Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Percentage Accurate: 99.9% → 99.9%

Time: 3.5s

Alternatives: 10

Speedup: 1.1×

• 26.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 5, \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma y 5.0 (* (+ (+ (fma 2.0 z y) y) t) x)))

C

double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (((fma(2.0, z, y) + y) + t) * x));
}

Julia

function code(x, y, z, t)
	return fma(y, 5.0, Float64(Float64(Float64(fma(2.0, z, y) + y) + t) * x))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(N[(N[(N[(2.0 * z + y), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + \color{blue}{y \cdot 5} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

   4. lift-+.f64 N/A

      \[\leadsto x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

   5. lift-+.f64 N/A

      \[\leadsto x \cdot \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) + y \cdot 5 \]

   6. lift-+.f64 N/A

      \[\leadsto x \cdot \left(\left(\left(\color{blue}{\left(y + z\right)} + z\right) + y\right) + t\right) + y \cdot 5 \]

   7. lift-+.f64 N/A

      \[\leadsto x \cdot \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) + y \cdot 5 \]

   8. +-commutative N/A

      \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

   9. lower-fma.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) \cdot x\right)} \]
4. Add Preprocessing

Alternative 2: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, \mathsf{fma}\left(2, z, t\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (fma 2.0 x 5.0) y (* (fma 2.0 z t) x)))

C

double code(double x, double y, double z, double t) {
	return fma(fma(2.0, x, 5.0), y, (fma(2.0, z, t) * x));
}

Julia

function code(x, y, z, t)
	return fma(fma(2.0, x, 5.0), y, Float64(fma(2.0, z, t) * x))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(2.0 * x + 5.0), $MachinePrecision] * y + N[(N[(2.0 * z + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + 2 \cdot x\right)} \]
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto y \cdot \left(5 + 2 \cdot x\right) + \color{blue}{x \cdot \left(t + 2 \cdot z\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(5 + 2 \cdot x\right) \cdot y + \color{blue}{x} \cdot \left(t + 2 \cdot z\right) \]

   3. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(5 + 2 \cdot x, \color{blue}{y}, x \cdot \left(t + 2 \cdot z\right)\right) \]

   4. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot x + 5, y, x \cdot \left(t + 2 \cdot z\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, x \cdot \left(t + 2 \cdot z\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, \left(t + 2 \cdot z\right) \cdot x\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, \left(t + 2 \cdot z\right) \cdot x\right) \]

   8. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, \left(2 \cdot z + t\right) \cdot x\right) \]

   9. lower-fma.f64 98.5

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, \mathsf{fma}\left(2, z, t\right) \cdot x\right) \]

4. Applied rewrites 98.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, x, 5\right), y, \mathsf{fma}\left(2, z, t\right) \cdot x\right)} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.0061:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(z + z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 (+ z y) t) x)))
   (if (<= x -1.95e-27) t_1 (if (<= x 0.0061) (fma y 5.0 (* (+ z z) x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, (z + y), t) * x;
	double tmp;
	if (x <= -1.95e-27) {
		tmp = t_1;
	} else if (x <= 0.0061) {
		tmp = fma(y, 5.0, ((z + z) * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, Float64(z + y), t) * x)
	tmp = 0.0
	if (x <= -1.95e-27)
		tmp = t_1;
	elseif (x <= 0.0061)
		tmp = fma(y, 5.0, Float64(Float64(z + z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.95e-27], t$95$1, If[LessEqual[x, 0.0061], N[(y * 5.0 + N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.94999999999999986e-27 or 0.00610000000000000039 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

         \[\leadsto \left(\left(2 \cdot y + 2 \cdot z\right) + t\right) \cdot x \]

      4. distribute-lft-out N/A

         \[\leadsto \left(2 \cdot \left(y + z\right) + t\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, y + z, t\right) \cdot x \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, z + y, t\right) \cdot x \]

      7. lower-+.f64 97.7

         \[\leadsto \mathsf{fma}\left(2, z + y, t\right) \cdot x \]

