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

Percentage Accurate: 99.9% → 100.0%

Time: 6.3s

Alternatives: 14

Speedup: 1.2×

• 26.6% 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: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(N[(2.0 * N[(z + 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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 100.0

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 100.0

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

   8. lift-+.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift-+.f64 N/A

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

   11. associate-+l+ N/A

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

   12. +-commutative N/A

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

   13. lift-+.f64 N/A

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

   14. count-2 N/A

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

   15. lower-fma.f64 100.0

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

   16. lift-+.f64 N/A

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

   17. +-commutative N/A

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

   18. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 47.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+151}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{+18}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e+151)
   (* t x)
   (if (<= x -1.82e+18)
     (* (* x y) 2.0)
     (if (<= x 3.6e-19)
       (* 5.0 y)
       (if (<= x 1.9e+75) (* (* z x) 2.0) (* t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e+151) {
		tmp = t * x;
	} else if (x <= -1.82e+18) {
		tmp = (x * y) * 2.0;
	} else if (x <= 3.6e-19) {
		tmp = 5.0 * y;
	} else if (x <= 1.9e+75) {
		tmp = (z * x) * 2.0;
	} 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 <= (-3.6d+151)) then
        tmp = t * x
    else if (x <= (-1.82d+18)) then
        tmp = (x * y) * 2.0d0
    else if (x <= 3.6d-19) then
        tmp = 5.0d0 * y
    else if (x <= 1.9d+75) then
        tmp = (z * x) * 2.0d0
    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 <= -3.6e+151) {
		tmp = t * x;
	} else if (x <= -1.82e+18) {
		tmp = (x * y) * 2.0;
	} else if (x <= 3.6e-19) {
		tmp = 5.0 * y;
	} else if (x <= 1.9e+75) {
		tmp = (z * x) * 2.0;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e+151:
		tmp = t * x
	elif x <= -1.82e+18:
		tmp = (x * y) * 2.0
	elif x <= 3.6e-19:
		tmp = 5.0 * y
	elif x <= 1.9e+75:
		tmp = (z * x) * 2.0
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e+151)
		tmp = Float64(t * x);
	elseif (x <= -1.82e+18)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (x <= 3.6e-19)
		tmp = Float64(5.0 * y);
	elseif (x <= 1.9e+75)
		tmp = Float64(Float64(z * x) * 2.0);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.6e+151)
		tmp = t * x;
	elseif (x <= -1.82e+18)
		tmp = (x * y) * 2.0;
	elseif (x <= 3.6e-19)
		tmp = 5.0 * y;
	elseif (x <= 1.9e+75)
		tmp = (z * x) * 2.0;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e+151], N[(t * x), $MachinePrecision], If[LessEqual[x, -1.82e+18], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, 3.6e-19], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 1.9e+75], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], N[(t * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.6e151 or 1.9000000000000001e75 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 54.0

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

   5. Applied rewrites 54.0%

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

   if -3.6e151 < x < -1.82e18

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+l+ N/A

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

      12. +-commutative N/A

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

      13. lift-+.f64 N/A

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

      14. count-2 N/A

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

      15. lower-fma.f64 100.0

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

      16. lift-+.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 57.9

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

   7. Applied rewrites 57.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 57.9%

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

   if -1.82e18 < x < 3.6000000000000001e-19

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 64.4

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

   5. Applied rewrites 64.4%

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

   if 3.6000000000000001e-19 < x < 1.9000000000000001e75

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 58.0

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

   5. Applied rewrites 58.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+151}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{+18}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+18} \lor \neg \left(x \leq 0.022\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.82e+18) (not (<= x 0.022)))
   (* (fma (+ z y) 2.0 t) x)
   (+ (* x (fma 2.0 z t)) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.82e+18) || !(x <= 0.022)) {
		tmp = fma((z + y), 2.0, t) * x;
	} else {
		tmp = (x * fma(2.0, z, t)) + (y * 5.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.82e+18) || !(x <= 0.022))
		tmp = Float64(fma(Float64(z + y), 2.0, t) * x);
	else
		tmp = Float64(Float64(x * fma(2.0, z, t)) + Float64(y * 5.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.82e+18], N[Not[LessEqual[x, 0.022]], $MachinePrecision]], N[(N[(N[(z + y), $MachinePrecision] * 2.0 + t), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.82e18 or 0.021999999999999999 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 42.6

