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

Percentage Accurate: 99.8% → 99.9%

Time: 3.3s

Alternatives: 9

Speedup: 1.1×

• 26.8% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lift-*.f64 N/A

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

   9. lower-fma.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

3. Applied rewrites 99.9%

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

Alternative 2: 43.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot x\right) \cdot 2\\ \mathbf{if}\;t \leq -5 \cdot 10^{+85}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-297}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+174}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* z x) 2.0)))
   (if (<= t -5e+85)
     (* t x)
     (if (<= t -4.5e-51)
       t_1
       (if (<= t -2.75e-297)
         (* 5.0 y)
         (if (<= t 7e+21) t_1 (if (<= t 5e+174) (* 5.0 y) (* t x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * x) * 2.0;
	double tmp;
	if (t <= -5e+85) {
		tmp = t * x;
	} else if (t <= -4.5e-51) {
		tmp = t_1;
	} else if (t <= -2.75e-297) {
		tmp = 5.0 * y;
	} else if (t <= 7e+21) {
		tmp = t_1;
	} else if (t <= 5e+174) {
		tmp = 5.0 * y;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * x) * 2.0d0
    if (t <= (-5d+85)) then
        tmp = t * x
    else if (t <= (-4.5d-51)) then
        tmp = t_1
    else if (t <= (-2.75d-297)) then
        tmp = 5.0d0 * y
    else if (t <= 7d+21) then
        tmp = t_1
    else if (t <= 5d+174) then
        tmp = 5.0d0 * y
    else
        tmp = t * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * x) * 2.0;
	double tmp;
	if (t <= -5e+85) {
		tmp = t * x;
	} else if (t <= -4.5e-51) {
		tmp = t_1;
	} else if (t <= -2.75e-297) {
		tmp = 5.0 * y;
	} else if (t <= 7e+21) {
		tmp = t_1;
	} else if (t <= 5e+174) {
		tmp = 5.0 * y;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * x) * 2.0
	tmp = 0
	if t <= -5e+85:
		tmp = t * x
	elif t <= -4.5e-51:
		tmp = t_1
	elif t <= -2.75e-297:
		tmp = 5.0 * y
	elif t <= 7e+21:
		tmp = t_1
	elif t <= 5e+174:
		tmp = 5.0 * y
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * x) * 2.0)
	tmp = 0.0
	if (t <= -5e+85)
		tmp = Float64(t * x);
	elseif (t <= -4.5e-51)
		tmp = t_1;
	elseif (t <= -2.75e-297)
		tmp = Float64(5.0 * y);
	elseif (t <= 7e+21)
		tmp = t_1;
	elseif (t <= 5e+174)
		tmp = Float64(5.0 * y);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * x) * 2.0;
	tmp = 0.0;
	if (t <= -5e+85)
		tmp = t * x;
	elseif (t <= -4.5e-51)
		tmp = t_1;
	elseif (t <= -2.75e-297)
		tmp = 5.0 * y;
	elseif (t <= 7e+21)
		tmp = t_1;
	elseif (t <= 5e+174)
		tmp = 5.0 * y;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[t, -5e+85], N[(t * x), $MachinePrecision], If[LessEqual[t, -4.5e-51], t$95$1, If[LessEqual[t, -2.75e-297], N[(5.0 * y), $MachinePrecision], If[LessEqual[t, 7e+21], t$95$1, If[LessEqual[t, 5e+174], N[(5.0 * y), $MachinePrecision], N[(t * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000001e85 or 4.9999999999999997e174 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 65.7

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

   4. Applied rewrites 65.7%

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

   if -5.0000000000000001e85 < t < -4.49999999999999974e-51 or -2.75000000000000015e-297 < t < 7e21

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 36.7

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

   4. Applied rewrites 36.7%

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

   if -4.49999999999999974e-51 < t < -2.75000000000000015e-297 or 7e21 < t < 4.9999999999999997e174