   4. Applied rewrites 97.7%

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

   if -1.94999999999999986e-27 < x < 0.00610000000000000039

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + \color{blue}{y \cdot 5} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      5. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) + y \cdot 5 \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\left(\left(\color{blue}{\left(y + z\right)} + z\right) + y\right) + t\right) + y \cdot 5 \]

      7. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) + y \cdot 5 \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) \cdot x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot z\right)} \cdot x\right) \]
   5. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(2 \cdot z\right) \cdot x\right) \]

      2. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(2 \cdot z\right) \cdot x\right) \]

      3. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(2 \cdot z\right) \cdot x\right) \]

      4. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(z + \color{blue}{z}\right) \cdot x\right) \]

      5. lower-+.f64 79.5

         \[\leadsto \mathsf{fma}\left(y, 5, \left(z + \color{blue}{z}\right) \cdot x\right) \]

   6. Applied rewrites 79.5%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z + z\right)} \cdot x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{if}\;x \leq -2.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 (+ z y) t) x)))
   (if (<= x -2.8) t_1 (if (<= x 2.8e-11) (fma y 5.0 (* t x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, (z + y), t) * x;
	double tmp;
	if (x <= -2.8) {
		tmp = t_1;
	} else if (x <= 2.8e-11) {
		tmp = fma(y, 5.0, (t * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, Float64(z + y), t) * x)
	tmp = 0.0
	if (x <= -2.8)
		tmp = t_1;
	elseif (x <= 2.8e-11)
		tmp = fma(y, 5.0, Float64(t * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.8], t$95$1, If[LessEqual[x, 2.8e-11], N[(y * 5.0 + N[(t * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999998 or 2.8e-11 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

         \[\leadsto \left(\left(2 \cdot y + 2 \cdot z\right) + t\right) \cdot x \]

      4. distribute-lft-out N/A

         \[\leadsto \left(2 \cdot \left(y + z\right) + t\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, y + z, t\right) \cdot x \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, z + y, t\right) \cdot x \]

      7. lower-+.f64 98.6

         \[\leadsto \mathsf{fma}\left(2, z + y, t\right) \cdot x \]

   4. Applied rewrites 98.6%

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

   if -2.7999999999999998 < x < 2.8e-11

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + \color{blue}{y \cdot 5} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      5. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) + y \cdot 5 \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\left(\left(\color{blue}{\left(y + z\right)} + z\right) + y\right) + t\right) + y \cdot 5 \]

      7. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) + y \cdot 5 \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) \cdot x\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{t} \cdot x\right) \]
   5. Step-by-step derivation

      1. associate-+l+ 78.5

         \[\leadsto \mathsf{fma}\left(y, 5, t \cdot x\right) \]

      2. count-2-rev 78.5

         \[\leadsto \mathsf{fma}\left(y, 5, t \cdot x\right) \]

      3. distribute-lft-in 78.5

         \[\leadsto \mathsf{fma}\left(y, 5, t \cdot x\right) \]

   6. Applied rewrites 78.5%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{t} \cdot x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 79.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(2, z, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 x 5.0) y)))
   (if (<= y -2.05e+29) t_1 (if (<= y 2.7e+51) (* (fma 2.0 z t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, x, 5.0) * y;
	double tmp;
	if (y <= -2.05e+29) {
		tmp = t_1;
	} else if (y <= 2.7e+51) {
		tmp = fma(2.0, z, t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, x, 5.0) * y)
	tmp = 0.0
	if (y <= -2.05e+29)
		tmp = t_1;
	elseif (y <= 2.7e+51)
		tmp = Float64(fma(2.0, z, t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.05e+29], t$95$1, If[LessEqual[y, 2.7e+51], N[(N[(2.0 * z + t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0500000000000002e29 or 2.69999999999999992e51 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      3. +-commutative N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      4. lower-fma.f64 79.8

         \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot y \]

   4. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right) \cdot y} \]

   if -2.0500000000000002e29 < y < 2.69999999999999992e51

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(t + 2 \cdot z\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(t + 2 \cdot z\right) \cdot \color{blue}{x} \]