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

   5. Applied rewrites 42.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 99.8

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

   8. Applied rewrites 99.8%

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

   if -1.82e18 < x < 0.021999999999999999

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.5

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

   5. Applied rewrites 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+18} \lor \neg \left(x \leq 0.022\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00023 \lor \neg \left(x \leq 7 \cdot 10^{-26}\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, y, t\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.00023) (not (<= x 7e-26)))
   (* (fma (+ z y) 2.0 t) x)
   (fma y 5.0 (* (fma 2.0 y t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00023) || !(x <= 7e-26)) {
		tmp = fma((z + y), 2.0, t) * x;
	} else {
		tmp = fma(y, 5.0, (fma(2.0, y, t) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.00023) || !(x <= 7e-26))
		tmp = Float64(fma(Float64(z + y), 2.0, t) * x);
	else
		tmp = fma(y, 5.0, Float64(fma(2.0, y, t) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.00023], N[Not[LessEqual[x, 7e-26]], $MachinePrecision]], N[(N[(N[(z + y), $MachinePrecision] * 2.0 + t), $MachinePrecision] * x), $MachinePrecision], N[(y * 5.0 + N[(N[(2.0 * y + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e-4 or 6.9999999999999997e-26 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 42.6

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

   5. Applied rewrites 42.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 98.4

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

   8. Applied rewrites 98.4%

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

   if -2.3000000000000001e-4 < x < 6.9999999999999997e-26

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+l+ N/A

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

      12. +-commutative N/A

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

      13. lift-+.f64 N/A

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

      14. count-2 N/A

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

      15. lower-fma.f64 100.0

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

      16. lift-+.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.8

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

   7. Applied rewrites 88.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00023 \lor \neg \left(x \leq 7 \cdot 10^{-26}\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, y, t\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00023 \lor \neg \left(x \leq 7 \cdot 10^{-26}\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, y, t\right), x, 5 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.00023) (not (<= x 7e-26)))
   (* (fma (+ z y) 2.0 t) x)
   (fma (fma 2.0 y t) x (* 5.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00023) || !(x <= 7e-26)) {
		tmp = fma((z + y), 2.0, t) * x;
	} else {
		tmp = fma(fma(2.0, y, t), x, (5.0 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.00023) || !(x <= 7e-26))
		tmp = Float64(fma(Float64(z + y), 2.0, t) * x);
	else
		tmp = fma(fma(2.0, y, t), x, Float64(5.0 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.00023], N[Not[LessEqual[x, 7e-26]], $MachinePrecision]], N[(N[(N[(z + y), $MachinePrecision] * 2.0 + t), $MachinePrecision] * x), $MachinePrecision], N[(N[(2.0 * y + t), $MachinePrecision] * x + N[(5.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e-4 or 6.9999999999999997e-26 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 42.6

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

   5. Applied rewrites 42.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 98.4

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

   8. Applied rewrites 98.4%

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

   if -2.3000000000000001e-4 < x < 6.9999999999999997e-26

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 88.7

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

   5. Applied rewrites 88.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00023 \lor \neg \left(x \leq 7 \cdot 10^{-26}\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, y, t\right), x, 5 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 2, t\right) \cdot x\\ \mathbf{if}\;x \leq -8 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma y 2.0 t) x)))
   (if (<= x -8e-20)
     t_1
     (if (<= x 3.6e-19) (* 5.0 y) (if (<= x 1.15e+37) (* (* z x) 2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, 2.0, t) * x;
	double tmp;
	if (x <= -8e-20) {
		tmp = t_1;
	} else if (x <= 3.6e-19) {
		tmp = 5.0 * y;
	} else if (x <= 1.15e+37) {
		tmp = (z * x) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(y, 2.0, t) * x)
	tmp = 0.0
	if (x <= -8e-20)
		tmp = t_1;
	elseif (x <= 3.6e-19)
		tmp = Float64(5.0 * y);
	elseif (x <= 1.15e+37)
		tmp = Float64(Float64(z * x) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 2.0 + t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -8e-20], t$95$1, If[LessEqual[x, 3.6e-19], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 1.15e+37], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999956e-20 or 1.15000000000000001e37 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 44.6

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

   5. Applied rewrites 44.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 98.3

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

   8. Applied rewrites 98.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 73.9%

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

   if -7.99999999999999956e-20 < x < 3.6000000000000001e-19

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 67.5

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

   5. Applied rewrites 67.5%

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

   if 3.6000000000000001e-19 < x < 1.15000000000000001e37

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 65.8

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

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, t\right) \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20} \lor \neg \left(x \leq 6.8 \cdot 10^{-26}\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(2 \cdot z\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8e-20) (not (<= x 6.8e-26)))
   (* (fma (+ z y) 2.0 t) x)
   (fma y 5.0 (* (* 2.0 z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8e-20) || !(x <= 6.8e-26)) {
		tmp = fma((z + y), 2.0, t) * x;
	} else {
		tmp = fma(y, 5.0, ((2.0 * z) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8e-20) || !(x <= 6.8e-26))
		tmp = Float64(fma(Float64(z + y), 2.0, t) * x);
	else
		tmp = fma(y, 5.0, Float64(Float64(2.0 * z) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8e-20], N[Not[LessEqual[x, 6.8e-26]], $MachinePrecision]], N[(N[(N[(z + y), $MachinePrecision] * 2.0 + t), $MachinePrecision] * x), $MachinePrecision], N[(y * 5.0 + N[(N[(2.0 * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999956e-20 or 6.80000000000000026e-26 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 42.5