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 32.9

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

   4. Applied rewrites 32.9%

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

Alternative 3: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + x\right) \cdot y\\ \mathbf{if}\;x \leq -7 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-29}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-80}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+284}:\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ x x) y)))
   (if (<= x -7e+165)
     t_1
     (if (<= x -4e-29)
       (* t x)
       (if (<= x 1.56e-80) (* 5.0 y) (if (<= x 9e+284) (* t x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + x) * y;
	double tmp;
	if (x <= -7e+165) {
		tmp = t_1;
	} else if (x <= -4e-29) {
		tmp = t * x;
	} else if (x <= 1.56e-80) {
		tmp = 5.0 * y;
	} else if (x <= 9e+284) {
		tmp = t * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + x) * y
    if (x <= (-7d+165)) then
        tmp = t_1
    else if (x <= (-4d-29)) then
        tmp = t * x
    else if (x <= 1.56d-80) then
        tmp = 5.0d0 * y
    else if (x <= 9d+284) then
        tmp = t * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + x) * y;
	double tmp;
	if (x <= -7e+165) {
		tmp = t_1;
	} else if (x <= -4e-29) {
		tmp = t * x;
	} else if (x <= 1.56e-80) {
		tmp = 5.0 * y;
	} else if (x <= 9e+284) {
		tmp = t * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + x) * y
	tmp = 0
	if x <= -7e+165:
		tmp = t_1
	elif x <= -4e-29:
		tmp = t * x
	elif x <= 1.56e-80:
		tmp = 5.0 * y
	elif x <= 9e+284:
		tmp = t * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + x) * y)
	tmp = 0.0
	if (x <= -7e+165)
		tmp = t_1;
	elseif (x <= -4e-29)
		tmp = Float64(t * x);
	elseif (x <= 1.56e-80)
		tmp = Float64(5.0 * y);
	elseif (x <= 9e+284)
		tmp = Float64(t * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + x) * y;
	tmp = 0.0;
	if (x <= -7e+165)
		tmp = t_1;
	elseif (x <= -4e-29)
		tmp = t * x;
	elseif (x <= 1.56e-80)
		tmp = 5.0 * y;
	elseif (x <= 9e+284)
		tmp = t * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -7e+165], t$95$1, If[LessEqual[x, -4e-29], N[(t * x), $MachinePrecision], If[LessEqual[x, 1.56e-80], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 9e+284], N[(t * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.99999999999999991e165 or 8.9999999999999996e284 < x

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. count-2-rev N/A

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

      6. associate-+l+ N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 41.9

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

   6. Applied rewrites 41.9%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 41.9

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

   9. Applied rewrites 41.9%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. count-2-rev N/A

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

       4. lower-+.f64 41.9

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

   11. Applied rewrites 41.9%

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

   if -6.99999999999999991e165 < x < -3.99999999999999977e-29 or 1.55999999999999994e-80 < x < 8.9999999999999996e284

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 35.3

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

   4. Applied rewrites 35.3%

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

   if -3.99999999999999977e-29 < x < 1.55999999999999994e-80

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 62.4

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

   4. Applied rewrites 62.4%

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

Alternative 4: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(z + z\right) \cdot x\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 (+ z y) t) x)))
   (if (<= x -1.9e-22)
     t_1
     (if (<= x 1.55e-181)
       (fma y 5.0 (* (+ z z) x))
       (if (<= x 3.4e-78) (fma y 5.0 (* t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, (z + y), t) * x;
	double tmp;
	if (x <= -1.9e-22) {
		tmp = t_1;
	} else if (x <= 1.55e-181) {
		tmp = fma(y, 5.0, ((z + z) * x));
	} else if (x <= 3.4e-78) {
		tmp = fma(y, 5.0, (t * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, Float64(z + y), t) * x)
	tmp = 0.0
	if (x <= -1.9e-22)
		tmp = t_1;
	elseif (x <= 1.55e-181)
		tmp = fma(y, 5.0, Float64(Float64(z + z) * x));
	elseif (x <= 3.4e-78)
		tmp = fma(y, 5.0, Float64(t * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.9e-22], t$95$1, If[LessEqual[x, 1.55e-181], N[(y * 5.0 + N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-78], N[(y * 5.0 + N[(t * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000012e-22 or 3.40000000000000012e-78 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-out N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 93.6

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

   4. Applied rewrites 93.6%

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

   if -1.90000000000000012e-22 < x < 1.55000000000000011e-181

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. associate-+l+ N/A

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

      2. count-2-rev N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 81.1

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

   6. Applied rewrites 81.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 81.1

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

   8. Applied rewrites 81.1%

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

   if 1.55000000000000011e-181 < x < 3.40000000000000012e-78

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in t around inf

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

      1. associate-+l+ 74.2

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

      2. count-2-rev 74.2

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

      3. distribute-lft-in 74.2

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

   6. Applied rewrites 74.2%

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

Alternative 5: 56.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+85}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-43}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e+85)
   (* t x)
   (if (<= t -1.2e-43)
     (* (* z x) 2.0)
     (if (<= t 5e+174) (* (fma 2.0 x 5.0) y) (* t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+85) {
		tmp = t * x;
	} else if (t <= -1.2e-43) {
		tmp = (z * x) * 2.0;
	} else if (t <= 5e+174) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e+85)
		tmp = Float64(t * x);
	elseif (t <= -1.2e-43)
		tmp = Float64(Float64(z * x) * 2.0);
	elseif (t <= 5e+174)
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e+85], N[(t * x), $MachinePrecision], If[LessEqual[t, -1.2e-43], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t, 5e+174], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], N[(t * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000001e85 or 4.9999999999999997e174 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 65.7