      3. +-commutative N/A

         \[\leadsto \left(2 \cdot z + t\right) \cdot x \]

      4. lower-fma.f64 78.4

         \[\leadsto \mathsf{fma}\left(2, z, t\right) \cdot x \]

   4. Applied rewrites 78.4%

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

Alternative 6: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{if}\;y \leq -5 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-233}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;y \leq 0.0015:\\ \;\;\;\;\left(x + x\right) \cdot z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 x 5.0) y)))
   (if (<= y -5e-23)
     t_1
     (if (<= y -7.7e-233)
       (* t x)
       (if (<= y 0.0015) (* (+ x x) z) (if (<= y 9.2e+29) (* t x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, x, 5.0) * y;
	double tmp;
	if (y <= -5e-23) {
		tmp = t_1;
	} else if (y <= -7.7e-233) {
		tmp = t * x;
	} else if (y <= 0.0015) {
		tmp = (x + x) * z;
	} else if (y <= 9.2e+29) {
		tmp = t * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, x, 5.0) * y)
	tmp = 0.0
	if (y <= -5e-23)
		tmp = t_1;
	elseif (y <= -7.7e-233)
		tmp = Float64(t * x);
	elseif (y <= 0.0015)
		tmp = Float64(Float64(x + x) * z);
	elseif (y <= 9.2e+29)
		tmp = Float64(t * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5e-23], t$95$1, If[LessEqual[y, -7.7e-233], N[(t * x), $MachinePrecision], If[LessEqual[y, 0.0015], N[(N[(x + x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 9.2e+29], N[(t * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e-23 or 9.2000000000000004e29 < y

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      3. +-commutative N/A

         \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      4. lower-fma.f64 76.0

         \[\leadsto \mathsf{fma}\left(2, x, 5\right) \cdot y \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right) \cdot y} \]

   if -5.0000000000000002e-23 < y < -7.70000000000000007e-233 or 0.0015 < y < 9.2000000000000004e29

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} \]
   3. Step-by-step derivation

      1. lower-*.f64 40.0

         \[\leadsto t \cdot \color{blue}{x} \]

   4. Applied rewrites 40.0%

      \[\leadsto \color{blue}{t \cdot x} \]

   if -7.70000000000000007e-233 < y < 0.0015

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{z} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 45.4

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

   4. Applied rewrites 45.4%

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

Alternative 7: 48.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + x\right) \cdot z\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-299}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ x x) z)))
   (if (<= z -7.6e+31)
     t_1
     (if (<= z -3e-299) (* t x) (if (<= z 8.5e-17) (* 5.0 y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + x) * z;
	double tmp;
	if (z <= -7.6e+31) {
		tmp = t_1;
	} else if (z <= -3e-299) {
		tmp = t * x;
	} else if (z <= 8.5e-17) {
		tmp = 5.0 * y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x + x) * z
    if (z <= (-7.6d+31)) then
        tmp = t_1
    else if (z <= (-3d-299)) then
        tmp = t * x
    else if (z <= 8.5d-17) then
        tmp = 5.0d0 * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + x) * z;
	double tmp;
	if (z <= -7.6e+31) {
		tmp = t_1;
	} else if (z <= -3e-299) {
		tmp = t * x;
	} else if (z <= 8.5e-17) {
		tmp = 5.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + x) * z
	tmp = 0
	if z <= -7.6e+31:
		tmp = t_1
	elif z <= -3e-299:
		tmp = t * x
	elif z <= 8.5e-17:
		tmp = 5.0 * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + x) * z)
	tmp = 0.0
	if (z <= -7.6e+31)
		tmp = t_1;
	elseif (z <= -3e-299)
		tmp = Float64(t * x);
	elseif (z <= 8.5e-17)
		tmp = Float64(5.0 * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + x) * z;
	tmp = 0.0;
	if (z <= -7.6e+31)
		tmp = t_1;
	elseif (z <= -3e-299)
		tmp = t * x;
	elseif (z <= 8.5e-17)
		tmp = 5.0 * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7.6e+31], t$95$1, If[LessEqual[z, -3e-299], N[(t * x), $MachinePrecision], If[LessEqual[z, 8.5e-17], N[(5.0 * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6000000000000003e31 or 8.5e-17 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot x\right) \cdot \color{blue}{z} \]