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

   5. Applied rewrites 42.5%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 97.0

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

   8. Applied rewrites 97.0%

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

   if -7.99999999999999956e-20 < x < 6.80000000000000026e-26

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+l+ N/A

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

      12. +-commutative N/A

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

      13. lift-+.f64 N/A

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

      14. count-2 N/A

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

      15. lower-fma.f64 100.0

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

      16. lift-+.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 79.3

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

   7. Applied rewrites 79.3%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20} \lor \neg \left(x \leq 6.8 \cdot 10^{-26}\right):\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(2 \cdot z\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8e-20)
   (* t x)
   (if (<= x 3.6e-19) (* 5.0 y) (if (<= x 1.9e+75) (* (* z x) 2.0) (* t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-20) {
		tmp = t * x;
	} else if (x <= 3.6e-19) {
		tmp = 5.0 * y;
	} else if (x <= 1.9e+75) {
		tmp = (z * x) * 2.0;
	} 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 <= (-8d-20)) then
        tmp = t * x
    else if (x <= 3.6d-19) then
        tmp = 5.0d0 * y
    else if (x <= 1.9d+75) then
        tmp = (z * x) * 2.0d0
    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 <= -8e-20) {
		tmp = t * x;
	} else if (x <= 3.6e-19) {
		tmp = 5.0 * y;
	} else if (x <= 1.9e+75) {
		tmp = (z * x) * 2.0;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8e-20:
		tmp = t * x
	elif x <= 3.6e-19:
		tmp = 5.0 * y
	elif x <= 1.9e+75:
		tmp = (z * x) * 2.0
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8e-20)
		tmp = Float64(t * x);
	elseif (x <= 3.6e-19)
		tmp = Float64(5.0 * y);
	elseif (x <= 1.9e+75)
		tmp = Float64(Float64(z * x) * 2.0);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8e-20)
		tmp = t * x;
	elseif (x <= 3.6e-19)
		tmp = 5.0 * y;
	elseif (x <= 1.9e+75)
		tmp = (z * x) * 2.0;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8e-20], N[(t * x), $MachinePrecision], If[LessEqual[x, 3.6e-19], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 1.9e+75], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], N[(t * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999956e-20 or 1.9000000000000001e75 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 48.1

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

   5. Applied rewrites 48.1%

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

   if -7.99999999999999956e-20 < x < 3.6000000000000001e-19

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 67.5

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

   5. Applied rewrites 67.5%

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

   if 3.6000000000000001e-19 < x < 1.9000000000000001e75

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 58.0

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

   5. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+75}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16} \lor \neg \left(y \leq 1.35 \cdot 10^{+111}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e+16) (not (<= y 1.35e+111)))
   (* (fma 2.0 x 5.0) y)
   (* (fma (+ z y) 2.0 t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e+16) || !(y <= 1.35e+111)) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = fma((z + y), 2.0, t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e+16) || !(y <= 1.35e+111))
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = Float64(fma(Float64(z + y), 2.0, t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e+16], N[Not[LessEqual[y, 1.35e+111]], $MachinePrecision]], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(z + y), $MachinePrecision] * 2.0 + t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e16 or 1.3499999999999999e111 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 84.7

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

   5. Applied rewrites 84.7%

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

   if -1.25e16 < y < 1.3499999999999999e111

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 85.2

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

   8. Applied rewrites 85.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16} \lor \neg \left(y \leq 1.35 \cdot 10^{+111}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+16)
   (* (fma 2.0 x 5.0) y)
   (if (<= y 1.35e+111) (* (fma (+ z y) 2.0 t) x) (fma y 5.0 (* (+ y y) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+16) {
		tmp = fma(2.0, x, 5.0) * y;
	} else if (y <= 1.35e+111) {
		tmp = fma((z + y), 2.0, t) * x;
	} else {
		tmp = fma(y, 5.0, ((y + y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+16)
		tmp = Float64(fma(2.0, x, 5.0) * y);
	elseif (y <= 1.35e+111)
		tmp = Float64(fma(Float64(z + y), 2.0, t) * x);
	else
		tmp = fma(y, 5.0, Float64(Float64(y + y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+16], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 1.35e+111], N[(N[(N[(z + y), $MachinePrecision] * 2.0 + t), $MachinePrecision] * x), $MachinePrecision], N[(y * 5.0 + N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e16

