e+137) (fma z y t) (* (* y y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e+25) {
		tmp = (x * y) * y;
	} else if (y <= 3.8e+137) {
		tmp = fma(z, y, t);
	} else {
		tmp = (y * y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e+25)
		tmp = Float64(Float64(x * y) * y);
	elseif (y <= 3.8e+137)
		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, -6.2e+25], N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 3.8e+137], N[(z * y + t), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999996e25

   1. Initial program 99.9%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 91.3

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 69.7

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

   8. Applied rewrites 69.7%

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

   if -6.1999999999999996e25 < y < 3.79999999999999963e137

   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

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

      2. *-commutative N/A

         \[\leadsto z \cdot y + t \]

      3. lower-fma.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if 3.79999999999999963e137 < 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

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

Alternative 5: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot y\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* x y) y)))
   (if (<= y -6.2e+25) t_1 (if (<= y 3.8e+137) (fma z y t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * y) * y;
	double tmp;
	if (y <= -6.2e+25) {
		tmp = t_1;
	} else if (y <= 3.8e+137) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * y) * y)
	tmp = 0.0
	if (y <= -6.2e+25)
		tmp = t_1;
	elseif (y <= 3.8e+137)
		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[(x * y), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6.2e+25], t$95$1, If[LessEqual[y, 3.8e+137], N[(z * y + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999996e25 or 3.79999999999999963e137 < y

   1. Initial program 99.9%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 93.0

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

   5. Applied rewrites 93.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 73.8

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

   8. Applied rewrites 73.8%

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

   if -6.1999999999999996e25 < y < 3.79999999999999963e137

   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

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

      2. *-commutative N/A

         \[\leadsto z \cdot y + t \]

      3. lower-fma.f64 82.1

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

   5. Applied rewrites 82.1%

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

Alternative 6: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+75) (* z y) (if (<= z 8.5e+69) t (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+75) {
		tmp = z * y;
	} else if (z <= 8.5e+69) {
		tmp = t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-5.8d+75)) then
        tmp = z * y
    else if (z <= 8.5d+69) then
        tmp = 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 tmp;
	if (z <= -5.8e+75) {
		tmp = z * y;
	} else if (z <= 8.5e+69) {
		tmp = t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+75:
		tmp = z * y
	elif z <= 8.5e+69:
		tmp = t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+75)
		tmp = Float64(z * y);
	elseif (z <= 8.5e+69)
		tmp = t;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e+75)
		tmp = z * y;
	elseif (z <= 8.5e+69)
		tmp = t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e+75], N[(z * y), $MachinePrecision], If[LessEqual[z, 8.5e+69], t, N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999997e75 or 8.5000000000000002e69 < z

   1. Initial program 100.0%

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

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

      2. lower-*.f64 59.3

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

   5. Applied rewrites 59.3%

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

   if -5.7999999999999997e75 < z < 8.5000000000000002e69

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 47.3%

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

Alternative 7: 65.9% 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

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

   2. *-commutative N/A

      \[\leadsto z \cdot y + t \]

   3. lower-fma.f64 65.9

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

5. Applied rewrites 65.9%

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

Alternative 8: 38.8% accurate, 17.0× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

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

5. Applied rewrites 38.8%

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

Reproduce

herbie shell --seed 2025089 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))