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

   4. Applied rewrites 65.7%

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

   if -5.0000000000000001e85 < t < -1.2000000000000001e-43

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 33.4

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

   4. Applied rewrites 33.4%

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

   if -1.2000000000000001e-43 < t < 4.9999999999999997e174

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 55.5

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

   4. Applied rewrites 55.5%

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

Alternative 6: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 (+ z y) t) x)))
   (if (<= x -3.8e-28) t_1 (if (<= x 3.4e-78) (fma y 5.0 (* t x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, (z + y), t) * x;
	double tmp;
	if (x <= -3.8e-28) {
		tmp = t_1;
	} else if (x <= 3.4e-78) {
		tmp = fma(y, 5.0, (t * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, Float64(z + y), t) * x)
	tmp = 0.0
	if (x <= -3.8e-28)
		tmp = t_1;
	elseif (x <= 3.4e-78)
		tmp = fma(y, 5.0, Float64(t * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -3.8e-28], t$95$1, If[LessEqual[x, 3.4e-78], N[(y * 5.0 + N[(t * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000009e-28 or 3.40000000000000012e-78 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-out N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 93.4

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

   4. Applied rewrites 93.4%

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

   if -3.80000000000000009e-28 < x < 3.40000000000000012e-78

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in t around inf

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

      1. associate-+l+ 80.8

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

      2. count-2-rev 80.8

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

      3. distribute-lft-in 80.8

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

   6. Applied rewrites 80.8%

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

Alternative 7: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(2, z, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 x 5.0) y)))
   (if (<= y -1.02e+65) t_1 (if (<= y 1.1e+91) (* (fma 2.0 z t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, x, 5.0) * y;
	double tmp;
	if (y <= -1.02e+65) {
		tmp = t_1;
	} else if (y <= 1.1e+91) {
		tmp = fma(2.0, z, t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, x, 5.0) * y)
	tmp = 0.0
	if (y <= -1.02e+65)
		tmp = t_1;
	elseif (y <= 1.1e+91)
		tmp = Float64(fma(2.0, z, t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.02e+65], t$95$1, If[LessEqual[y, 1.1e+91], N[(N[(2.0 * z + t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000005e65 or 1.1e91 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 83.4

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

   4. Applied rewrites 83.4%

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

   if -1.02000000000000005e65 < y < 1.1e91

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 75.2

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

   4. Applied rewrites 75.2%

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

Alternative 8: 46.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-29}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-80}:\\ \;\;\;\;5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e-29) (* t x) (if (<= x 1.56e-80) (* 5.0 y) (* t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e-29) {
		tmp = t * x;
	} else if (x <= 1.56e-80) {
		tmp = 5.0 * y;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4d-29)) then
        tmp = t * x
    else if (x <= 1.56d-80) then
        tmp = 5.0d0 * y
    else
        tmp = t * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e-29) {
		tmp = t * x;
	} else if (x <= 1.56e-80) {
		tmp = 5.0 * y;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e-29:
		tmp = t * x
	elif x <= 1.56e-80:
		tmp = 5.0 * y
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e-29)
		tmp = Float64(t * x);
	elseif (x <= 1.56e-80)
		tmp = Float64(5.0 * y);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e-29)
		tmp = t * x;
	elseif (x <= 1.56e-80)
		tmp = 5.0 * y;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e-29], N[(t * x), $MachinePrecision], If[LessEqual[x, 1.56e-80], N[(5.0 * y), $MachinePrecision], N[(t * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999977e-29 or 1.55999999999999994e-80 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 36.3

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

   4. Applied rewrites 36.3%

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

   if -3.99999999999999977e-29 < x < 1.55999999999999994e-80

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 62.4

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

   4. Applied rewrites 62.4%

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

Alternative 9: 30.0% 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 99.8%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 30.0

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

4. Applied rewrites 30.0%

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

Reproduce

herbie shell --seed 2025093 
(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)))