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 80.2

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

   5. Applied rewrites 80.2%

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

   if -1.25e16 < y < 1.3499999999999999e111

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 85.2

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

   8. Applied rewrites 85.2%

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

   if 1.3499999999999999e111 < y

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+l+ N/A

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

      12. +-commutative N/A

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

      13. lift-+.f64 N/A

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

      14. count-2 N/A

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

      15. lower-fma.f64 100.0

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

      16. lift-+.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 90.3

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

   7. Applied rewrites 90.3%

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

   9. Applied rewrites 90.3%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(z + y, 2, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+15} \lor \neg \left(y \leq 3.2 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, z, t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e+15) (not (<= y 3.2e+26)))
   (* (fma 2.0 x 5.0) y)
   (* (fma 2.0 z t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e+15) || !(y <= 3.2e+26)) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = fma(2.0, z, t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e+15) || !(y <= 3.2e+26))
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = Float64(fma(2.0, z, t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e+15], N[Not[LessEqual[y, 3.2e+26]], $MachinePrecision]], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(2.0 * z + t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3e15 or 3.20000000000000029e26 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -4.3e15 < y < 3.20000000000000029e26

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 81.1

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

   5. Applied rewrites 81.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+15} \lor \neg \left(y \leq 3.2 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, z, t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+15} \lor \neg \left(y \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e+15) (not (<= y 8.5e+19)))
   (* (fma 2.0 x 5.0) y)
   (* (fma y 2.0 t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e+15) || !(y <= 8.5e+19)) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = fma(y, 2.0, t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e+15) || !(y <= 8.5e+19))
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = Float64(fma(y, 2.0, t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e+15], N[Not[LessEqual[y, 8.5e+19]], $MachinePrecision]], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(y * 2.0 + t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3e15 or 8.5e19 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 81.4

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

   5. Applied rewrites 81.4%

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

   if -4.3e15 < y < 8.5e19

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{\left(1 \cdot \left(t + 2 \cdot \left(y + z\right)\right)\right)} \cdot x \]

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{1} \cdot \left(t + \left(2 \cdot y + 2 \cdot z\right)\right)\right) \cdot x \]

      8. distribute-lft-in N/A

         \[\leadsto \left(1 \cdot \left(t + \color{blue}{2 \cdot \left(y + z\right)}\right)\right) \cdot x \]

      9. +-commutative N/A

         \[\leadsto \left(1 \cdot \color{blue}{\left(2 \cdot \left(y + z\right) + t\right)}\right) \cdot x \]

      10. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(1 \cdot \left(2 \cdot \left(y + z\right)\right) + 1 \cdot t\right)} \cdot x \]

      11. *-lft-identity N/A

          \[\leadsto \left(\color{blue}{2 \cdot \left(y + z\right)} + 1 \cdot t\right) \cdot x \]

      12. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y + z\right) \cdot 2} + 1 \cdot t\right) \cdot x \]

      13. *-lft-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 88.0

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

   8. Applied rewrites 88.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 54.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+15} \lor \neg \left(y \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20} \lor \neg \left(x \leq 7.5 \cdot 10^{-26}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8e-20) (not (<= x 7.5e-26))) (* t x) (* 5.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8e-20) || !(x <= 7.5e-26)) {
		tmp = t * x;
	} else {
		tmp = 5.0 * 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 ((x <= (-8d-20)) .or. (.not. (x <= 7.5d-26))) then
        tmp = t * x
    else
        tmp = 5.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8e-20) || !(x <= 7.5e-26)) {
		tmp = t * x;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8e-20) or not (x <= 7.5e-26):
		tmp = t * x
	else:
		tmp = 5.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8e-20) || !(x <= 7.5e-26))
		tmp = Float64(t * x);
	else
		tmp = Float64(5.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8e-20) || ~((x <= 7.5e-26)))
		tmp = t * x;
	else
		tmp = 5.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8e-20], N[Not[LessEqual[x, 7.5e-26]], $MachinePrecision]], N[(t * x), $MachinePrecision], N[(5.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999956e-20 or 7.4999999999999994e-26 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 42.5

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

   5. Applied rewrites 42.5%

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

   if -7.99999999999999956e-20 < x < 7.4999999999999994e-26

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-20} \lor \neg \left(x \leq 7.5 \cdot 10^{-26}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.5% accurate, 4.3× 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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. lower-*.f64 35.3

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

5. Applied rewrites 35.3%

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

6. Final simplification 35.3%

   \[\leadsto 5 \cdot y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025016 
(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)))