      3. count-2-rev N/A

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

      4. lower-+.f64 53.2

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

   4. Applied rewrites 53.2%

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

   if -7.6000000000000003e31 < z < -2.99999999999999984e-299

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} \]
   3. Step-by-step derivation

      1. lower-*.f64 36.7

         \[\leadsto t \cdot \color{blue}{x} \]

   4. Applied rewrites 36.7%

      \[\leadsto \color{blue}{t \cdot x} \]

   if -2.99999999999999984e-299 < z < 8.5e-17

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 36.0

         \[\leadsto 5 \cdot \color{blue}{y} \]

   4. Applied rewrites 36.0%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + x\right) \cdot y\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 1500:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+255}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ x x) y)))
   (if (<= x -7.8e+208)
     t_1
     (if (<= x -1.95e-27)
       (* t x)
       (if (<= x 1500.0) (* 5.0 y) (if (<= x 2.65e+255) t_1 (* t x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + x) * y;
	double tmp;
	if (x <= -7.8e+208) {
		tmp = t_1;
	} else if (x <= -1.95e-27) {
		tmp = t * x;
	} else if (x <= 1500.0) {
		tmp = 5.0 * y;
	} else if (x <= 2.65e+255) {
		tmp = t_1;
	} else {
		tmp = t * x;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x + x) * y
    if (x <= (-7.8d+208)) then
        tmp = t_1
    else if (x <= (-1.95d-27)) then
        tmp = t * x
    else if (x <= 1500.0d0) then
        tmp = 5.0d0 * y
    else if (x <= 2.65d+255) then
        tmp = t_1
    else
        tmp = t * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + x) * y;
	double tmp;
	if (x <= -7.8e+208) {
		tmp = t_1;
	} else if (x <= -1.95e-27) {
		tmp = t * x;
	} else if (x <= 1500.0) {
		tmp = 5.0 * y;
	} else if (x <= 2.65e+255) {
		tmp = t_1;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + x) * y
	tmp = 0
	if x <= -7.8e+208:
		tmp = t_1
	elif x <= -1.95e-27:
		tmp = t * x
	elif x <= 1500.0:
		tmp = 5.0 * y
	elif x <= 2.65e+255:
		tmp = t_1
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + x) * y)
	tmp = 0.0
	if (x <= -7.8e+208)
		tmp = t_1;
	elseif (x <= -1.95e-27)
		tmp = Float64(t * x);
	elseif (x <= 1500.0)
		tmp = Float64(5.0 * y);
	elseif (x <= 2.65e+255)
		tmp = t_1;
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + x) * y;
	tmp = 0.0;
	if (x <= -7.8e+208)
		tmp = t_1;
	elseif (x <= -1.95e-27)
		tmp = t * x;
	elseif (x <= 1500.0)
		tmp = 5.0 * y;
	elseif (x <= 2.65e+255)
		tmp = t_1;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -7.8e+208], t$95$1, If[LessEqual[x, -1.95e-27], N[(t * x), $MachinePrecision], If[LessEqual[x, 1500.0], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 2.65e+255], t$95$1, N[(t * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8000000000000001e208 or 1500 < x < 2.6499999999999999e255

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + \color{blue}{y \cdot 5} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} + y \cdot 5 \]

      5. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) + y \cdot 5 \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\left(\left(\color{blue}{\left(y + z\right)} + z\right) + y\right) + t\right) + y \cdot 5 \]

      7. lift-+.f64 N/A

         \[\leadsto x \cdot \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) + y \cdot 5 \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) \cdot x\right)} \]

   4. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \left(5 + 2 \cdot x\right) \]

      2. associate-+l+ N/A

         \[\leadsto y \cdot \left(5 + 2 \cdot x\right) \]

      3. +-commutative N/A

         \[\leadsto y \cdot \left(5 + 2 \cdot x\right) \]

      4. count-2-rev N/A

         \[\leadsto y \cdot \left(5 + 2 \cdot x\right) \]

      5. associate-+l+ N/A

         \[\leadsto y \cdot \left(5 + 2 \cdot x\right) \]

      6. associate-+l+ N/A

         \[\leadsto y \cdot \left(5 + 2 \cdot x\right) \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{y} \cdot \left(5 + 2 \cdot x\right) \]

      8. *-commutative N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      9. lower-*.f64 N/A

         \[\leadsto \left(5 + 2 \cdot x\right) \cdot \color{blue}{y} \]

      10. +-commutative N/A

          \[\leadsto \left(2 \cdot x + 5\right) \cdot y \]

      11. *-commutative N/A

          \[\leadsto \left(x \cdot 2 + 5\right) \cdot y \]

      12. lower-fma.f64 40.0

          \[\leadsto \mathsf{fma}\left(x, 2, 5\right) \cdot y \]

   6. Applied rewrites 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, 5\right) \cdot y} \]

   7. Taylor expanded in x around inf

      \[\leadsto \left(2 \cdot x\right) \cdot y \]
   8. Step-by-step derivation

      1. count-2-rev N/A

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

      2. lift-+.f64 39.5

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

   9. Applied rewrites 39.5%

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

   if -7.8000000000000001e208 < x < -1.94999999999999986e-27 or 2.6499999999999999e255 < x

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} \]
   3. Step-by-step derivation

      1. lower-*.f64 37.2

         \[\leadsto t \cdot \color{blue}{x} \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{t \cdot x} \]

   if -1.94999999999999986e-27 < x < 1500

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 58.9

         \[\leadsto 5 \cdot \color{blue}{y} \]

   4. Applied rewrites 58.9%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 44.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 0.0061:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.95e-27) (* t x) (if (<= x 0.0061) (* 5.0 y) (* t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.95e-27) {
		tmp = t * x;
	} else if (x <= 0.0061) {
		tmp = 5.0 * y;
	} else {
		tmp = t * x;
	}
	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 (x <= (-1.95d-27)) then
        tmp = t * x
    else if (x <= 0.0061d0) then
        tmp = 5.0d0 * y
    else
        tmp = t * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.95e-27) {
		tmp = t * x;
	} else if (x <= 0.0061) {
		tmp = 5.0 * y;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.95e-27:
		tmp = t * x
	elif x <= 0.0061:
		tmp = 5.0 * y
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.95e-27)
		tmp = Float64(t * x);
	elseif (x <= 0.0061)
		tmp = Float64(5.0 * y);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.95e-27)
		tmp = t * x;
	elseif (x <= 0.0061)
		tmp = 5.0 * y;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.95e-27], N[(t * x), $MachinePrecision], If[LessEqual[x, 0.0061], N[(5.0 * y), $MachinePrecision], N[(t * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.94999999999999986e-27 or 0.00610000000000000039 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} \]
   3. Step-by-step derivation

      1. lower-*.f64 37.3

         \[\leadsto t \cdot \color{blue}{x} \]

   4. Applied rewrites 37.3%

      \[\leadsto \color{blue}{t \cdot x} \]

   if -1.94999999999999986e-27 < x < 0.00610000000000000039

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 59.4

         \[\leadsto 5 \cdot \color{blue}{y} \]

   4. Applied rewrites 59.4%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 30.0% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ 5 \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 5.0 y))

C

double code(double x, double y, double z, double t) {
	return 5.0 * y;
}

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 = 5.0d0 * y
end function

Java

public static double code(double x, double y, double z, double t) {
	return 5.0 * y;
}

Python

def code(x, y, z, t):
	return 5.0 * y

Julia

function code(x, y, z, t)
	return Float64(5.0 * y)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 5.0 * y;
end

Wolfram

code[x_, y_, z_, t_] := N[(5.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{5 \cdot y} \]
3. Step-by-step derivation

   1. lower-*.f64 30.0

      \[\leadsto 5 \cdot \color{blue}{y} \]

4. Applied rewrites 30.0%

   \[\leadsto \color{blue}{5 \cdot y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))